CHAPTER 5

Te st D e t a ils
Sr .
N o.
N a m e of M odu le
Fe e s
( Rs.)
Te st
N o. of
M a x im u m
Du ra t ion Qu e st ion s
M a rk s
( in
m in u t e s)
Pa ss
M a rk s
(% )
Ce rt if ica t e
Va lidit y
( in ye a rs)
1
Financial Mark et s: A Beginners' Module
15 00
12 0
60
2
Mut ual Funds : A Beginners' Module
15 00
12 0
60
10 0
50
5
10 0
50
3
Currency Derivat iv es: A Beginner's
Module # # #
75 0
60
5
50
10 0
50
5
4
Equit y Derivat iv es: A Beginner's
Module # # #
75 0
60
50
10 0
50
5
5
I nt erest Rat e Derivat iv es: A Beginner's
Module
15 00
12 0
60
10 0
50
5
6
Securit ies Mark et ( Basic) Module
15 00
10 5
60
10 0
60
5
7
Capit al Mark et ( Dealers) Module *
15 00
10 5
60
10 0
50
5
8
Derivat iv es Mark et ( Dealers) Module * *
15 00
12 0
60
10 0
60
3
9
FI MMDA- NSE Debt Mark et ( Basic) Module
15 00
12 0
60
10 0
60
5
10
I nv est m ent Analy sis and Port folio
Managem ent Module
15 00
12 0
60
10 0
60
5
11
NI SM- Series- I : Currency Derivat iv es
Cert ificat ion Ex am inat ion
10 00
12 0
60
10 0
60
3
12
NI SM- Series- I I -A: Regist rars t o an I ssue
and Share Transfer Agent s Corporat e Cert ificat ion Ex am inat ion
10 00
12 0
10 0
10 0
50
3
13
NI SM- Series- I I - B: Regist rars t o an I ssue
and Share Transfer Agent s - Mut ual Fund
Cert ificat ion Ex am inat ion
10 00
12 0
10 0
10 0
50
3
14
NSDL- Deposit ory Operat ions Module
15 00
75
60
10 0
60 #
5
15
Com m odit ies Mark et Module
18 00
12 0
60
10 0
50
3
16
AMFI - Mut ual Fund ( Basic) Module
10 00
90
62
10 0
50
No lim it
17
AMFI - Mut ual Fund ( Adv isors) Module # #
10 00
12 0
72
10 0
50
5
18
Surv eillance in St ock Ex changes Module
15 00
12 0
50
10 0
60
5
19
Corporat e Gov ernance Module
15 00
90
10 0
10 0
60
5
20
Com pliance Officers ( Brok ers) Module
15 00
12 0
60
10 0
60
5
21
Com pliance Officers ( Corporat es) Module
15 00
12 0
60
10 0
60
5
22
I nform at ion Securit y Audit ors Module
( Part- 1)
22 50
12 0
90
10 0
60
2
I nform at ion Securit y Audit ors Module
( Part- 2)
22 50
12 0
90
10 0
60
23
FPSB I ndia Ex am 1 t o 4* * *
20 00
per
ex am
12 0
75
14 0
60
NA
24
Opt ions Trading St rat egies Module
15 00
12 0
60
10 0
60
5
*
Candidat es hav e t he opt ion t o t ak e t he CMDM t est in English, Guj arat i or Hindi language. The work book for t he
m odule is present ly available in ENGLI SH.
**
Candidat es hav e t he opt ion t o t ak e t he DMDM t est in English, Guj arat i or Hindi language. The work book for t he
m odule is also available in ENGLI SH, GUJARATI and HI NDI languages.
#
Candidat es securing 80% or m ore m ark s in NSDL- Deposit ory Operations Module ONLY will be certified as 'Trainers'.
##
Candidat es hav e t he opt ion t o t ak e t he AMFI ( Adv ) t est in English, Guj arat i or Hindi languages. The work book for
t he m odule, which is available for a fee at AMFI , rem ains in ENGLI SH.
# # # Rev ision in t est fees and t est param et ers wit h effect from April 01, 2010. Please refer t o circular NSE/ NCFM/
13815 dat ed 01-Jan- 2010 for det ails.
***
Modules of Financial Planning St andards Board I ndia ( Cert ified Financial Planner Certificat ion) i.e. ( i) Risk Analy sis
& I nsurance Planning (ii) Ret irem ent Planning & Em ploy ee Benefit s ( iii) I nv est m ent Planning and ( iv ) Tax Planning
& Est at e Planning.
The curriculum for each of t he m odule ( ex cept FPSB I ndia Ex am 1 t o 4) is available on our websit e: www.nseindia.com
> NCFM > Curriculum & St udy Mat erial.
CON TEN TS
CH APTER 1 : OBJECTI VES OF I N VESTM EN T D ECI SI ON S ......................................... 1
1.1
I nt roduct ion ............................................................................................... 1
1.2
Types of invest ors ....................................................................................... 1
1.2.1
I ndividuals ............................................................................................. 1
1.2.2
I nst it ut ions ............................................................................................ 2
1.2.2.1
Mut ual funds ................................................................................. 2
1.2.2.2
Pension funds ................................................................................ 2
1.2.2.3
Endowm ent funds .......................................................................... 3
1.2.2.4 I nsurance com panies ( Life and Non- life) ............................................. 3
1.2.2.5 Banks ............................................................................................. 3
1.3
1.4
Const raint s ................................................................................................. 4
1.3.1
Liquidit y ................................................................................................ 4
1.3.2
I nvest m ent horizons ............................................................................... 4
1.3.3
Taxat ion ................................................................................................ 5
Goals of I nvest ors ....................................................................................... 5
CH APTER 2 : FI N AN CI AL M ARKETS ........................................................................ 6
2.1
I nt roduct ion ............................................................................................... 6
2.2
Prim ary and Secondary Market s .................................................................... 6
2.3
Trading in Secondary Market s ....................................................................... 7
2.4
2.3.1
Types of Orders ...................................................................................... 7
2.3.2
Mat ching of Orders ................................................................................. 8
The Money Market ....................................................................................... 9
2.4.1
T- Bills ................................................................................................... 9
2.4.2
Com m ercial Paper .................................................................................. 9
2.4.3
Cert ificat es of Deposit ........................................................................... 10
2.5
Repos and Reverses ................................................................................... 10
2.6
The Bond Market ....................................................................................... 11
2.6.1
Treasury Not es ( T- Not es) and T- Bonds .................................................... 11
2.6.2
St at e and Municipal Governm ent bonds ................................................... 11
2.6.3
Corporat e Bonds .................................................................................. 11
2.6.4
I nt ernat ional Bonds .............................................................................. 12
1
2.6.5
2.7
Ot her t ypes of bonds ............................................................................ 12
Com m on St ocks ........................................................................................ 13
2.7.1
Types of shares .................................................................................... 14
CH APTER 3 FI XED I N COM E SECURI TI ES ............................................................. 1 5
3.1
I nt roduct ion: The Tim e Value of Money ........................................................ 15
3.2
Sim ple and Com pound I nt erest Rat es .......................................................... 15
3.2.1
Sim ple I nt erest Rat e ............................................................................. 15
3.2.2
Com pound I nt erest Rat e ....................................................................... 16
3.3
Real and Nom inal I nt erest Rat es ................................................................. 18
3.4
Bond Pricing Fundam ent als ......................................................................... 19
3.4.1
3.5
3.6
3.7
Clean and dirt y prices and accrued int erest .............................................. 20
Bond Yields .............................................................................................. 20
3.5.1
Coupon yield ........................................................................................ 20
3.5.2
Current Yield ........................................................................................ 20
3.5.3
Yield t o m at urit y ................................................................................... 21
3.5.4
Yield t o call .......................................................................................... 23
I nt erest Rat es ........................................................................................... 24
3.6.1
Short Rat e ........................................................................................... 24
3.6.2
Spot Rat e ............................................................................................ 24
3.6.3
Forward Rat e ....................................................................................... 25
3.6.4
The t erm st ruct ure of int erest rat es ........................................................ 26
Macaulay Durat ion and Modified Durat ion ..................................................... 28
CH APTER 4 CAPI TAL M ARKET EFFI CI EN CY .......................................................... 3 2
4.1
I nt roduct ion ............................................................................................. 32
4.2
Market Efficiency ....................................................................................... 32
4.3
4.2.1
Weak- form Market Efficiency .................................................................. 32
4.2.2
Sem i- st rong Market Efficiency ................................................................ 32
4.2.3
St rong Market Efficiency ........................................................................ 33
Depart ures from t he EMH ........................................................................... 33
CH APTER 5 : FI N AN CI AL AN ALYSI S AN D VALUATI ON .......................................... 3 5
5.1
I nt roduct ion ............................................................................................. 35
5.2
The Analysis of Financial St at em ent ............................................................. 35
2
5.3
5.4
5.5
5.2.1
I ncom e St at em ent ( Profit & Loss) ........................................................... 36
5.2.2
The Balance Sheet ................................................................................ 36
5.2.3
Cash Flow St at em ent ............................................................................ 37
Financial Rat ios ( Ret urn, Operat ion and, Profit abilit y Rat ios) .......................... 38
5.3.1
Measures of Profit abilit y: RoA, RoE ......................................................... 39
5.3.2
Measures of Liquidit y ............................................................................ 39
5.3.3
Capit al St ruct ure and Solvency Rat ios ..................................................... 39
5.3.4
Operat ing Perform ance ......................................................................... 39
5.3.5
Asset Ut ilizat ion ................................................................................... 39
The valuat ion of com m on st ocks ................................................................. 40
5.4.1
Absolut e ( I nt rinsic) Valuat ion ................................................................. 40
5.4.2
Relat ive Valuat ion ................................................................................. 44
Technical Analysis ..................................................................................... 49
5.5.1
Challenges t o Technical Analysis ............................................................. 50
CH APTER 6 : M OD ERN PORTFOLI O TH EORY ......................................................... 51
6.1
I nt roduct ion ............................................................................................. 51
6.2
Diversificat ion and Port folio Risks ................................................................ 51
6.2.1
6.3
6.4
Port folio variance - General case ............................................................ 56
Equilibrium Module: The Capit al Asset Pricing Module .................................... 57
6.3.1
Mean- Variance I nvest ors and Market Behaviour ....................................... 58
6.3.2
Est im at ion of Bet a ................................................................................ 63
Mult ifact or Modules ................................................................................... 64
CH APTER 7 : VALUATI ON OF D ERI VATI VES ......................................................... 66
7.1
I nt roduct ion ............................................................................................. 66
7.2
Forwards and Fut ures ................................................................................ 66
7.3
Call and Put Opt ions .................................................................................. 68
7.4
Forward and Fut ure Pricing ......................................................................... 68
7.5
7.4.1
Cost - of carry and convenience yield ........................................................ 69
7.4.2
Backwardat ion and Cont ango ................................................................. 70
Opt ion Pricing ........................................................................................... 70
7.5.1
Payoffs from opt ion cont ract s ................................................................. 70
7.5.2
Put - call parit y relat ionship ..................................................................... 72
7.6 Black- Scholes form ula ...................................................................................... 73
3
CH APTER 8 : I N VESTM EN T M AN AGEM EN T ............................................................ 7 5
8.1
I nt roduct ion ............................................................................................. 75
8.2
I nvest m ent Com panies .............................................................................. 75
8.2.1
Benefit s of invest m ent s in m anaged funds ............................................... 76
8.3
Act ive vs. Passive Port folio Managem ent ...................................................... 76
8.4
Cost s of Managem ent : Ent ry/ Exit Loads and Fees .......................................... 78
8.5
Net Asset Value ......................................................................................... 78
8.6
Classificat ion of funds ................................................................................ 79
8.7
8.8
8.6.1
Open ended and closed- ended funds ....................................................... 79
8.6.2
Equit y funds ........................................................................................ 79
8.6.3
Bond funds .......................................................................................... 80
8.6.4
I ndex funds ......................................................................................... 80
8.6.5
Money m arket funds ............................................................................. 80
8.6.6
Fund of funds ....................................................................................... 80
Ot her I nvest m ent Com panies ..................................................................... 80
8.7.1
Unit I nvest m ent Trust s ( UTI ) ................................................................. 80
8.7.2
REI TS ( Real Est at e I nvest m ent Trust s) .................................................... 81
8.7.3
Hedge Funds ........................................................................................ 81
Perform ance assessm ent of m anaged funds ................................................. 81
8.8.1
Sharpe Rat io ........................................................................................ 82
8.8.2
Treynor Rat io ....................................................................................... 82
8.8.3
Jensen m easure or ( Port folio Alpha) ........................................................ 82
M OD EL TEST
................................................................................................. 8 2
4
D ist r ibu t ion of w e igh t s in t h e
I n ve st m e n t An a lysis a n d Por t folio M a n a ge m e n t M odu le Cu r r icu lu m
Ch apt e r
No
1
Tit le
W e igh s ( % )
Obj ect ives of I nvest m ent Decisions
9
2
Financial Market s
13
3
Fixed I ncom e Securit ies
12
4
Capit al Market Efficiency
8
5
Financial Analysis and Valuat ion
23
6
Modern Port folio Theory
10
7
Valuat ion of Derivat ives
12
8
I nvest m ent Managem ent
13
Not e: Candidat es are advised t o refer t o NSE's websit e: www.nseindia.com , click on 'NCFM'
link and t hen go t o 'Announcem ent s' link, regarding revisions/ updat ions in NCFM m odules or
launch of new m odules, if any.
Copyright © 2010 by Nat ional St ock Exchange of I ndia Lt d. ( NSE)
Exchange Plaza, Bandra Kurla Com plex,
Bandra ( East ) , Mum bai 400 051 I NDI A
All cont ent included in t his book, such as t ext , graphics, logos, im ages, dat a com pilat ion et c.
are t he propert y of NSE. This book or any part t hereof should not be copied, reproduced,
duplicat ed, sold, resold or exploit ed for any com m ercial purposes. Furt herm ore, t he book in it s
ent iret y or any part cannot be st ored in a ret rieval syst em or t ransm it t ed in any form or by any
m eans, elect ronic, m echanical, phot ocopying, recording or ot herwise.
5
CH APTER 1 : Obj ectives of I nvest m ent Decisions
1 .1
I n t r odu ct ion
I n an econom y, people indulge in econom ic act ivit y t o support t heir consum pt ion requirem ent s.
Savings arise from deferred consum pt ion, t o be invest ed, in ant icipat ion of fut ure ret urns.
I nvest m ent s could be m ade int o financial asset s, like st ocks, bonds, and sim ilar inst rum ent s
or int o real asset s, like houses, land, or com m odit ies.
Our aim in t his book is t o provide a brief overview of t hree aspect s of invest m ent : t he various
opt ions available t o an invest or in financial inst rum ent s, t he t ools used in m odern finance t o
opt im ally m anage t he financial port folio and last ly t he professional asset m anagem ent indust ry
as it exist s t oday.
Ret urns m ore oft en t han not differ across t heir risk profiles, generally rising wit h t he expect ed
risk, i.e., higher t he ret urns, higher t he risk. The underlying obj ect ive of port folio m anagem ent
is t herefore t o creat e a balance bet ween t he t rade- off of ret urns and risk across m ult iple asset
classes. Port folio m anagem ent is t he art of m anaging t he expect ed ret urn requirem ent for t he
corresponding risk t olerance. Sim ply put , a good port folio m anager ’s obj ect ive is t o m axim ize
t he ret urn subj ect t o t he risk- t olerance level or t o achieve a pre- specified level of ret urn wit h
m inim um risk.
I n our first chapt er, we st art wit h t he various t ypes of invest ors in t he m arket s t oday, t heir
ret urn requirem ent s and t he various const raint s t hat an invest or faces.
1 .2
Ty pe s of in v e st or s
There is wide diversit y am ong invest ors, depending on t heir invest m ent st yles, m andat es,
horizons, and asset s under m anagem ent . Prim arily, invest ors are eit her individuals, in t hat
t hey invest for t hem selves or inst it ut ions, where t hey invest on behalf of ot hers. Risk appet it es
and ret urn requirem ent s great ly vary across invest or classes and are key det erm inant s of t he
invest ing st yles and st rat egies followed as also t he const raint s faced. A quick look at t he broad
groups of invest ors in t he m arket illust rat es t he point .
1 .2 .1
I n dividu a ls
While in t erm s of num bers, individuals com prise t he single largest group in m ost m arket s, t he
size of t he port folio of each invest or is usually quit e sm all. I ndividuals differ across t heir risk
appet it e and ret urn requirem ent s. Those averse t o risk in t heir port folios would be inclined
t owards safe invest m ent s like Governm ent securit ies and bank deposit s, while ot hers m ay be
risk t akers who would like t o invest and / or speculat e in t he equit y m arket s. Requirem ent s of
individuals also evolve according t o t heir life-cycle posit ioning. For exam ple, in I ndia, an individual
6
in t he 25- 35 years age group m ay plan for purchase of a house and vehicle, an individual
belonging t o t he age group of 35- 45 years m ay plan for children’s educat ion and children’s
m arriage, an individual in his or her fift ies would be planning for post - ret irem ent life. The
invest m ent port folio t hen changes depending on t he capit al needed for t hese requirem ent s.
1 .2 .2
I n st itu t ion s
I nst it ut ional invest ors com prise t he largest act ive group in t he financial m arket s. As m ent ioned
earlier, inst it ut ions are represent at ive organizat ions, i.e., t hey invest capit al on behalf of ot hers,
like individuals or ot her inst it ut ions. Asset s under m anagem ent are generally large and m anaged
professionally by fund m anagers. Exam ples of such organizat ions are m ut ual funds, pension
funds, insurance com panies, hedge funds, endowm ent funds, banks, privat e equit y and vent ure
capit al firm s and ot her financial inst it ut ions. We briefly describe som e of t hem here.
Box N o. 1 .1 :
The I ndian financial m arket s are also wit nessing act ive part icipat ion by inst it ut ions wit h
foreign inst it ut ional invest ors, dom est ic m ut ual funds, and dom est ic insurance com panies
com prising t he t hree m aj or groups, owning m ore t han a t hird of t he shareholding in list ed
com panies, wit h t he Governm ent and prom ot ers anot her 50% . Over t he years t he share of
inst it ut ions has risen in share ownership of com panies.
1 .2 .2 .1
M u t u a l fu n ds
I ndividuals are usually const rained eit her by resources or by lim it s t o t heir knowledge of t he
invest m ent out look of various financial asset s (or bot h) and t he difficult y of keeping abreast of
changes t aking place in a rapidly changing econom ic environm ent . Given t he sm all port folio
size t o m anage, it m ay not be opt im al for an individual t o spend his or her t im e analyzing
various possible invest m ent st rat egies and devise invest m ent plans and st rat egies accordingly.
I nst ead, t hey could rely on professionals who possess t he necessary expert ise t o m anage t hier
funds wit hin a broad, pre-specified plan. Mut ual funds pool invest ors’ m oney and invest according
t o pre- specified, broad param et ers. These funds are m anaged and operat ed by professionals
whose rem unerat ions are linked t o t he perform ance of t he funds. The profit or capit al gain
from t he funds, aft er paying t he m anagem ent fees and com m ission is dist ribut ed am ong t he
individual invest ors in proport ion t o t heir holdings in t he fund. Mut ual funds vary great ly,
depending on t heir invest m ent obj ect ives, t he set of asset classes t hey invest in, and t he
overall st rat egy t hey adopt t owards invest m ent s.
1 .2 .2 .2
Pe n sion fu n ds
Pension funds are creat ed ( eit her by em ployers or em ployee unions) t o m anage t he ret irem ent
funds of t he em ployees of com panies or t he Governm ent . Funds are cont ribut ed by t he em ployers
and em ployees during t he working life of t he em ployees and t he obj ect ive is t o provide benefit s
7
t o t he em ployees post t heir ret irem ent . The m anagem ent of pension funds m ay be in- house or
t hrough som e financial int erm ediary. Pension funds of large organizat ions are usually very
large and form a subst ant ial invest or group for various financial inst rum ent s.
1 .2 .2 .3
En dow m e n t fu n ds
Endowm ent funds are generally non- profit organizat ions t hat m anage funds t o generat e a
st eady ret urn t o help t hem fulfill t heir invest m ent obj ect ives. Endowm ent funds are usually
init iat ed by a non-refundable capit al cont ribut ion. The cont ribut or generally specifies t he purpose
(specific or general) and appoint s t rust ees t o m anage t he funds. Such funds are usually m anaged
by charit able organizat ions, educat ional organizat ion, non- Governm ent organizat ions, et c.
The invest m ent policy of endowm ent funds needs t o be approved by t he t rust ees of t he funds.
1 .2 .2 .4
I n su r a n ce com pa n ie s ( Life a n d N on - life )
I nsurance com panies, bot h life and non- life, hold large port folios from prem ium s cont ribut ed
by policyholders t o policies t hat t hese com panies underwrit e. There are m any different kinds
of insurance polices and t he prem ium s differ accordingly. For exam ple, unlike t erm insurance,
assurance or endowm ent policies ensure a ret urn of capit al t o t he policyholder on m at urit y,
along wit h t he deat h benefit s. The prem ium for such poliices m ay be higher t han t erm policies.
The invest m ent st rat egy of insurance com panies depends on act uarial est im at es of t im ing and
am ount of fut ure claim s. I nsurance com panies are generally conservat ive in t heir at t it ude
t owards risks and t heir asset invest m ent s are geared t owards m eet ing current cash flow needs
as well as m eet ing perceived fut ure liabilit ies.
1 .2 .2 .5
Ban k s
Asset s of banks consist m ainly of loans t o businesses and consum ers and t heir liabilit ies
com prise of various form s of deposit s from consum ers. Their m ain source of incom e is from
what is called as t he int erest rat e spread, which is t he difference bet ween t he lending rat e
( rat e at which banks earn) and t he deposit rat e ( rat e at which banks pay) . Banks generally do
not lend 100% of t heir deposit s. They are st at ut orily required t o m aint ain a cert ain port ion of
t he deposit s as cash and anot her port ion in t he form of liquid and safe asset s ( generally
Governm ent securit ies) , which yield a lower rat e of ret urn. These requirem ent s, known as t he
Cash Reserve Rat io ( CRR rat io) and St at ut ory Liquidit y Rat io ( SLR rat io) in I ndia, are st ipulat ed
by t he Reserve Bank of I ndia and banks need t o adhere t o t hem .
I n addit ion t o t he broad cat egories m ent ioned above, invest ors in t he m arket s are also classified
based on t he obj ect ives wit h which t hey t rade. Under t his classificat ion, t here are hedgers,
speculat ors and arbit rageurs. Hedgers invest t o provide a cover for risks on a port folio t hey
already hold, speculat ors t ake addit ional risks t o earn supernorm al ret urns and arbit rageurs
t ake sim ult aneous posit ions ( say in t wo equivalent asset s or sam e asset in t wo different
8
m arket s et c.) t o earn riskless profit s arising out of t he price different ial if t hey exist .
Anot her cat egory of invest ors include day- t raders who t rade in order t o profit from int ra- day
price changes. They generally t ake a posit ion at t he beginning of t he t rading session and
square off t heir posit ion lat er during t he day, ensuring t hat t hey do not carry any open posit ion
t o t he next t rading day. Traders in t he m arket s not only invest direct ly in securit ies in t he socalled cash m arket s, t hey also invest in derivat ives, inst rum ent s t hat derive t heir value from
t he underlying securit ies.
1 .3
Con st r a in t s
Port folio m anagem ent is usually a const rained opt im izat ion exercise: Every invest or has som e
const raint ( lim it s) wit hin which she want s t he port folio t o lie, t ypical exam ples being t he risk
profile, t he t im e horizon, t he choice of securit ies, opt im al use of t ax rules et c. The professional
port folio advisor or m anager also needs t o consider t he const raint set of t he invest ors while
designing t he port folio; besides having som e const raint s of his or her own, like liquidit y, m arket
risk, cash levels m andat ed across cert ain asset classes et c.
We provide a quick out line of t he various const raint s and lim it at ions t hat are faced by t he
broad cat egories of invest ors m ent ioned above.
1 .3 .1
Liqu idit y
I n invest m ent decisions, liquidit y refers t o t he m arket abilit y of t he asset , i.e., t he abilit y and
ease of an asset t o be convert ed int o cash and vice versa. I t is generally m easured across t wo
different param et ers, viz., ( i) m arket breadt h, which m easures t he cost of t ransact ing a given
volum e of t he securit y, t his is also referred t o as t he im pact cost ; and ( ii) m arket dept h, which
m easures t he unit s t hat can be t raded for a given price im pact , sim ply put , t he size of t he
t ransact ion needed t o bring about a unit change in t he price. Adequat e liquidit y is usually
charact erized by high levels of t rading act ivit y. High dem and and supply of t he securit y would
generally result in low im pact cost s of t rading and reduce liquidit y risk.
1 .3 .2
I n ve st m e n t h or izon s
The invest m ent horizon refers t o t he lengt h of t im e for which an invest or expect s t o rem ain
invest ed in a part icular securit y or port folio, before realizing t he ret urns. Knowing t he invest m ent
horizon helps in securit y select ion in t hat it gives an idea about invest ors’ incom e needs and
desired risk exposure. I n general, invest ors wit h short er invest m ent horizons prefer asset s
wit h low risk, like fixed- incom e securit ies, whereas for longer invest m ent horizons invest ors
look at riskier asset s like equit ies. Risk- adj ust ed ret urns for equit y are generally found t o be
higher for longer invest m ent horizon, but lower in case of short invest m ent horizons, largely
due t o t he high volat ilit y in t he equit y m arket s. Furt her, cert ain securit ies require com m it m ent
9
t o invest for a cert ain m inim um invest m ent period, for exam ple in I ndia, t he Post Office savings
or Governm ent sm all- saving schem es like t he Nat ional Savings Cert ificat e ( NSC) have a
m inim um m at urit y of 3- 6 years.
I nvest m ent horizon also facilit at es in m aking a decision bet ween invest ing in a liquid or relat ively
illiquid invest m ent . I f an invest or want s t o invest for a longer period, liquidit y cost s m ay not be
a significant fact or, whereas if t he invest m ent horizon is a short period ( say 1 m ont h) t hen t he
im pact cost ( liquidit y) becom es significant as it could form a m eaningful com ponent of t he
expect ed ret urn.
1 .3 .3
Ta x at ion
The invest m ent decision is also affect ed by t he t axat ion laws of t he land. I nvest ors are always
concerned wit h t he net and not gross ret urns and t herefore t ax-free invest m ent s or invest m ent s
subj ect t o lower t ax rat e m ay t rade at a prem ium as com pared t o invest m ent s wit h t axable
ret urns. The following exam ple will give a bet t er underst anding of t he concept :
Ta ble 1 .1 :
Asse t
Type
Ex pe ct e d Re t u r n
N e t Re t u r n
A
10% t axable bonds ( 30% t ax)
10%
10% * ( 1- 0.3) = 7%
B
8% t ax- free bonds
8%
8%
Alt hough asset A carries a higher coupon rat e, t he net ret urn for t he invest ors would be higher
for asset B and hence asset B would t rade at a prem ium as com pared t o asset A. I n som e
cases t axat ion benefit s on cert ain t ypes of incom e are available on specific invest m ent s. Such
t axat ion benefit s should also be considered before deciding t he invest m ent port folio.
1 .4
Goa ls of I n v e st or s
There are specific needs for all t ypes of invest ors. For individual invest ors, ret irem ent , children’s
m arriage / educat ion, housing et c. are m aj or event t riggers t hat cause an increase in t he
dem ands for funds. An invest m ent decision will depend on t he invest or ’s plans for t he above
needs. Sim ilarly, t here are cert ain specific needs for inst it ut ional invest ors also. For exam ple,
for a pension fund t he invest m ent policy will depend on t he average age of t he plan’s part icipant s.
I n addit ion t o t he few m ent ioned here, t here are ot her const raint s like t he level of requisit e
knowledge ( invest ors m ay not be aware of cert ain financial inst rum ent s and t heir pricing) ,
invest m ent size ( e.g., sm all invest ors m ay not be able t o invest in Cert ificat e of Deposit s) ,
regulat ory provisions ( count ry m ay im pose rest rict ion on invest m ent s in foreign count ries)
et c. which also serve t o out line t he invest m ent choices faced by invest ors.
10
CH APTER 2 : Fina ncia l M a r k e t s
2 .1
I n t r odu ct ion
There are a wide range of financial securit ies available in t he m arket s t hese days. I n t his
chapt er, we t ake a look at different financial m arket s and t ry t o explain t he various inst rum ent s
where invest ors can pot ent ially park t heir funds.
Financial m arket s can m ainly be classified int o m oney m arket s and capit al m arket s. I nst rum ent s
in t he m oney m arket s include m ainly short - t erm , m arket able, liquid, low- risk debt securit ies.
Capit al m arket s, in cont rast , include longer- t erm and riskier securit ies, which include bonds
and equit ies. There is also a wide range of derivat ives inst rum ent s t hat are t raded in t he
capit al m arket s.
Bot h bond m arket and m oney m arket inst rum ent s are fixed-incom e securit ies but bond m arket
inst rum ent s are generally of longer m at urit y period as com pared t o m oney m arket inst rum ent s.
Money m arket inst rum ent s are of very short m at urit y period. The equit ies m arket can be
furt her classified int o t he prim ary and t he secondary m arket . Derivat ive m arket inst rum ent s
are m ainly fut ures, forwards and opt ions on t he underlying inst rum ent s, usually equit ies
and bonds.
2 .2
Pr im a r y a n d Se con da r y M a r k e t s
A prim ary m arket is t hat segm ent of t he capit al m arket , which deals wit h t he raising of capit al
from invest ors via issuance of new securit ies. New st ocks/ bonds are sold by t he issuer t o t he
public in t he prim ary m arket . When a part icular securit y is offered t o t he public for t he first
t im e, it is called an I nit ial Public Offering (I PO) . When an issuer want s t o issue m ore securit ies
of a cat egory t hat is already in exist ence in t he m arket it is referred t o as Follow- up Offerings.
Exam ple: Reliance Power Lt d.’s offer in 2008 was an I PO because it was for t he first t im e t hat
Reliance Power Lt d. offered securit ies t o t he public. Whereas, BEML’s public offer in 2007 was
a Follow- up Offering as BEML shares were already issued t o t he public before 2007 and were
available in t he secondary m arket .
I t is generally easier t o price a securit y during a Follow- up Offering since t he m arket price of
t he securit y is act ually available before t he com pany com es up wit h t he offer, whereas in t he
case of an I PO it is very difficult t o price t he offer since t here is no prevailing m arket for t he
securit y. I t is in t he int erest of t he com pany t o est im at e t he correct price of t he offer, since
t here is a risk of failure of t he issue in case of non- subscript ion if t he offer is overpriced. I f t he
issue is underpriced, t he com pany st ands t o lose not ionally since t he securit ies will be sold at
a price lower t han it s int rinsic value, result ing in lower realizat ions.
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The secondary m arket ( also known as ‘aft erm arket ’) is t he financial m arket where securit ies,
which have been issued before are t raded. The secondary m arket helps in bringing pot ent ial
buyers and sellers for a part icular securit y t oget her and helps in facilit at ing t he t ransfer of t he
securit y bet ween t he part ies. Unlike in t he prim ary m arket where t he funds m ove from t he
hands of t he invest ors t o t he issuer ( com pany/ Governm ent , et c.) , in case of t he secondary
m arket , funds and t he securit ies are t ransferred from t he hands of one invest or t o t he hands
of anot her. Thus t he prim ary m arket facilit at es capit al form at ion in t he econom y and secondary
m arket provides liquidit y t o t he securit ies.
There is anot her m arket place, which is widely referred t o as t he t hird m arket in t he invest m ent
world. I t is called t he over- t he- count er m arket or OTC m arket . The OTC m arket refers t o all
t ransact ions in securit ies t hat are not undert aken on an Exchange. Securit ies t raded on an
OTC m arket m ay or m ay not be t raded on a recognized st ock exchange. Trading in t he OTC
m arket is generally open t o all regist ered broker- dealers. There m ay be regulat ory rest rict ions
on t rading som e product s in t he OTC m arket s. For exam ple, in I ndia equit y derivat ives is one
of t he product s which is regulat orily not allowed t o be t raded in t he OTC m arket s. I n addit ion
t o t hese t hree, direct t ransact ions bet ween inst it ut ional invest ors, undert aken prim arily wit h
t ransact ion cost s in m ind, are referred t o as t he fourt h m arket .
2 .3
Tr a din g in Se con da r y M a r k e t s
Trading in secondary m arket happens t hrough placing of orders by t he invest ors and t heir
m at ching wit h a count er order in t he t rading syst em . Orders refer t o inst ruct ions provided by
a cust om er t o a brokerage firm , for buying or selling a securit y wit h specific condit ions. These
condit ions m ay be relat ed t o t he price of t he securit y ( lim it order or m arket order or st op loss
orders) or relat ed t o t im e ( a day order or im m ediat e or cancel order) . Advances in t echnology
have led t o m ost secondary m arket s of t he world becom ing elect ronic exchanges. Disaggregat ed
t raders across regions sim ply log in t he exchange, and use t heir t rading t erm inals t o key in
orders for t ransact ion in securit ies. We out line som e of t he m ost popular orders below:
2 .3 .1
Type s of Or de r s
Lim it Pr ice / Or de r : I n t hese orders, t he price for t he order has t o be specified while ent ering
t he order int o t he syst em . The order get s execut ed only at t he quot ed price or at a bet t er price
( a price lower t han t he lim it price in case of a purchase order and a price higher t han t he lim it
price in case of a sale order) .
M a r k e t Pr ice / Or de r : Here t he const raint is t he t im e of execut ion and not t he price. I t get s
execut ed at t he best price obt ainable at t he t im e of ent ering t he order. The syst em im m ediat ely
execut es t he order, if t here is a pending order of t he opposit e t ype against which t he order can
m at ch. The m at ching is done aut om at ically at t he best available price ( which is called as t he
12
m arket price) . I f it is a sale order, t he order is m at ched against t he best bid ( buy) price and if
it is a purchase order, t he order is m at ched against t he best ask ( sell) price. The best bid price
is t he order wit h t he highest buy price and t he best ask price is t he order wit h t he lowest
sell price.
St op Loss ( SL) Pr ice / Or de r : St op- loss orders which are ent ered int o t he t rading syst em ,
get act ivat ed only when t he m arket price of t he relevant securit y reaches a t hreshold price.
When t he m arket reaches t he t hreshold or pre- det erm ined price, t he st op loss order is t riggered
and ent ers int o t he syst em as a m arket / lim it order and is execut ed at t he m arket price / lim it
order price or bet t er price. Unt il t he t hreshold price is reached in t he m arket t he st op loss
order does not ent er t he m arket and cont inues t o rem ain in t he order book. A sell order in t he
st op loss book get s t riggered when t he last t raded price in t he norm al m arket reaches or falls
below t he t rigger price of t he order. A buy order in t he st op loss book get s t riggered when t he
last t raded price in t he norm al m arket reaches or exceeds t he t rigger price of t he order. The
t rigger price should be less t han t he lim it price in case of a purchase order and vice versa.
Tim e Re la t e d Con dit ion s
D a y Or de r ( D a y) : A Day order is valid for t he day on which it is ent ered. The order, if not
m at ched, get s cancelled aut om at ically at t he end of t he t rading day. At t he Nat ional St ock
Exchange ( NSE) all orders are Day orders. That is t he orders are m at ched during t he day and
all unm at ched orders are flushed out of t he syst em at t he end of t he t rading day.
I m m edia t e or Ca n ce l or de r ( I OC) : An I OC order allows t he invest or t o buy or sell a securit y
as soon as t he order is released int o t he m arket , failing which t he order is rem oved from t he
syst em . Part ial m at ch is possible for t he order and t he unm at ched port ion of t he order is
cancelled im m ediat ely.
2 .3 .2
M a t ch in g of or de r s
When t he orders are received, t hey are t im e- st am ped and t hen im m ediat ely processed for
pot ent ial m at ch. The best buy order is t hen m at ched wit h t he best sell order. For t his purpose,
t he best buy order is t he one wit h highest price offered, also called t he highest bid, and t he
best sell order is t he one wit h lowest price also called t he lowest ask ( i.e., orders are looked at
from t he point of view of t he opposit e part y) . I f a m at ch is found t hen t he order is execut ed
and a t rade happens. An order can also be execut ed against m ult iple pending orders, which
will result in m ore t han one t rade per order. I f an order cannot be m at ched wit h pending
orders, t he order is st ored in t he pending orders book t ill a m at ch is found or t ill t he end of t he
day whichever is earlier. The m at ching of orders at NSE is done on a price- t im e priorit y i.e., in
t he following sequence:
•
Best Price
•
Wit hin Price, by t im e priorit y
13
Orders lying unm at ched in t he t rading syst em are ‘passive’ orders and orders t hat com e in t o
m at ch t he exist ing orders are called ‘act ive’ orders. Orders are always m at ched at t he passive
order price. Given t heir nat ure, m arket orders are inst ant ly execut ed, as com pared t o lim it
orders, which rem ain in t he t rading syst em unt il t heir m arket prices are reached. The set of
such orders across st ocks at any point in t im e in t he exchange, is called t he Lim it Order Book
( LOB) of t he exchange. The t op five bids/ asks ( lim it orders all) for any securit y are usually
visible t o m arket part icipant s and const it ut e t he Market By Price ( MBP) of t he securit y.
2 .4
Th e M on e y M a r k e t
The m oney m arket is a subset of t he fixed- incom e m arket . I n t he m oney m arket , part icipant s
borrow or lend for short period of t im e, usually up t o a period of one year. These inst rum ent s
are generally t raded by t he Governm ent , financial inst it ut ions and large corporat e houses.
These securit ies are of very large denom inat ions, very liquid, very safe but offer relat ively low
int erest rat es. The cost of t rading in t he m oney m arket ( bid- ask spread) is relat ively sm all due
t o t he high liquidit y and large size of t he m arket . Since m oney m arket inst rum ent s are of high
denom inat ions t hey are generally beyond t he reach of individual invest ors. However, individual
invest ors can invest in t he m oney m arket s t hrough m oney- m arket m ut ual funds. We t ake a
quick look at t he various product s available for t rading in t he m oney m arket s.
2 .4 .1
T- Bills
T- Bills or t reasury bills are largely risk- free ( guarant eed by t he Governm ent and hence carry
only sovereign risk - risk t hat t he governm ent of a count ry or an agency backed by t he
governm ent , will refuse t o com ply wit h t he t erm s of a loan agreem ent ) , short- t erm , very liquid
inst rum ent s t hat are issued by t he cent ral bank of a count ry. The m at urit y period for T- bills
ranges from 3-12 m ont hs. T-bills are circulat ed bot h in prim ary as well as in secondary m arket s.
T- bills are usually issued at a discount t o t he face value and t he invest or get s t he face value
upon m at urit y. The issue price ( and t hus rat e of int erest ) of T- bills is generally decided at an
auct ion, which individuals can also access. Once issued, T- bills are also t raded in t he secondary
m arket s.
I n I ndia, T- bills are issued by t he Reserve Bank of I ndia for m at urit ies of 91- days, 182 days
and 364 days. They are issued weekly ( 91- days m at urit y) and fort night ly ( 182- days and 364days m at urit y) .
2 .4 .2
Com m e r cia l Pa pe r
Com m ercial papers ( CP) are unsecured m oney m arket inst rum ent s issued in t he form of a
prom issory not e by large corporat e houses in order t o diversify t heir sources of short - t erm
borrowings and t o provide addit ional invest m ent avenues t o invest ors. I ssuing com panies are
required t o obt ain invest m ent - grade credit rat ings from approved rat ing agencies and in som e
14
cases, t hese papers are also backed by a bank line of credit . CPs are also issued at a discount
t o t heir face value. I n I ndia, CPs can be issued by com panies, prim ary dealers ( PDs) , sat ellit e
dealers ( SD) and ot her large financial inst it ut ions, for m at urit ies ranging from 15 days period
t o 1-year period from t he dat e of issue. CP denom inat ions can be Rs. 500,000 or m ult iples
t hereof. Furt her, CPs can be issued eit her in t he form of a prom issory not e or in dem at erialized
form t hrough any of t he approved deposit ories.
2 .4 .3
Ce r t ifica t e s of D e posit
A cert ificat e of deposit ( CD) , is a t erm deposit wit h a bank wit h a specified int erest rat e. The
durat ion is also pre- specified and t he deposit cannot be wit hdrawn on dem and. Unlike ot her
bank t erm deposit s, CDs are freely negot iable and m ay be issued in dem at erialized form or as
a Usance Prom issory Not e. CDs are rat ed ( som et im es m andat ory) by approved credit rat ing
agencies and norm ally carry a higher ret urn t han t he norm al t erm deposit s in banks (prim arily
due t o a relat ively large principal am ount and t he low cost of raising funds for banks) . Norm al
t erm deposit s are of sm aller t icket - sizes and t im e period, have t he flexibilit y of prem at ure
wit hdrawal and carry a lower int erest rat e t han CDs. I n m any count ries, t he cent ral bank
provides insurance ( e.g. Federal Deposit I nsurance Corporat ion ( FDI C) in t he U.S., and t he
Deposit I nsurance and Credit Guarant ee Corporat ion ( DI CGC) in I ndia) t o bank deposit ors up
t o a cert ain am ount ( Rs. 100000 in I ndia) . CDs are also t reat ed as bank deposit for t his
purpose.
I n I ndia, scheduled banks can issue CDs wit h m at urit y ranging from 7 days – 1 year and
financial inst it ut ions can issue CDs wit h m at urit y ranging from 1 year – 3 years. CD are issued
for denom inat ions of Rs. 1,00,000 and in m ult iples t hereof.
2 .5
Re pos a n d Re v e r se Re pos
Repos ( or Repurchase agreem ent s) are a very popular m ode of short - t erm ( usually overnight )
borrowing and lending, used m ainly by invest ors dealing in Governm ent securit ies. The
arrangem ent involves selling of a t ranche of Governm ent securit ies by t he seller ( a borrower
of funds) t o t he buyer ( t he lender of funds) , backed by an agreem ent t hat t he borrower will
repurchase t he sam e at a fut ure dat e ( usually t he next day) at an agreed price. The difference
bet ween t he sale price and t he repurchase price represent s t he yield t o t he buyer ( lender of
funds) for t he period. Repos allow a borrower t o use a financial securit y as collat eral for a cash
loan at a fixed rat e of int erest . Since Repo arrangem ent s have T- bills as collat erals and are for
a short m at urit y period, t hey virt ually elim inat e t he credit risk.
Reverse repo is t he m irror im age of a repo, i.e., a repo for t he borrower is a reverse repo for
t he lender. Here t he buyer ( t he lender of funds) buys Governm ent securit ies from t he seller ( a
borrower of funds) agreeing t o sell t hem at a specified higher price at a fut ure dat e.
15
2 .6
Th e Bon d M a r k e t
Bond m arket s consist of fixed- incom e securit ies of longer durat ion t han inst rum ent s in t he
m oney m arket . The bond m arket inst rum ent s m ainly include t reasury not es and t reasury
bonds, corporat e bonds, Governm ent bonds et c.
2 .6 .1
Tr e a su r y N ot e s ( T- N ot e s) a n d T- Bon ds
Treasury not es and bonds are debt securit ies issued by t he Cent ral Governm ent of a count ry.
Treasury not es m at urit y range up t o 10 years, whereas t reasury bonds are issued for m at urit y
ranging from 10 years t o 30 years. Anot her dist inct ion bet ween T-not es and T- bonds is t hat Tbonds usually consist of a call/ put opt ion aft er a cert ain period. I n order t o m ake t hese
inst rum ent s at t ract ive, t he int erest incom e is usually m ade t ax- free.
I nt erest on bot h t hese inst rum ent s is usually paid sem i- annually and t he paym ent is referred
t o as coupon paym ent s. Coupons are at t ached t o t he bonds and each bondholder has t o
present t he respect ive coupons on different int erest paym ent dat e t o receive t he int erest
am ount . Sim ilar t o T- bills, t hese bonds are also sold t hrough auct ion and once sold t hey are
t raded in t he secondary m arket . The securit ies are usually redeem ed at face value on t he
m at urit y dat e.
2 .6 .2
St a t e a n d M u n icipa l Gove r n m e n t bon ds
Apart from t he cent ral Governm ent , various St at e Governm ent s and som et im es m unicipal
bodies are also em powered t o borrow by issuing bonds. They usually are also backed by
guarant ees from t he respect ive Governm ent . These bonds m ay also be issued t o finance
specific proj ect s ( like road, bridge, airport s et c.) and in such cases, t he debt s are eit her repaid
from fut ure revenues generat ed from such project s or by t he Governm ent from it s own funds.
Sim ilar t o T- not es and T- bonds, t hese bonds are also grant ed t ax- exem pt st at us.
I n I ndia, t he Governm ent securit ies ( includes t reasury bills, Cent ral Governm ent securit ies
and St at e Governm ent securit ies) are issued by t he Reserve Bank of I ndia on behalf of t he
Governm ent of I ndia.
2 .6 .3
Cor por a t e Bon ds
Bonds are also issued by large corporat e houses for borrowing m oney from t he public for a
cert ain period. The st ruct ure of corporat e bonds is sim ilar t o T- Not es in t erm s of coupon
paym ent , m at urit y am ount ( face value) , issue price ( discount t o face value) et c. However,
since t he default risk is higher for corporat e bonds, t hey are usually issued at a higher discount
t han equivalent Governm ent bonds. These bonds are not exem pt from t axes. Corporat e bonds
are classified as secured bonds (if backed by specific collat eral) , unsecured bonds (or debent ures
which do not have any specific collat eral but have a preference over t he equit y holders in t he
16
event of liquidat ion) or subordinat ed debent ures ( which have a lower priorit y t han bonds in
claim over a firm s’ asset s) .
2 .6 .4
I n t e r n a t ion a l Bon ds
These bonds are issued overseas, in t he currency of a foreign count ry which represent s a large
pot ent ial m arket of invest ors for t he bonds. Bonds issued in a currency ot her t han t hat of t he
count ry which issues t hem are usually called Eurobonds. However, now t hey are called by
various nam es depending on t he currency in which t hey are issued. Eurodollar bonds are US
dollar- denom in at ed bon ds issu ed ou t side t h e Un it ed St at es. Eur o- yen bon ds are y en denom inat ed bonds issued out side Japan.
Som e int ernat ional bonds are issued in foreign count ries in currency of t he count ry of t he
invest ors. The m ost popular of such bonds are Yankee bond and Sam urai Bonds. Yankee
bonds are US dollar denom inat ed bonds issued in U.S. by a non- U.S. issuer and Sam urai
bonds are yen- denom inat ed bonds issued in Japan by non-Japanese issuers.
2 .6 .5
Ot h e r t ype s of bon ds
Bonds could also be classified according t o t heir st ruct ure/ charact erist ics. I n t his sect ion, we
discuss t he various clauses t hat can be associat ed wit h a bond.
Ze r o Cou pon Bon ds
Zero coupon bonds ( also called as deep- discount bonds or discount bonds) refer t o bonds
which do not pay any int erest ( or coupons) during t he life of t he bonds. The bonds are issued
at a discount t o t he face value and t he face value is repaid at t he m at urit y. The ret urn t o t he
bondholder is t he discount at which t he bond is issued, which is t he difference bet ween t he
issue price and t he face value.
Con ve r t ible Bon ds
Convert ible bonds offer a right ( but not t he obligat ion) t o t he bondholder t o get t he bond
convert ed int o predet erm ined num ber of equit y st ock of t he issuing com pany, at cert ain, prespecified t im es during it s life. Thus, t he holder of t he bond get s an addit ional value, in t erm s
of an opt ion t o convert t he bond int o st ock ( equit y shares) and t hereby part icipat e in t he
growt h of t he com pany’s equit y value. The invest or receives t he pot ent ial upside of conversion
int o equit y while prot ect ing downside wit h cash flow from t he coupon paym ent s.The issuer
com pany is also benefit ed since such bonds generally offer reduced int erest rat e. However, t he
value of t he equit y shares in t he m arket generally falls upon issue of such bonds in ant icipat ion
of t he st ock dilut ion t hat would t ake place when t he opt ion ( t o convert t he bonds int o equit y)
is exercised by t he bondholders.
17
Ca lla ble Bon ds
I n case of callable bonds, t he bond issuer holds a call opt ion, which can be exercised aft er
som e pre- specified period from t he dat e of t he issue. The opt ion gives t he right t o t he issuer
t o repurchase ( cancel) t he bond by paying t he st ipulat ed call price. The call price m ay be m ore
t han t he face value of t he bond. Since t he opt ion gives a right t o t he issuer t o redeem t he
bond, it carries a higher discount ( higher yield) t han norm al bonds. The right is exercised if t he
coupon rat e is higher t han t he prevailing int erest rat e in t he m arket .
Pu t t a ble Bon ds
A put t able bond is t he opposit e of callable bonds. These bonds have an em bedded put opt ion.
The bondholder has a right ( but not t he obligat ion) t o sell back t he bond t o t he issuer aft er a
cert ain t im e at a pre- specified price. The right has a cost and hence one would expect a lower
yield in such bonds. The bondholders generally exercise t he right if t he prevailing int erest rat e
in t he m arket is higher t han t he coupon rat e.
Since t he call opt ion and t he put opt ion are m ut ually exclusive, a bond m ay have bot h opt ion
em bedded.
Fix e d r a t e a n d floa t in g r a t e of in t e r e st
I n case of fixed rat e bonds, t he int erest rat e is fixed and does not change over t im e, whereas
in t he case of float ing rat e bonds, t he int erest rat e is variable and is a fixed percent age over a
cert ain pre- specified benchm ark rat e. The benchm ark rat e m ay be any ot her int erest rat e such
as T- bill rat e, t he t hree- m ont h LI BOR rat e, MI BOR rat e ( in I ndia) , bank rat e, et c. The coupon
rat e is usually reset every six m ont hs ( t im e bet ween t wo int erest paym ent dat es) .
2 .7
Com m on St ock s
Sim ply put , t he shareholders of a com pany are it s owners. As owners, t hey part icipat e in t he
m anagem ent of t he com pany by appoint ing it s board of direct ors and voicing t heir opinions,
and vot ing in t he general m eet ings of t he com pany. The board of direct ors have general
oversight of t he com pany, appoint s t he m anagem ent t eam t o look aft er t he day- t o- day running
of t he business, set overall policies aim ed at m axim izin g profit s and shareholder value.
Shareholders of a com pany are said t o have lim it ed liabilit y. The t erm m eans t hat t he liabilit y
of shareholders is lim it ed t o t he unpaid am ount on t he shares. This im plies t hat t he m axim um
loss of shareholder in a com pany is lim it ed t o her original invest m ent . Being t he owners,
shareholders have t he last claim on t he asset s of t he com pany at t he t im e of liquidat ion, while
debt - or bondholders always have precedence over equit y shareholders.
At it s incorporat ion, every com pany is aut horized t o issue a fixed num ber of shares, each
priced at par value, or face value in I ndia. The face value of shares is usually set at nom inal
18
levels ( Rs. 10 or Re. 1 in I ndia for t he m ost part ) . Corporat ions generally ret ain port ions of
t heir aut horized st ock as reserved st ock, for fut ure issuance at any point in t im e.
Shares are usually valued m uch higher t han t he face value and t his init ial invest m ent in t he
com pany by shareholders represent s t heir paid- in capit al in t he com pany. The com pany t hen
generat es earnings from it s operat ing, invest ing and ot her act ivit ies. A port ion of t hese earnings
are dist ribut ed back t o t he shareholders as dividend, t he rest ret ained for fut ure invest m ent s.
The sum t ot al of t he paid- in capit al and ret ained earnings is called t he book value of equit y of
t he com pany.
2 .7 .1
Type s of sh a r e s
I n I ndia, shares are m ainly of t wo t ypes: equit y shares and preference shares. I n addit ion t o
t he m ost com m on t ype of shares, t he equit y share, each represent ing a unit of t he overall
ownership of t he com pany, t here is anot her cat egory, called preference shares. These preferred
shares have precedence over com m on st ock in t erm s of dividend paym ent s and t he residual
claim t o it s asset s in t he event of liquidat ion. However, preference shareholders are generally
not ent it led t o equivalent vot ing right s as t he com m on st ockholders.
I n I ndia, preference shares are redeem able ( callable by issuing firm ) and preference dividends
are cum ulat ive. By cum ulat ive dividends, we m ean t hat in case t he preference dividend rem ains
unpaid in a part icular year, it get s accum ulat ed and t he com pany has t he obligat ion t o pay t he
accrued dividend and current year ’s dividend t o preferred st ockholders before it can dist ribut e
dividends t o t he equit y shareholders. An addit ional feat ure of preferred st ock in I ndia is t hat
during such t im e as t he preference dividend rem ains unpaid, preference shareholders enj oy
all t he right s ( e.g. vot ing right s) enj oyed by t he com m on equit y shareholders. Som e com panies
also issue convert ible preference shares which get convert ed t o com m on equit y shares in
fut ure at som e specified conversion rat io.
I n addit ion t o t he equit y and fixed- incom e m arket s, t he derivat ives m arket is one of I ndia’s
largest and m ost liquid. We t ake a short t our of derivat ives in t he 5t h chapt er of t his m odule.
19
CH APTER 3 : Fix e d I ncom e Se cur it ie s
3 .1
I n t r odu ct ion : Th e Tim e Va lu e of M on e y
Fixed- incom e securit ies are securit ies where t he periodic ret urns, t im e when t he ret urns fall
due and t he m at urit y am ount of t he securit y are pre- specified at t he t im e of issue. Such
securit ies generally form part of t he debt capit al of t he issuing firm . Som e of t he com m on
exam ples are bonds, t reasury bills and cert ificat es of deposit .
3 .2
Sim ple a n d Com pou n d I n t e r e st Ra t e s
I n sim ple t erm s, an int erest paym ent refers t o t he paym ent m ade by t he borrower t o t he
lender as t he price for use of t he borrowed m oney over a period of t im e. The int erest cost
covers t he opport unit y cost of m oney, i.e., t he ret urn t hat could have been generat ed had t he
lender invest ed in som e ot her asset s and a com pensat ion for default risk (risk t hat t he borrower
will not refund t he m oney on m at urit y) . The rat e of int erest m ay be fixed or float ing, in t hat it
m ay be linked t o som e ot her benchm ark int erest rat e or in som e cases t o t he inflat ion in t he
econom y.
I nt erest calculat ions are eit her sim ple or com pound. While sim ple int erest is calculat ed on t he
principal am ount alone, for a com pound int erest rat e calculat ion we assum e t hat all int erest
paym ent s are re- invest ed at t he end of each period. I n case of com pound int erest rat e, t he
subsequent period’s int erest is calculat ed on t he original principal and all accum ulat ed int erest
during past periods.
I n case of bot h sim ple and com pound int erest rat es, t he int erest rat e st at ed is generally
annual. I n case of com pound int erest rat e, we also m ent ion t he frequency for which com pounding
is done. For exam ple, such com pounding m ay be done sem i- annually, quart erly, m ont hly,
daily or even inst ant aneously ( cont inuously com pounded) .
3 .2 .1
Sim ple I n t e r e st Ra t e
The form ula for est im at ing sim ple int erest is :
I =P* R* T
Where,
P = principal am ount
R = Sim ple I nt erest Rat e for one period ( usually 1 year)
T = Num ber of periods ( years)
20
Ex a m ple 3 .1
What is t he am ount an invest or will get on a 3-year fixed deposit of Rs. 10000 t hat pays
8% sim ple int erest ?
Answer: Here we have
P = 10000, R = 8% and T = 3 years
I = P * R * T = 10000 * 8 % * 3 = 2400
Am ount = Principal + I nt erest = 10000+ 2400 = 12400.
3 .2 .2
Com pou n d I n t e r e st Ra t e
I n addit ion t o t he t hree param et ers ( Principal am ount ( P) , I nt erest Rat e ( R) , Tim e ( T) ) used
for calculat ion of int erest in case of sim ple int erest rat e m et hod, t here is an addit ional param et er
t hat affect s t he t ot al int erest paym ent s. The fourt h param et er is t he com pounding period,
which is usually represent ed in t erm s of num ber of t im es t he com pounding is done in a year
( m ) . So for sem i- annual com pounding t he value for m = 2; for quart erly com pounding, m = 4
and so on.
Let us consider an in t erest rat e of 10 % com pounded sem i- annually an d an invest m ent
of Rs. 1 0 0 f or a period of 1 y ear. Th e in v est m en t w ill becom e Rs. 1 0 5 in 6 m on t h s
and for t he second h alf, t he int erest will be calculat ed on Rs. 105 , wh ich w ill com e t o
105* 5% = 5.25. The t ot al am ount t he invest or will receive at t he end of 1 year will becom e
1 05 + 5. 25 = 11 0. 2 5. Th e equivalen t int er est rat e, if com poun ded ann u ally becom es
R

( ( 110.25- 100) / 100) * 100 = 10.25% . The equivalent annual int erest rat e is 1 +

m

m
–1.
The form ula used for calculat ing t ot al am ount under t his m et hod is as under:
T*m
R

A = P 1 +

m

–P
Where
A = Am ount on m at urit y
R = int erest rat e
m = num ber of com pounding in a year
T = m at urit y in years
Ex a m ple 3 .2
What is t he am ount an invest or will get on a 3-year fixed deposit of Rs. 10000 t hat pay 8%
int erest com pounded half yearly?
21
Answer:
Here P = 10000, R = 8% and T = 3, m = 2. The t ot al int erest incom e com es t o:
T m

R * 
I nt erest = P 1 +

–P
m

 
2* 3

0 . 08  
= 10000 * 1 +
  – 10000 = Rs. 2653 . 20
2  


Am ount = Principal + I nt erest = 10000+ 2653.20 = 12653.20.
Ex a m ple 3 .3
Consider t he sam e invest m ent . What is t he am ount if t he int erest rat e is com pounded m ont hly?
Answer:
Here P = 10000, R = 8% and T = 3, m = 12. The t ot al int erest incom e com es t o:
T m

R * 
I nt erest = P 1 +

–P
m

 
12 * 3


0 . 08 
= 10000 * 1 +

 – 10000 = Rs. 2702 . 37
12 



Am ount = Principal + I nt erest = 10000+ 2702.37 = 12702.37.
Con t in u ou s com pou n din g
Consider a sit uat ion, where inst ead of m ont hly or quart erly com pounding, t he int erest rat e is
com pounded cont inuously t hroughout t he year i.e. m rises indefinit ely. I f m approaches infinit y,
∞
R

t he equivalent annual int erest rat e is 1 +  – 1 , which can be shown ( using t ools from
∞

different ial calculus) , t o t end t o [ 2 . 718 r – 1] or e r – 1 in t he lim it , ( where e= 2.71828… is t he
base for nat ural logarit hm s) . Furt her, for convenience, we use ‘r ’ (in sm all let t ers) t o represent
cont inuously com pound int erest rat e.
Thus, an invest m ent of Re. 1 at 8% cont inuously com pounded int erest becom es e 0 . 08 = 1 . 0833
aft er 1 year and t he equivalent annual int erest rat e becom es 0.0833 or 8.33% . I f t he invest m ent
is for T years, t he m at urit y am ount is sim ply 1* e rT , where e = 2.718.
Cont inuous com pounding is widely assum ed in finance t heory, and used in various asset pricing
m odels—t he fam ous Black- Scholes m odel t o price a European opt ion is an illust rat ive exam ple.
Ex a m ple 3 .4
Consider t he sam e invest m ent ( Rs. 10000 for 3 years) . What is t he am ount received on
22
m at urit y if t he int erest rat e is 8% com pounded cont inuously?
Answer:
Here P = 10000, e = 2.718, r = 8% and T = 3
The final value of t he invest m ent is P * e rT .
I t com es t o 10000 * e 0 . 08 * 3 = 12712 . 50 .
3 .3
Re a l a n d N om in a l I n t e r e st Ra t e s
The relat ionship bet ween int erest rat es and inflat ion rat es is very significant . Norm ally, t he
cash flow from bonds and deposit s are cert ain and known in advance. However, t he value of
goods and services in an econom y m ay change due t o changes in t he general price level
( inflat ion) . This brings an uncert aint y about t he purchasing power of t he cash flow from an
invest m ent . Take a sm all exam ple. I f inflat ion ( say 12% ) is rising and is great er t han t he
int erest rat e ( say 10% annually) in a part icular year, t hen an invest or in a bond wit h 10%
int erest rat e annually st ands t o lose. Goods wort h Rs. 100 at t he beginning of t he year are
wort h Rs. 112 by t he end of t he year but an invest m ent of Rs. 100 becom es only Rs. 110 by
end of t he year. This im plies t hat an invest or who has deposit ed m oney in a risk- free asset will
find goods beyond his reach.
An econom ist would look at t his in t erm s of nom inal cash flow and real cash flows. Nom inal
cash flow m easures t he cash flow in t erm s of t oday’s prices and real cash flow m easures t he
cash flow in t erm s of it s base year ’s purchasing power, i.e., t he year in which t he asset was
bought / invest ed. I f t he int erest rat e is 10% , an invest m ent of Rs. 100 becom es Rs. 110 at t he
end of t he year. However, if inflat ion rat e is 5% t hen each Rupee will be wort h 5% less next
year. This m eans at t he end of t he year, Rs. 110 will be wort h only 110/ 1.05 = Rs. 104.76 in
t erm s of t he purchasing power at t he beginning of t he year. The real payoff is Rs. 104.76 and
t he real int erest rat e is 4.76% . The relat ionship bet ween real and nom inal int erest rat e can be
est ablished as under:
Real Cash Flow =
Nom inal Cash Flow
( 1 + inflat ion rat e)
And
(1 + real int erest rat e =
1 + nom inal int erest rat e
1 + inf lat ion rat e
I n our exam ple, t he real int erest rat e can be direct ly calculat ed using t he form ula:
1 + 0 . 10 
Real interest rat e = 
 – 1 = 0.0476 or 4.76%
 1 + . 05 
23
3 .4
Bon d Pr icin g Fu n da m e n t a ls
The cash inflow for an invest or in a bond includes t he coupon paym ent s and t he paym ent on
m at urit y ( which is t he face value) of t he bond. Thus t he price of t he bond should represent t he
sum t ot al of t he discount ed value of each of t hese cash flows ( such a t ot al is called t he present
value of t he bond) . The discount rat e used for valuing t he bond is generally higher t han t he
risk- free rat e t o cover addit ional risks such as default risk, liquidit y risks, et c.
Bond Price = PV ( Coupons and Face Value)
Not e t hat t he coupon paym ent s are at different point s of t im e in t he fut ure, usually t wice each
year. The face value is paid at t he m at urit y dat e. Therefore, t he price is calculat ed using t he
following form ula:
Bond Price =
∑ (1 + y )
C( t )
( 1)
t
t
Where C( t ) is t he cash flow at t im e t and y is t he discount rat e. Since t he coupon rat e is
generally fixed and t he m at urit y value is known at t he t im e of issue of t he bond, t he form ula
can be re- writ t en as under:
T
Bond Price =
∑ (1 + y )
Coupon
t
t
+
Face Value
( 2)
(1 + y ) T
Here t represent s t he t im e left for each coupon paym ent and T is t he t im e t o m at urit y. Also
not e t hat t he discount rat e m ay differ for cash flows across t im e periods.
Ex a m ple 3 .5
Calculat e t he value of a 3-year bond wit h face value of Rs. 1000 and coupon rat e being 8%
paid annually. Assum e t hat t he discount rat e is 10% .
Here:
Face value = Rs. 1000
Coupon Paym ent = 8% of Rs. 1000 = Rs. 80
Discount Rat e = 10%
t= 1 to 3
T= 3
Bond Pr ice =
80
80
80
1000
+
+
+
= 950 . 26
3
1 + 0 . 1 ( 1 + 0 . 1) 2
( 1 + 0 . 1)
( 1 + 0 . 1) 3
Now let us see what happens if t he discount rat e is lower t han t he coupon rat e:
24
Ex a m ple 3 .6
Calculat e t he bond price if t he discount rat e is 6% .
Bond Pr ice =
80
80
80
+
+
2
1 + 0 . 06
(1 + 0 . 06 )
(1 + 0 . 06 ) 3
= 1053 . 46
Since t he discount rat e is higher t han t he coupon rat e, t he bond is t raded at a discount . I f t he
discount rat e is less t han t he coupon rat e, t he bond t rades at a prem ium .
3 .4 .1
Cle a n a n d dir t y pr ice s a n d a ccr u e d in t e r e st
Bonds are not t raded only on coupon dat es but are t raded t hroughout t he year. The m arket
price of t he bonds also includes t he accrued int erest on t he bond since t he m ost recent coupon
paym ent dat e. The price of t he bond including t he accrued int erest since issue or t he m ost
recent coupon paym ent dat e is called t he ‘dirt y price’ and t he price of t he bond excluding t he
accrued int erest is called t he ‘clean price’. Clean price is t he price of t he bond on t he m ost
recent coupon paym ent dat e, when t he accrued int erest is zero.
Dirt y Price = Clean price + Accrued int erest
For report ing purpose ( in press or on t rading screens) , bonds are quot ed at ‘clean price’ for
ease of com parison across bonds wit h differing int erest paym ent dat es ( dirt y prices ‘j um p’ on
int erest paym ent dat es). Changes in t he m ore st able clean prices are reflect ive of m acroeconom ic
condit ions, usually of m ore int erest t o t he bond m arket .
3 .5
Bon d Yie lds
Bond yield are m easured using t he following m easures:
3 .5 .1
Cou pon yie ld
I t is calculat ed using t he following form ula:
Coupon Yield =
3 .5 .2
Coupon Paym ent
Face Value
Cu r r e n t Yie ld
I t is calculat ed using t he following form ula:
Coupon Yield =
Coupon Paym ent
Current Market Price of t he Bond
The m ain drawback of coupon yield and current yield is t hat t hey consider only t he int erest
paym ent ( coupon paym ent s) and ignore t he capit al gains or losses from t he bonds. Since t hey
consider only coupon paym ent s, t hey are not m easurable for bonds t hat do not pay any
int erest , such as zero coupon bonds. The ot her m easures of yields are yield t o m at urit y and
25
yield t o call. These m easures consider int erest paym ent s as well as capit al gains ( or losses)
during t he life of t he bond.
3 .5 .3
Yie ld t o m a t u r it y
Yield t o m at urit y ( also called YTM) is t he m ost popular concept used t o com pare bonds. I t
refers t o t he int ernal rat e of ret urn earned from holding t he bond t ill m at urit y. Assum ing a
const ant int erest rat e for various m at urit ies, t here will be only one rat e t hat equalizes t he
present value of t he cash flows t o t he observed m arket price in equat ion ( 2) given earlier. That
rat e is referred t o as t he yield t o m at urit y.
Ex a m ple 3 .7
What is t he YTM for a 5-year, 8% bond ( int erest is paid annually) t hat is t rading in t he m arket
for Rs. 924.20?
Here,
t= 1 to 5
T= 5
Face Value = 1000
Coupon paym ent = 8% of Rs. 1,000 = 80
Put t ing t he values in equat ion ( 1) , we have:
5
924 . 20 =
∑ (1 + y )
80
t
1
+
1000
(1 + y ) 5
Solving for y, which is t he YTM, we get t he yield t o m at urit y for t he bond t o be 10% .
Yield and Bond Price:
There is a negat ive relat ionship bet ween yields and bond price. The bond price falls when yield
increases and vice versa.
Ex a m ple 3 .8
What will be t he m arket price of t he above bond ( Exam ple 3 7) if t he YTM is 12% .
t= 1 to 5
T= 5
Face Value = 1000
Coupon paym ent = 8% of 1,000 = 80
Put t ing t he values in equat ion ( 1) , t he bond price com es t o:
26
5
∑ (1 + 0 . 12 )
Bond Pr ice =
80
t
1
+
1000
(1 + 0 . 12 ) 5
= 901 . 20
Furt her, for a long- t erm bond, t he cash flows are m ore dist ant in t he fut ure and hence t he
im pact of change in int erest rat e is higher for such cash flows. Alt ernat ively, for short - t erm
bonds, t he cash flows are not far and discount ing does not have m uch effect on t he bond price.
Thus, price of long- t erm bonds are m ore sensit ive t o int erest rat e changes.
Bond equivalent yield and Effect ive annual yield: This is anot her im port ant concept t hat is of
im port ance in case of bonds and not es t hat pay coupons at t im e int erval which is less t han 1
year ( for exam ple, sem i- annually or quart erly) . I n such cases, t he yield t o m at urit y is t he
discount rat e solved using t he following form ula, wherein we assum e t hat t he annual discount
rat e is t he product of t he int erest rat e for int erval bet ween t wo coupon paym ent s and t he
num ber of coupon paym ent s in a year:
T
∑
Bond Price =
t
Coupon
y
1 + 
2

t
+
Face Value
T
1 + y 


2

( 3)
YTM calculat ed using t he above form ula is called bond equivalent yield.
However, if we assum e t hat one can reinvest t he coupon paym ent s at t he bond equivalent
yield ( YTM) , t he effect ive int erest rat e will be different . For exam ple, a sem i- annual int erest
rat e of 10% p.a. in effect am ount s t o
1 + 0 . 10 


2 

2
= 1 . 1025 or 10 . 25 % .
Yield rat e calculat ed using t he above form ula is called effect ive annual yield.
Ex a m ple 3 .9
Calculat e t he bond equivalent yield (YTM) for a 5-year, 8% bond (sem i-annual coupon paym ent s),
t hat is t rading in t he m arket for Rs. 852.80? What is t he effect ive annual yield for t he bond?
Here,
t = 1 t o 10
T = 10
Face Value = 1000
Coupon paym ent = 4% of 1,000 = 40
Bond Price = 852.80
27
Put t ing t he values in equat ion ( 3) , we have:
852 . 80 =
10
∑
40
y
1 + 
2

1
t
+
1000
10
1 + y 


2

Solving, we get t he Yield t o Mat urit y ( y) = 0.12 or 12% .
The effect ive yield rat e is
y

1 + 
2

3 .5 .4
2
2
0 . 12 

– 1 = 1 +
 – 1 = 0 . 1236 or 12 . 36 %
2 

Yie ld t o ca ll
Yield t o call is calculat ed for callable bond. A callable bond is a bond where t he issuer has a
right ( but not t he obligat ion) t o call/ redeem t he bond before t he act ual m at urit y. Generally t he
callable dat e or t he dat e when t he com pany can exercise t he right , is pre- specified at t he t im e
of issue. Furt her, in t he case of callable bonds, t he callable price ( redem pt ion price) m ay be
different from t he face value. Yield t o call is calculat ed wit h t he sam e form ula used for calculat ing
YTM ( Equat ion 2) , wit h an assum pt ion t hat t he issuer will exercise t he call opt ion on t he
exercise dat e.
Ex a m ple 3 .1 0
Calculat e t he yield t o call for a 5-year, 7% callable bond ( sem i- annual coupon paym ent s) , t hat
is t rading in t he m arket for Rs. 877.05. The bond is callable at t he end of 3rd year at a call
price of Rs. 1040.
Here:
t= 1 to 6
T= 6
Coupon paym ent = 3.5% of 1,000 = 35
Callable Value = 1040
Bond Price = 877.05
Put t ing t he values in t he following equat ion:
Bond Price =
T
∑
t
Coupon
y
1 + 
2

t
+
Callable Value
T
y

1 + 
2

we have:
28
877 . 05 =
6
∑
1
35
y
1 + 
2

t
+
1000
1 + y 


2

6
Solving for y, we get t he yield t o call = 12%
3 .6
I n t e r e st Ra t e s
While com put ing t he bond prices and YTM, we assum ed t hat t he int erest rat e is const ant
across different m at urit ies. However, t his m ay not be t rue for different reasons. For exam ple,
invest ors m ay perceive longer m at urit y periods t o be riskier and hence m ay dem and higher
int erest rat e for cash flow occurring at dist ant t im e int ervals t han t hose occurring at short t im e
int ervals. I n t his sect ion, we account for t he fact t hat t he int erest dem anded by invest ors also
depends on t he t im e horizon of t he invest m ent . Let us first int roduce cert ain com m on concept s.
3 .6 .1
Sh or t Ra t e
Short rat e for t im e t , is t he expect ed ( annualized) int erest rat e at which an ent it y can borrow
f or a gi v en t i m e i n t er v al st ar t i n g f r om t i m e t . Sh or t r at e is u su al l y d en om i n at ed
as r t .
3 .6 .2
Spot Ra t e
Yield t o m at urit y for a zero coupon bond is called spot rat e. Since zero coupon bonds of
varying m at urit ies are t raded in t he m arket sim ult aneously, we can get an array of spot rat es
for different m at urit ies.
Relat ionship bet ween short rat e and spot rat e:
I nvest ors discount fut ure cash flows using int erest rat e applicable for t hat period. Therefore,
t he PV of an invest m ent of T years is calculat ed as under:
PV ( I nvest m ent ) =
( I nit ial I nvest m ent )
(1 + r1 ) (1 + r2 ) ...(1 + rT )
Ex a m ple 3 .1 1
I f t he short rat e for a 1-year invest m ent at year 1 is 7% and year 2 is 8% , what is t he present
value of a 2-year zero coupon bond wit h face value Rs. 1000 :
P=
1000
1000
=
= 865 . 35
1 . 07 * 1 . 08 1 . 1556
For a 2-year zero coupon bond t rading at 865.35, t he YTM can be calculat ed by solving t he
following equat ion:
865 . 35 =
1000
(1 + y 2 ) 2
The result ing value for y is 7.4988% , which is not hing but t he 2-year spot rat e.
29
3 .6 .3
For w a r d Ra t e
One can assum e t hat all bonds wit h equal risks m ust offer ident ical rat es of ret urn over any
holding period, because if it is not t rue t hen t here will be an arbit rage opport unit y in t he
m arket . I f we assum e t hat all equally risky bonds will have ident ical rat es of ret urn, we can
calculat e short rat es for a fut ure int erval by knowing t he spot rat es for t he t wo ends of t he
int erval. For exam ple, we can calculat e 1-year short rat e at year 3, if we have t he 3-years spot
rat e and 4-years spot rat e ( or in ot her words are t here are 3-year zero coupon and a 4-year
zero coupon t reasury bonds t rading in t he m arket ) . This is because, t he proceeds from an
invest m ent in a 3-year zero coupon bond on t he m at urit y day, reinvest ed for 1 year should
result in a cash flow equal t o t he cash flow from an invest m ent in a 4-year zero coupon bond
( since t he holding period is t he sam e for bot h t he st rat egies) .
Ex a m ple 3 .1 2
I f t he 3-year spot rat e and 4-year spot rat es are 8.997% and 9.371% respect ively, find t he
1-year short rat e at end of year 3.
Given t he spot rat es, proceeds from invest m ent of Re. 1 in a 3-year zero coupon bond will be
1* 1.08997 3 = 1.2949.
I f we reinvest t his ( m at urit y) am ount in a 1-year zero coupon bond, t he proceeds at year 4 will
be 1.2949* ( 1+ r 3 ) .
This should be equal t o t he proceeds from an invest m ent of Rs. 1 in a 4-year zero coupon
bond, assum ing equal holding period ret urn.
Proceeds from invest m ent of Re. 1 in a 4-year zero coupon bond is 1* 1.09371 4 = 1.4309
Solving,
1.2949 * (1 + r3 ) = 1.4309
r 3 = 0.11 or 11% , which is not hing but t he 1 year short rat e at t he end of year 3.
Fut ure short rat es com put ed using t he m arket price of t he prevailing zero coupon bonds’ price
( or prevailing spot rat es) are called forward int erest rat es. We use t he not at ion f i t o represent
t he 1-year forward int erest rat e st art ing at year i. For exam ple, f 2 denot es t he 1-year forward
int erest rat e st art ing from year 2.
3 .6 .4
Th e t e r m st r u ct u r e of in t e r e st r a t e s
We have discussed various int erest rat es ( spot , forward, discount rat es) , and also seen t heir
behaviour, and connect ions wit h each ot her. The t erm st ruct ure of int erest rat es is t he set of
relat ionships bet ween rat es of bonds of different m at urit ies. I t is som et im es also called t he
30
yield curve. Form ally put , t he t erm st ruct ure of int erest rat es defines t he array of discount
fact ors on a collect ion of default - free pure discount ( zero- coupon) bonds t hat differ only in
t heir t erm t o m at urit y. The m ost com m on approxim at ion t o t he t erm st ruct ure of int erest rat es
is t he yield t o m at urit y curve, which generally is a sm oot h curve and reflect s t he rat es of
ret urn on various default - free pure discount ( zero- coupon) bonds held t o m at urit y along wit h
t heir t erm t o m at urit y.
The use of forward int erest rat es has long been st andard in financial analysis such as in pricing
new financial inst rum ent s and in discovering arbit rage possibilit ies. Yield curves are also used
as a key t ool by cent ral banks in t he det erm inat ion of t he m onet ary policy t o be followed in a
count ry. The forward int erest rat e is int erpret ed as indicat ing m arket expect at ions of t he t im epat h of fut ure int erest rat es, fut ure inflat ion rat es and fut ure currency depreciat ion rat es.
Since forward rat es helps us indicat e t he expect ed fut ure t im e pat h of t hese variables, t hey
allow a separat ion of m arket expect at ions for t he short , m edium and long t erm m ore easily
t han t he st andard yield curve.
The m arket expect at ions hypot hesis and t he liquidit y preference t heory are t wo im port ant
explanat ions of t he t erm st ruct ure of int erest in t he econom y. The m arket expect at ion hypot hesis
assum es t hat various m at urit ies are perfect subst it ut es of each ot her and t hat t he forward
rat e equals t he m arket expect at ion of t he fut ure short int erest rat e i.e. f i = E( r i ) , where i is
a fut ure period. Assum ing m inim al arbit rage opport unit ies, t he expect ed int erest rat e can be
used t o const ruct a yield curve. For exam ple, we can find t he 2-year yield if we know t he
1-year short rat e and t he fut ures short rat e for t he second year by using t he following form ula:
( 1 + y 2 ) 2 = (1 + r1 ) * (1 + f 2 )
Since, as per t he expect at ion hypot hesis − f 2 = E( R2 ) , t he YTM can be det erm ined solely by
y
current and expect ed fut ure one- period int erest rat es.
Liquidit y preference t heory suggest s t hat invest ors prefer liquidit y and hence, a short - t erm
invest m ent is preferred t o a long-t erm invest m ent . Therefore, invest ors will be induced t o hold
a long- t erm invest m ent , only by paying a prem ium for t he sam e. This prem ium or t he excess
of t he forward rat e over t he expect ed int erest rat e is referred t o as t he liquidit y prem ium .
Therefore, t he forward rat e will exceed t he expect ed short rat e, i.e. f 2 > E( r2 ) , where f 2 – E( r2 )
represent t he liquidit y prem ium . The liquidit y prem ium causes t he yield curve t o be upward
sloping since long- t erm yields are higher t han short - t erm yields.
Ex a m ple 3 .1 3
Calculat e t he YTM for year 2- 5 if t he 1-year short rat e is 8% and t he fut ure rat es for years
2- 5 is 8.5% ( f 2 ) , 9% ( f 3 ) , 9.5% ( f 4 ) and 10% ( f 5 ) respect ively.
31
Answer:
y1 = r1 = 8%
(1 + y 2 ) 2 + (1 + r1 ) * (1 + f 2 ) ; y 2 = 2 (1 . 08 * 1 . 085) = 1 . 0825 , i.e. y 2 = 8.25%
(1 + y 3 ) 3 + (1 + y 2 ) 2 * (1 + f 3 ) ; y 3 = 3 (1 . 0825 2 * 1 . 09) = 1 . 0850 , i.e. y 3 = 8.50%
(1 + y 4 ) 4 + (1 + y 3 ) 3 * (1 + f 4 ) ; y 4 = 4 (1 . 0850 3 * 1 . 095) = 1 . 0875 , i.e. y 4 = 8.75%
(1 + y 5 ) 5 + (1 + y 4 ) 4 * (1 + f 5 ) ; y 5 = 5 (1 . 0875 4 * 1 . 10) = 1 . 09 , i.e. y 5 = 9.00%
I t can be seen t hat because of t he liquidit y prem ium , t he fut ure int erest rat e increases wit h
t im e and t his causes t he yield curve t o rise wit h t im e.
Box N o. 3 .1 :
Re la t ion sh ip be t w e e n spot , for w a r d, a n d discou n t r a t e s
Recall t hat discount fact ors are t he int erest rat es used at a given point in t im e t o discount
cash flows occurring in t he fut ure, in order t o obt ain t heir present value. So how do spot
rat es, forward rat es, and discount rat es relat e t o each ot her?
A discount funct ion ( d t,m ) is t he collect ion of discount fact ors at t im e t for all m at urit ies
m . Spot rat es ( st,m ) , i.e., t he yields earned on bonds which pay no coupon, are relat ed t o
discount fact ors according t o:
d t , m = e m * – S1 m
St , m = –
and
1
1nd t , m
m
The est im at ion of a zero coupon yield curve is based on an assum ed funct ional relat ionship
bet ween eit her par yields, spot rat es, forward rat es or discount fact ors on t he one hand
and m at urit ies on t he ot her. Par yield curves are t hose t hat reflect ret urn on bonds t hat
are priced at par, which j ust m eans t hat t he redem pt ion yield is equal t o t he coupon rat e
of t he bond.
There is a different forward rat e for every pair of m at urit y dat es. The relat ion bet ween
t he yield- t o- m at urit y ( YTM) and t he im plied forward rat e at m at urit y is analogous t o t he
relat ion bet ween average and m arginal cost s in econom ics. The YTM is t he average cost
of borrowing for m periods whereas t he im plied forward rat e is t he m arginal cost of
ext ending t he t im e period of t he loan, i.e. it describes t he m arginal one- period int erest
rat e im plied by t he current t erm st ruct ure of spot int erest rat e. Because spot int erest
32
rat es depend on t he t im e horizon, it is nat ural t o define t he forward rat es ft,m as t he
inst ant aneous rat es which when com pounded cont inuously up t o t he t im e t o m at urit y,
yield t he spot rat es ( inst ant aneous forward rat es are t hus rat es for which t he difference
bet ween set t lem ent t im e and m at urit y t im e approaches zero) .
1
m
St , m = –
m
∫f
( u ) du , or we can say
y
0

m
d t , m = exp  f ( u ) du 
 0

∫
Thus, knowing any of t he four m eans t hat t he ot her four can be readily com put ed.
However, t he real problem is t hat neit her of t hese curves is easily forecast able.
3 .7
M a ca u la y D u r a t ion a n d M odifie d D u r a t ion
The effect of int erest rat e risks on bond prices depends on m any fact ors, but m ainly on coupon
rat es, m at urit y dat e et c. Unlike in case of zero- coupon bonds, where t he cash flows are only at
t he end, in t he case of ot her bonds, t he cash flows are t hrough coupon paym ent s and t he
m at urit y paym ent . One needs t o average out t he t im e t o m at urit y and t im e t o various coupon
paym ent s t o find t he effect ive m at urit y for a bond. The m easure is called as durat ion of a
bond. I t is t he weight ed ( cash flow weight ed) average m at urit y of t he bond.
Durat ion =
T
∑t * w
t
t =1
The weight s ( Wt ) associat ed for each period are t he present value of t he cash flow at each
period as a proport ion t o t he bond price, i.e.
CFt
Wt =
PV of cash flow
(1 + y ) t
=
Bond Price
Bond Price
This m easure is t erm ed as Macaulay’s durat ion 1 or sim ply, durat ion. Higher t he durat ion of t he
bond, higher will be t he sensit ivit y t owards int erest rat e fluct uat ions and hence higher t he
volat ilit y in t he bond price.
This t ool is widely used in fixed incom e analysis. Banks and ot her financial inst it ut ions generally
creat e a port folio of fixed incom e securit ies t o fund known liabilit ies. The price changes for
fixed incom e securit ies are dependent m ainly on t he int erest rat e changes and t he average
1
The m et hod was designed by Frederick Macaulay in 1856 and hence nam ed as Macaulay Durat ion.
33
m at urit y ( durat ion) . I n order t o hedge against int erest rat e risks, it is essent ial for t hem t o
m at ch t he durat ion of t he port folio of fixed incom e securit ies wit h t hat of t he liabilit ies. A bank
t hus needs t o rebalance it s port folio of fixed- incom e securit ies periodically t o ensure t hat t he
aggregat e durat ion of t he port folio is kept equal t o t he t im e rem aining t o t he t arget dat e. One
should not e t hat t he durat ion of a short - t erm bond declines fast er t han t he durat ion of t he
long- t erm bond. When int erest rat es fall, t he reinvest m ent of int erest s ( unt il t he t arget dat e)
will yield a lower value but t he capit al gain arising from t he bond is higher. The increase or
decrease in t he coupon incom e arising from changes in t he reinvest m ent rat es will offset t he
opposit e changes in t he m arket values of t he bonds in t he port folios. The net realized yield at
t he t arget dat e will be equal t o t he yield t o m at urit y of t he original port folio. This is also called
bond port folio im m unizat ion.
Ex a m ple 3 .1 4
What is t he durat ion for a 5-year m at urit y, 7% ( sem i- annual) coupon bond wit h yield t o
m at urit y of 12% ?
Here:
t = 1 t o 10
T = 10
Coupon paym ent = 3.5% of 1,000 = 35
YTM = 12 % or 6% for half year.
Period
( a)
Tim e t ill
paym ent
( b)
Cash
Flow
(c )
PV of Cash Flow ( discount
= 6% per period)
( d)
Weight s
( b)* ( e)
( e)
(f)
( 33.02/ 816)
1
0.5
35
33.02
= 0.0405
0.0202
2
1
35
31.15
0.0382
0.0382
3
1.5
35
29.39
0.0360
0.0540
4
2
35
27.72
0.0340
0.0679
5
2.5
35
26.15
0.0321
0.0801
6
3
35
24.67
0.0302
0.0907
7
3.5
35
23.28
0.0285
0.0998
8
4
35
21.96
0.0269
0.1076
9
4.5
35
20.72
0.0254
0.1142
10
5
1035
577.94
0.7083
3.5413
816.00
1.0000
4.2142
Sum
34
The selling price of t he bond as calculat ed from colum n ( d) is Rs. 816.00. The durat ion of t he
bond is 4.2142 years.
Since for a zero coupon bond, t he cash flow is only on t he m at urit y dat e, t he durat ion equals
t he bond m at urit y. For coupon-paying bonds, t he durat ion will be less t han t he m at urit y period.
Since cash flows at each t im e are used as weight s, t he durat ion of a bond is inversely relat ed
t o t he coupon rat e. A bond wit h high coupon rat e will have lower durat ion as com pared t o a
bond wit h low coupon rat e.
Ex a m ple 3 .1 5
What is t he durat ion for a 5-year m at urit y zero coupon bond wit h yield t o m at urit y of 12% ?
Answer: One does not need t o do any calculat ion for answering t his quest ion. All cash flows
are only on t he m at urit y dat e and hence t he durat ion for t his bond is t he m at urit y dat e.
Alt hough durat ion helps us in m easuring t he effect ive m at urit y of t he bond, invest ors are
concerned m ore about t he bond price sensit ivit y wit h respect t o change in int erest rat es. I n
order t o m easure t he price sensit ivit y of t he bond wit h respect t o t he int erest rat e m ovem ent s,
we need t o find t he so-called m odified durat ion (MD) of t he bond. Modified durat ion is calculat ed
from durat ion ( D) using t he following form ula:
D
MD =
1+
y ,
n
Where,
y = yield t o m at urit y of t he bond
n = num ber of coupon paym ent s in a year.
The price change sensit ivit y of m odified durat ion is calculat ed using t he following form ula:
Price Change ( % ) = ( –) MD * Yield Change
Not e t he use of m inus (- ) t erm . This is because price of a bond is negat ively relat ed t o t he yield
of t he bond.
Ex a m ple 3 .1 6
Refer t o t he bond in Exam ple 3 14 i.e. 5-year m at urit y, 7% ( sem i- annual) coupon bond wit h
yield t o m at urit y of 12% . Calculat e t he change in bond price if t he YTM falls t o 11% .
Answer: I n Exam ple 3 14, we calculat ed t he durat ion t o be 4.2142 and t he bond price t o be
816. The m odified durat ion of t he bond is:
35
MD =
D
y
1+
n
=
4 . 2142
4 . 2142
=
= 3 . 976
. 12
1 . 06
1+
2
The price change will - 3.976* 1 = 3.976% or Rs. 816 * 3.976% = 32.45
New Price = 816 + 32.45 = 848.45
Check: The act ual m arket price of a 5-year m at urit y, 7% ( sem i- annual) coupon bond wit h YTM
= 11% would be:
Bond Price =
T
∑
t
Coupon
y
1 + 
2

t
+
Face Value
y

1 + 
2

T
=
10
∑
t =1
35
0 . 11 

1 +
2 

t
+
1000
10
0 . 11 


1 +
2 

= 849 . 25
Not e t hat t here is st ill som e m inor differences in t he act ual price and t he bond price calculat ed
using t he m odified durat ion form ula, due t o what is called ‘convexit y’. However, we would not
be covering t he concept in t his chapt er.
36
CH APTER 4 : Ca pit a l M a r k e t Efficie ncy
4 .1
I n t r odu ct ion
The Efficient Market s Hypot hesis ( EMH) is one of t he m ain pillars of m odern finance t heory,
and has had an im pact on m uch of t he lit erat ure in t he subj ect since t he 1960’s when it was
first proposed and on our underst anding about pot ent ial gains from act ive port folio m anagem ent .
Market s are efficient when prices of securit ies assim ilat e and reflect inform at ion about t hem .
While m arket s have been generally found t o be efficient , t he num ber of depart ures seen in
recent years has kept t his t opic open t o debat e.
4 .2
M a r k e t Efficie n cy
The ext ent t o which t he financial m arket s digest relevant inform at ion int o t he prices is an
im port ant issue. I f t he prices fully reflect all relevant inform at ion inst ant aneously, t hen m arket
prices could be reliably used for various econom ic decisions. For inst ance, a firm can assess
t he pot ent ial im pact of increased dividends by m easuring t he price im pact creat ed by t he
dividend increase. Sim ilarly, a firm can assess t he value of a new invest m ent t aken up by
ascert aining t he im pact on it s m arket price on t he announcem ent of t he invest m ent decision.
Policym akers can also judge t he im pact of various m acroeconom ic policy changes by assessing
t he m arket value im pact . The need t o have an underst anding about t he abilit y of t he m arket t o
im bibe inform at ion int o t he prices has led t o count less at t em pt s t o st udy and charact erize t he
levels of efficiency of different segm ent s of t he financial m arket s.
The early evidence suggest s a high degree of efficiency of t he m arket in capt uring t he price
relevant inform at ion. Form ally, t he level of efficiency of a m arket is charact erized as belonging
t o one of t he following ( i) weak- form efficiency ( ii) sem i- st rong form efficiency ( iii) st rongform efficiency.
4 .2 .1
W e a k - for m M a r k e t Efficie n cy
The weak- form efficiency or random walk would be displayed by a m arket when t he consecut ive
price changes ( ret urns) are uncorrelat ed. This im plies t hat any past pat t ern of price changes
are unlikely t o repeat by it self in t he m arket . Hence, t echnical analysis t hat uses past price or
volum e t rends do not t o help achieve superior ret urns in t he m arket . The weak- form efficiency
of a m arket can be exam ined by st udying t he serial correlat ions in a ret urn t im e series.
Absence of serial correlat ion indicat es a weak- form efficient m arket .
4 .2 .2
Se m i- st r on g M a r k e t Efficie n cy
The sem i- st rong form efficiency im plies t hat all t he publicly available inform at ion get s reflect ed
in t h e prices inst ant aneously. Hen ce, in such m arket s t he im pact of posit ive ( negat ive)
37
inform at ion about t he st ock would lead t o an inst ant aneous increase ( decrease) in t he prices.
Sem i- st rong form efficiency would m ean t hat no invest or would be able t o out perform t he
m arket wit h t rading st rat egies based on publicly available inform at ion.
The hypot hesis suggest s t hat only inform at ion t hat is not publicly available can benefit invest ors
seeking t o earn abnorm al ret urns on invest m ent s. All ot her inform at ion is account ed for in t he
st ocks price and regardless of t he am ount of fundam ent al and t echnical analysis one perform s,
above norm al ret urns will not be had.
The sem i- st rong form efficiency can be t est ed wit h event - st udies. A t ypical event st udy would
involve assessm ent of t he abnorm al ret urns around a significant inform at ion event such as
buyback announcem ent , st ock split s, bonus et c. Here, a t im e period close t o t he select ed
event including t he event dat e would be used t o exam ine t he abnorm al ret urns. I f t he m arket
is sem i-st rong form efficient , t he period aft er a favorable (unfavorable) event would not generat e
ret urns beyond ( less t han) what is suggest ed by an equilibrium pricing m odel ( such as CAPM,
which has been discussed lat er in t he book) .
4 .2 .3
St r on g M a r k e t Efficie n cy
The level of efficiency ideally desired for any m arket is st rong form efficiency. Such efficiency
would im ply t hat bot h publicly available inform at ion and privat ely ( non- pu blic) available
inform at ion are fully reflect ed in t he prices inst ant aneously and no one can earn excess ret urns.
A t est of st rong form efficiency would be t o ascert ain whet her insiders of a firm are able t o
m ake superior ret urns com pared t o t he m arket . Absence of superior ret urn by t he insiders
would im ply t hat t he m arket is st rongly efficient . Test ing t he st rong- form efficiency direct ly is
difficult . Therefore, t he claim about st rong form efficiency of any m arket at t he best rem ains
t enuous.
I n t he years im m ediat ely following t he proposal of t he m arket efficiency, t est s of various form s
of efficiency had suggest ed t hat t he m arket s are reasonably efficient . Over t im e, t his led t o
t he gradual accept ance of t he efficiency of m arket s.
4 .3
D e pa r t u r e s fr om t h e EM H
Evidence accum ulat ed t hrough research over t he past t wo decades, however, suggest s t hat
during m any episodes t he m arket s are not efficient even in t he weak form . The ret urns are
found t o be correlat ed bot h for short as well as long lags during such episodes. The downward
and upward t rending of prices is well docum ent ed across different m arket s ( m om ent um effect ) .
Then t here is a whole host of ot her docum ent ed deviat ions from efficiency. They include, t he
predict abilit y of fut ure ret urns based on cert ain event s and high volat ilit y of prices com pared
t o volat ilit y of t he underlying fundam ent als. All t hese evidences have st art ed t o offer a challenge
t o t he earlier claim of efficiency of t he m arket . The lack of reliabilit y about t he level of efficiency
of t he m arket prices m akes it less reliable as a guideline for decision- m aking.
38
Alt ernat ive prescript ions about t he behaviour of m arket s are widely discussed t hese days.
Most of t hese prescript ions are based on t he irrat ionalit y of t he m arket s in eit her processing
t he inform at ion relat ed t o an event or based on biased invest or preferences. For inst ance, if
t he invest ors on an average are overconfident about t heir invest m ent abilit y, t hey would not
pay close at t ent ion t o new price relevant inform at ion t hat arises in t he m arket . This leads t o
inadequat e price response t o t he inform at ion event and possibly cont inuat ion of t he t rend due
t o t he under react ion. This bias in processing inform at ion is claim ed t o be t he cause of price
m om ent um . Biased invest or preferences include aversion t o t he realizat ion of losses incurred
in a st ock. This again would lead t o under react ion.
The m arket efficiency claim was based on t he assum pt ion t hat irrat ional ( biased) invest ors
would be exploit ed by t he rat ional t raders, and would event ually lose out in t he m arket ,
leading t o t heir exit . Therefore, even in t he presence of biased t raders t he m arket was expect ed
t o evolve as efficient . However, m ore recent evidence suggest t hat t he irrat ional t raders are
not exit ing t he m arket as expect ed, inst ead at m any inst ances t hey appear t o m ake profit s at
t he expense of t he rat ional t raders.
Som e of t he well-known anom alies—or depart ures from m arket efficiency—are calendar effect s
like t he January effect and various day- of- t he- week effect s and t he so- called size effect . The
January effect was first docum ent ed in t he US m arket s—st ock ret urns were found t o be higher
in January t han in any ot her m ont h. Since t hen, it has been em pirically t est ed in a num ber of
int ernat ional m arket s, like Tokyo, London, and Paris am ong ot hers. While t he evidence has
been m ixed, t he fact t hat it exist s im plies a persist ent deviat ion from m arket efficiency.
St ock ret urns are generally expect ed t o be independent across weekdays, but a num ber of
st udies have found ret urns on Monday t o be lower t han in t he rest of t he week. One of t he
reasons put forward t o explain t his anom aly is t hat ret urns on Monday are expect ed t o be
different , given t hat t hey are across Friday- end- t o- Monday- m orning, a m uch longer period
t han any ot her day, and hence wit h m ore inform at ion. This is why t his depart ure from m arket
efficiency is also som et im es called t he weekend effect .
The alt ernat ive prescript ions about t he behaviour of m arket s based on various sources and
form s of invest or irrat ionalit y are collect ively known as behavioral finance. I t im plies t hat ( i)
t he est im at ion of expect ed ret urns based on m et hods such as t he capit al asset pricing m odel
is unreliable, and ( ii) t here could be m any profit able t rading st rat egies based on t he collect ive
irrat ionalit y of t he m arket s.
Depart ures from m arket efficiency, or t he delays in m arket s reaching equilibrium ( and t hus
efficiency) leave scope for act ive port folio m anagers t o exploit m ispricing in securit ies t o t heir
benefit . A num ber of invest m ent st rat egies are t ailored t o profit from such phenom ena, as we
would see in lat er chapt ers.
39
CH APTER 5 : Fina ncia l Ana lysis a nd Va lua t ion
5 .1
I n t r odu ct ion
I nvest m ent s in capit al m arket s prim arily involve t ransact ions in shares, bonds, debent ures,
and ot her financial product s issued by com panies. The decision t o invest in t hese securit ies is
t hus linked t o t he evaluat ion of t hese com panies, t heir earnings, and pot ent ial for fut ure
growt h. I n t his chapt er we look at one of t he m ost im port ant t ools used for t his purpose,
Valuat ion. The fundam ent al valuat ion of any asset ( and com panies are indeed asset s int o
which we invest ) is an exam inat ion of fut ure ret urns, in ot her words, t he cash flows expect ed
from t he asset . The ‘value’ of t he asset is t hen sim ply what t hese cash flows are wort h t oday,
i.e., t heir present discount ed value. Valuat ion is all about how well we predict t hese cash flows,
t heir growt h in fut ure, t aking int o account fut ure risks involved.
5 .2
Th e An a ly sis of Fin a n cia l St a t e m e n t s
A com pany’s financial st at em ent s provide t he m ost accurat e inform at ion t o it s m anagem ent
and shareholders about it s operat ions, efficiency in t he allocat ion of it s capit al and it s earnings
profile. Three basic account ing st at em ent s form t he backbone of financial analysis of a com pany:
t he incom e st at em ent ( profit & loss) , t he balance sheet , and t he st at em ent of cash flows. Let
us quickly sum m arize each of t hese.
5 .2 .1
I n com e St a t e m e n t ( Pr ofit & Loss)
A profit & loss st at em ent provides an account of t he t ot al revenue generat ed by a firm during
a period ( usually a financial year or a quart er) , t he expenses involved and t he m oney earned.
I n it s sim plest form , revenue generat ion or sales accrues from selling t he product s m anufact ured,
or services rendered by t he com pany. Operat ing expenses include t he cost s of t hese goods
and services and t he cost s incurred during t he m anufact ure. Beyond operat ing expenses are
int erest cost s based on t he debt profile of t he com pany. Taxes payable t o t he Governm ent are
t hen debit ed t o provide t he Profit Aft er Tax ( PAT) or t he net incom e t o t he shareholders of t he
com pany.
Act ual P&L st at em ent s of com panies are usually m uch m ore com plicat ed t han t his, wit h socalled ‘ot her incom e’ ( incom e from non- core act ivit ies) , ‘negat ive’ int erest expenses ( from
cash reserves wit h t he com pany) , preferred dividends, and non- recurring, except ional incom e
or expenses. The exam ple given below is t hat of a large com pany in t he Pharm aceut ical sect or
over t he period 2006- 2008.
40
I llu st r a t ion 5 .1
I n com e St a t e m e n t ( US$ M )
2006
2007
2008
Net sales
16,380
21,340
33,565
Cost of sales
( 5,332)
( 6,584)
( 8,190)
SG&A
( 1,408)
( 1,771)
( 2,738)
Research & developm ent
( 1,534)
( 2,440)
( 2,725)
Ot her operat ing it em s
( 3,650)
( 4,620)
( 5,369)
4 ,4 5 7
5 ,9 2 6
1 4 ,5 4 3
543
1,336
305
0
0
0
869
1,072
1,146
0
0
0
5 ,8 6 9
8 ,3 3 4
1 5 ,9 9 4
( 239)
67
( 485)
Minorit y int erest
3
( 559)
( 640)
Preferred dividends
0
0
0
100
0
0
5 ,7 3 3
7 ,8 4 3
1 4 ,8 6 9
EBI T
Tot al ot her non- operat ing it em s
Associat es
Net int erest incom e/ expense
Except ional it em s
Pr e t a x pr ofit
Taxat ion
Net ext raordinary it em s
Re por t e d n e t in com e
5 .2 .2
Th e Ba la n ce Sh e e t
Asset s owned by a com pany are financed eit her by equit y or debt and t he balance sheet of a
com pany is a snapshot of t his capit al st ruct ure of t he firm at a point in t im e; t he sources and
applicat ions of funds of t he com pany.
A com pan y ow n s f ix ed asset s ( m ach in er y, an d ot h er in f r ast r u ct u r e) , cu r r en t asset s
( m anufact uring goods in progress, m oney it expect s t o receive from business part ners—
receivables, invent ory et c.) , cash and ot her financial invest m ent s. I n addit ion t o t hese t hree,
a com pany could also own ot her asset s which carry value, but are not direct ly m arket able, like
pat ent s, t radem arks, and ‘goodwill’—value not linked t o asset s, but realized from acquisit ions.
These asset s are financed eit her by t he com pany’s equit y (invest m ent s by shareholders) or by
debt . The illust rat ive exam ple shown below is t he balance sheet of a large Pharm aceut ical
com pany.
41
I llu st r a t ion 5 .2
Ba la n ce Sh e e t ( US$ m )
2006
2007
2008
15,628
14,106
17,290
Account s receivable
3,609
6,789
14,177
I nvent ory
5,117
6,645
7,728
Ot her current asset s
2,471
2,653
5,079
2 6 ,8 2 6
3 0 ,1 9 2
4 4 ,2 7 4
Net t angible fixed asset s
8,977
10,122
11,040
Tot al financial asset s
3,237
2,239
2,659
507
697
1,729
3 9 ,5 4 7
4 3 ,2 5 0
5 9 ,7 0 1
2,279
2,966
3,722
0
0
0
Tot al ot her current liabilit ies
1,236
80
2,651
Cu r r e n t lia bilit ie s
3 ,5 1 5
3 ,0 4 6
6 ,3 7 3
18,747
11,144
1,436
1,053
895
92
0
0
0
2 3 ,3 1 4
1 5 ,0 8 5
7 ,9 0 1
332
438
1,886
15,902
27,728
49,915
Sh a r e h olde r s’ fu n ds
1 6 ,2 3 3
2 8 ,1 6 6
5 1 ,8 0 0
Lia bilit ie s a n d sh a r e h olde r s’ fu n ds
3 9 ,5 4 7
4 3 ,2 5 0
5 9 ,7 0 1
Cash and m arket able securit ies
Cu r r e n t a sse t s
Net goodwill
Tot a l a sse t s
Account s payable
Short - t erm debt
Long- t erm debt
Tot al ot her non- current liabilit ies
Tot al provisions
Tot a l lia bilit ie s
Minorit y int erest – accum ulat ed
Shareholders’ equit y
5 .2 .3
Ca sh Flow St a t e m e n t
The cash flow st at em ent is t he m ost im port ant am ong t he t hree financial st at em ent s, part icularly
from a valuat ions perspect ive. As t he nam e im plies, such a st at em ent is used t o t rack t he cash
flows in t he com pany over a period. Cash flows are t racked across operat ing, invest ing, and
financing act ivit ies. Cash flows from operat ions include net incom e generat ion adj ust ed for
changes in working capit al ( like invent ories, receivables and payables) , and non- core accruals
(like depreciat ion, et c). A firm ’s invest m ent act ivit ies com prise fixed, and current asset s (capit aland operat ing expendit ure) , som et im es int o ot her firm s ( like an acquisit ion) , and generally
represent negat ive cash flows. Cash flows in financing act ivit ies are t he net result of t he firm ’s
borrowing, and paym ent s during t he period. The sum t ot al of cash flows from t hese t hree
heads represent s t he net change in cash balances of t he firm over t he period.
42
Cash generat ion from operat ing act ivit ies of t he firm , when adjust ed for it s capit al expendit ure
represent t he ‘free cash’ available t o it , for pot ent ial invest m ent act ivit ies, acquiring ot her
firm s or businesses, or dist ribut ion am ong it s shareholders. As we will see in lat er t opics, free
cash flows are t he key t o calculat ing t he so- called int rinsic value of an asset in any discount ed
valuat ion m odel. Our illust rat ive exam ple below shows t he cash flow st at em ent ( and free cash
flows) of a large pharm aceut ical com pany over t he period 2006- 2008.
I llu st r a t ion 5 .3
Ca sh Flow ( US$ M )
2006
2007
2008
Report ed net incom e
5,733
7,843
14,869
0
0
0
( 3)
559
640
610
813
969
75
( 511)
( 1,337)
Tot al ot her operat ing cash flow
( 1,365)
( 2,156)
( 753)
Net change in working capit al
( 3,177)
( 4,154)
( 9,340)
1 ,8 7 2
2 ,3 9 4
5 ,0 4 8
( 3,387)
( 2,000)
( 1,995)
3,511
1,367
( 5,242)
Tot al ot her invest ing cash flows
634
1,272
1,177
Ca sh fr om in ve st in g a ct ivit ie s
758
639
( 6 ,0 6 0 )
Change in borrowings
805
( 1,742)
768
0
0
0
Dividends paid
( 793)
( 2,629)
( 18)
Tot al ot her financing cash flows
( 156)
( 127)
( 88)
Ca sh fr om fin a n cin g a ct ivit ie s
( 144)
( 4 ,4 9 8 )
661
Ch a n ge in ca sh
3 ,5 1 8
( 1 ,4 6 5 )
( 352)
( 1 ,5 1 4 )
394
3 ,0 5 2
Preferred dividends
Minorit y int erest
Depreciat ion and am ort izat ion
Cash t ax adj ust m ent
Ca sh fr om ope r a t ion s
Capit al expendit ure
Net acquisit ions/ disposals
Equit y raised/ share buybacks
Fr e e ca sh flow
5 .3
Fin a n cia l Ra t ios ( Re t u r n , Ope r a t in g a n d, Pr ofit a bilit y Ra t ios)
Financial rat ios are m eaningful links bet ween different ent ries of financial st at em ent s, as by
t hem selves t he financial ent ries offer lit t le t o exam ine a com pany. I n addit ion t o providing
inform at ion about t he financial healt h and prospect s of a com pany, financial rat ios also allow
a com pany t o be viewed, in a relat ive sense, in com parison wit h it s own hist orical perform ance,
ot hers in it s sect or of t he econom y, or bet ween any t wo com panies in general. I n t his sect ion
we exam ine a few such rat ios, grouped int o cat egories t hat allow com parison of size, solvency,
43
operat ing perform ance, growt h profile and risks. The list below is by no m eans exhaust ive,
and m erely serves t o illust rat e a few of t he im port ant ones.
5 .3 .1
M e a su r e s of Pr ofit a bilit y: RoA, RoE
Re t u r n on Asse t s ( RoA) in it s sim plest form denot es t he firm ’s abilit y t o generat e profit s
given it s asset s :
RoA = ( Net I ncom e + I nt erest Expenses) * ( 1- Tax Rat e) / Average Tot al Asset s
Re t u r n on Equ it y ( RoE) is t he ret urn t o t he equit y invest or :
RoE = Net I ncom e / Shareholder Funds
Som et im es t his rat io is also calculat ed as RoAE, t o account for recent capit al raising by
t he firm
Ret urn on Average Equit y = Net I ncom e / Average Shareholder Funds
Ret urn on Tot al Capit al = Net I ncom e + Gross I nt erest Expense / Average t ot al capit al
5 .3 .2
M e a su r e s of Liqu idit y
Short - t erm liquidit y is im perat ive for a com pany t o rem ain solvent . The rat ios below get
increasingly conservat ive in t erm s of t he dem ands on a firm t o m eet near- t erm payables.
Current rat io = Current Asset s / Current Liabilit ies
Quick Rat io = ( Cash + Market able Securit ies + Receivables) / Current Liabilit ies
Acid t est rat io = ( Cash + Market able Securit ies) / Current Liabilit ies
Cash Rat io = ( Cash + Market able Securit ies) / Current Liabilit ies
5 .3 .3 . Ca pit a l St r u ct u r e a n d Solve n cy Ra t ios
Tot al debt t o t ot al capit al = ( Current Liabilit ies + Long- t erm Liabilit ies) /
( Equit y + Tot al Liabilit ies)
Long- t erm Debt - Equit y = Long- t erm Liabilit ies / Equit y
5 .3 .4
Ope r a t in g Pe r for m a n ce
Gross Profit Margin = Gross Profit / Net Sales
Operat ing Profit Margin = Operat ing I ncom e / Net Sales
Net Profit Margin = Net I ncom e / Net Sales
5 .3 .5
Asse t Ut iliza t ion
These rat ios look at t he effect iveness of a firm t o ut ilize it s asset s, especially it s fixed asset s.
A high t urnover im plies opt im al use of asset s. I n addit ion t o t he t wo below t here are ot hers like
Sales t o invent ories, and Sales t o Working capit al.
Tot al Asset Turnover = Net Sales / Average Tot al Asset s
Fixed Asset Turnover = Net Sales / Average Net Fixed Asset s
There are m any ot her cat egories, like t he ‘com m on size’ rat ios, which serve t o present t he
com pany in t erm s of one of it s own denom inat ors, like Net Sales, or t he m arket capit alizat ion;
and ot hers t hat specifically look at t he risk aspect of t hings ( business, financial, and liquidit y) .
44
We shall t ake a look at anot her t wo cat egories, t he m arket m easures, and valuat ion rat ios,
aft er t he discussion on valuat ions.
5 .4
Th e v a lu a t ion of com m on st ock s
I n chapt er 3, we exam ined a few of t he m aj or valuat ion m et hods for fixed incom e- generat ing
asset s. Using financial st at em ent s and rat ios, we now exam ine som e of t he concept s relat ing
t o share valuat ions and t o be m ore specific, we will deal wit h valuat ion of com m on st ocks.
Com m on shareholders are t he owners of t he firm , and as such are t he final st akeholders in it s
growt h, and risks; t hey appoint t he m anagem ent t o run it s day- t o-day affairs and t he Board of
Dir ect ors t o oversee t h e m anagem en t ’s act iv it ies. Th e cash f low s ( r et ur n ) t o com m on
shareholders from t he com pany are generally in t he form of current and fut ure dividends
dist ribut ed from t he profit s of t he firm . Alt ernat ively, an invest or can always sell her holdings
in t he m ar ket ( secon dary m ar ket ) , get t h e prevailin g m ar ket price, an d realize capit al
appreciat ion if t he ret urns are posit ive.
We now exam ine t he valuat ion of com m on shares in som e det ail. As m ent ioned above, t he
valuat ion of any asset is based on t he present value of it s fut ure cash flows. Such a m et hodology
provides what is called t he ‘int rinsic’ value of t he asset —a com m on st ock in our case. The
problem of valuing t he st ock t hen t ranslat es int o one of predict ing t he fut ure free cash flow
profile of t he com pany, and t hen using t he appropriat e discount fact or t o m easure what t hey
are wort h t oday. The appropriat ely nam ed discount ed- cash flow t echnique is also referred t o
as absolut e valuat ion, part icularly when com pared t o anot her widely- followed approach in
valuat ion, called relat ive valuat ion.
Relat ive valuat ion looks at pricing asset s on t he basis of t he pricing of ot her, sim ilar asset s—
inst ead of pricing t hem independent ly—t he core assum pt ion being t hat asset s wit h sim ilar
earnings and growt h profile, and facing t he sam e risks ought t o be priced com parably. Two
st ocks in t he sam e sect or of t he econom y could t hus be com pared, and t he sam e sect or ( and
it s st ocks) across count ries. The discussion on relat ive valuat ion follows t hat of absolut e or
int rinsic valuat ion.
5 .4 .1
Absolu t e ( I n t r in sic) Va lu a t ion
I nt rinsic value or t he fundam ent al value refers t o t he value of a securit y, which is int rinsic t o or
cont ained in t he securit y it self. I t is defined as t he present value of all expect ed cash flows t o
t he com pany. The est im at ion of int rinsic value is what we would be dealing wit h in det ails in
t his chapt er.
5 .4 .1 .1
D iscou n t e d Ca sh Flow s
The discount ed cash flow m et hod values t he share based on t he expect ed dividends from t he
45
shares. The price of a share according t o t he discount ed cash flow m et hod is calculat ed as
under:
P0 =
∞
∑ (1 + r )
Div t
t =1
t
Since t he profit s of t he firm are not cert ain, t he act ual fut ure dividends are not known in
advance. However, t he m arket form s an expect at ion of t he fut ure dividends and t he value of a
share is t he present value of expect ed fut ure dividends of t he com pany. I t can be shown t hat
t he form ula can be seen as an ext ension of t he form ula P0 =
Div 1 + P1
.
(1 + r )
As explained above, we can writ e t he share price at t he end of t he year 1 as a funct ion of t he
2nd year dividend and price of share at t he end of t he year 2. Or,
P1 =
Div 2 + P2
(1 + r )
Sim ilarly,
P2 =
Div 3 + P3
and so on.
(1 + r )
Put t ing t he values of P1 , P2 , P3 , P4 , we can writ e:
P0 =
Div 1 + P1
Div 1
Div N
PN
Div 2
Div 3
=
+
+
+ .... +
+
2
(1 + r )
1+ r
(1 + r )
(1 + r ) 3
(1 + r ) N
(1 + r ) N
PN
Now when N t ends t o infinit y, (1 + r)N t ends t o infinit y and t he value of
t ends t o zero
(1 + r ) N
and t herefore m ay be ignored. So t he current share price ( P0 ) can be writ t en as:
P0 =
∞
∑ (1 + r )
Div t
t =1
5 .4 .1 .2
t
Con st a n t D ivide n d Gr ow t h
Let us see a special case of t he above m odel when it is assum ed t hat am ount paid as dividends
grows at a const ant rat e ( say g) every year. I n t his case, t he cash flows in various years will be
as under:
Year
Cash Flow
0
- P0
1
Div 1
2
Div 2 = Div 1 * ( 1+ g)
3
Div 3 = Div 2 * ( 1+ g) = Div 1 * ( 1+ g) 2
4
Div 4 = Div 3 * ( 1+ g) = Div 2 * ( 1+ g) 2 = Div 1 * ( 1+ g) 3
I n t his circum st ance, where t he dividend am ount grows at a const ant rat e, t he const ant dividend
46
growt h m odel st at es t hat t he share price can be obt ained using t he sim ple form ula:
P0 =
Div 1
r – g
This form ula can be used only when t he expect ed rat e of ret urn ( r) is great er t han t he growt h
rat e ( g). Ot herwise, t he present value of t he growing perpet uit y will reach infinit e. This is even
t rue in real world. I t is not possible for a st ock’s dividend t o grow at a rat e g, which is great er
t han r for infinit e period. I t can only be for a lim it ed num ber of years. This m odel is not
applicable in such cases.
Exam ple: RNL has paid a dividend of Rs. 10 per share last year ( D 0 ) and it is expect ed t o grow
at 5% every year. I f an invest or ’s expect ed rat e of ret urn from RNL share is 7% , calculat e t he
m arket price of t he share as per t he dividend discount m odel.
Answer: The following are given:
Div 0 = 10; g = 5% or 0.05; r = 7% or 0.07.
Div 1 + Div 0 * (1 + g ) = 10 * 1 . 05 = 10 . 50
P0 =
Div 1
10 . 50
10 . 50
=
=
= 525
0 . 02
r – g 0 . 07 – 0 . 05
The m arket price of RNL share as per t he dividend discount m odel wit h const ant growt h rat e is
Rs. 525.
I f we know t he m arket price of t he share, t he dividend am ount and t he dividend growt h rat e,
t hen we can com put e t he expect ed rat e of ret urn ( r) by using t he following form ula:
r =
Div 1
+ g
P0
5 .4 .1 .3
Pr e se n t Va lu e of Gr ow t h oppor t u n it ie s ( PVGO)
One can split t he value of t he shares as com put ed in t he const ant growt h m odel int o t wo part s
– t he present value of t he share assum ing level st ream of earnings (a level st ream of earnings
is sim ply t he current incom e ext rapolat ed int o t he fut ure, wit h no growt h; in which case,
t here’s no need t o ret ain any of t he earnings) and t he present value of growt h opport unit ies.
The value of growt h opport unit ies is posit ive if t he firm ( and t he m arket ) believes t hat t he firm
has avenues t o invest which will generat e a ret urn t hat is m ore t han t he m arket expect ed rat e
of ret urn. Now when t he firm ’s incom e pot ent ial from addit ional invest m ent is m ore t han t he
m arket expect ed rat e of ret urn, t hen for every penny re- invest ed ( plowbacked rat her t han
dist ribut ed as dividend) will generat e a ret urn t hat is higher t han t he m arket expect at ion. The
47
value of such excess ret urn is referred t o as present value of growt h opport unit ies.
PVGO
= Share Price – Present value of level st ream of earnings
= Share price – EPS / r
The growt h in t he fut ure dividend arises because t he firm s, inst ead of dist ribut ing 100% of t he
earnings as dividends, plowbacks and invest s cert ain port ion of t he current year profit on
proj ect s whose yield will be great er t han t he m arket expect ed rat e of ret urn.
The growt h rat e in dividend ( g) , equals, t he Plowback rat io * ROE.
5 .4 .1 .4
D iscou n t e d Fr e e - ca sh flow va lu a t ion m ode ls
Using t he above concept s, we are now in a posit ion t o look at valuat ion using cash flows, wit h
t he discount ed free cash flow m odel. We first det erm ine t he value of t he ent erprise and t hen
value t he equit y by deduct ing t he debt value from t he firm value. Thus:
Market value of equit y ( V0 ) = Value of t he firm + Cash in hand – Debt Value
The price of t he share ( P0 ) is t he m arket value of t he equit y divided by t he num ber of shares
out st anding.
I t is sim ple t o calculat e t he debt value since t he paym ent s t o be m ade t o debt holders is
predet erm ined and cert ain. However, t he real problem lies wit h det erm ining t he value of t he
firm . As per t he discount ed free cash flow m odel, t he value of a firm is t he present value of t he
fut ure free cash flow of t he firm . The discount ing rat e is t he firm s weight ed average cost of
capit al ( WACC) and not t he m arket expect ed rat e of ret urn on equit y invest m ent . WACC is t he
cost of capit al t hat reflect s t he risk of t he overall business and not t he risk associat ed wit h t he
equit y invest m ent alone. WACC is calculat ed using t he following form ula:
WACC = r D (1 – T ) *
D
E
+ rE *
D+ E
D+ E
where
r D and r E is t he expect ed rat e of ret urn on debt and equit y
T = I ncom e Tax Rat e
D = t he m arket value of debt ; E = t he m arket value of equit y
The firm value ( V0 ) is calculat ed using t he following form ula:
V0 =
FCF1
FCF2
FCF3
+
+
1 + r w acc
(1 + rw acc ) 2
(1 + rw acc ) 3
+ .... +
FCFN
( 1 + rw acc ) N
+
( Ter m inal Valu eN )
(1 + rw acc ) N
The t erm inal value at year N is oft en com put ed by assum ing t hat t he FCF will grow at a
const ant growt h rat e beyond year N, i.e.
48
Term inal ValueN =
FCF * (1 + g FCF )
FCFN +1
=
( ( r ) WACC – g FCF ) ( ( r ) WACC – g FCF )
where g FCF is t he expect ed growt h rat e of t he firm s free cash flow
What is free cash flow ( FCF) ? The free cash m easures t he cash generat ed by t he firm t hat can
be dist ribut ed t o t he equit y shareholders aft er budget ing for capit al expendit ure and working
capit al requirem ent s. While com put ing FCF, we assum e t hat t he firm is a 100% equit y owned
com pany and hence we do not consider any paym ent t o debt or equit y holders while calculat ing
t he free cash flow. Thus t he form ula for com put ing FCF is:
Term inal VFCF = EBI T * ( 1 – T ) + Depn – Capit al Expendit ure – I ncrease in Working Capit al
where T in t he t ax rat e.
We st art wit h EBI T since we do not consider cash out flow in t he form of int erest paym ent s.
Depreciat ion lowers t he EBI T but is added back since it is a non- cash expendit ure ( does not
result in cash paym ent s) . Since t he firm has t o incur any planned capit al expendit ure and has
t o finance any working capit al requirem ent before dist ribut ing t he profit s t o t he shareholders
t he sam e is deduct ed while calculat ing t he free cash flows.
5 .4 .2
Re la t ive Va lu a t ion
Relat ive valuat ion m odels do calculat e t he share price but t hey are generally based on t he
valuat ion of com parable firm s in t he indust ry. Various valuat ion m ult iples such as price-earning
rat io, ent erprise value m ult iples, et c. are used by t he finance professionals which depends on
t he indust ry, current econom ic scenario, et c. Most of t hese m odels are generally used for
evaluat ion purpose as t o whet her a part icular st ock is overvalued or undervalued and less for
act ual valuat ion of t he shares.
As discussed in t he first chapt er, t he face value or nom inal value of a share is t he price print ed
on t he share cert ificat e. One should not confuse a share’s nom inal value wit h t he price at
which t he com pany issues shares t o t he public. The price at which a com pany issues shares
m ay be m ore or less t han t he face value. The issue price is generally m ore t han t he face value
and t he difference bet ween t he issue price and t he face value is called as share prem ium .
Market price is t he price at which t he share is t raded in t he m arket . I t is det erm ined by t he
dem and and supply of t he share in t he m arket and depends on t he m arket ( buyers and sellers)
est im at ion of t he present value of all fut ure cash flows t o t he com pany. I n an efficient m arket ,
we assum e t hat t he m arket is able t o gat her all inform at ion about t he com pany and price
accordingly. Market capit alizat ion of a com pany is t he t ot al value of all shares of t he com pany
and is calculat ed by m ult iplying t he m arket price per share wit h t he num ber of shares out st anding
in t he m arket .
49
The book va lu e or ca r r yin g va lu e in account ing, is t he value of an asset according t o it s
balance sheet account balance. For asset s, t he value is based on t he original cost of t he asset
less any depreciat ion, am ort izat ion or im pairm ent cost s m ade against t he asset . Book value
per share is calculat ed by dividing t he net asset s of t he com pany wit h t he num ber of shares
out st anding. The net asset of t he com pany is t he values of all asset s less values of all liabilit ies
out st anding in t he books of account s.
5 .4 .2 .1
Ea r n in g pe r Sh a r e ( EPS)
Earning per share is t he firm s’ net incom e divided by t he average num ber of shares out st anding
during t he year.
Calculat ed as:
EPS =
Net Proift – Dividend on Preference Shares
Average num ber of shares out st anding during t he year
5 .4 .2 .2
D ivide n d pe r Sh a r e ( D PS)
Dividends are a form of profit dist ribut ion t o t he shareholders. The firm m ay not dist ribut e t he
ent ire incom e t o t he shareholders, but decide t o ret ain som e port ion of it for financing growt h
opport unit ies. Alt ernat ively, a firm m ay pay dividends from past years profit during years
where t here is insufficient incom e. I n t his case, t he dividends am ount will be higher t han t he
earnings. The dividend per share is t he am ount t hat t he firm pays as dividend t o t he holder of
one share i.e. t ot al dividend / num ber of shares in issue.
The dividend payout rat io ( DPR) m easures t he percent age of incom e t hat t he com pany pays
out t o t he shareholders in t he form of dividends. The form ula for calculat ing DPR is:
DPR =
Dividends
DPS
=
Net I ncom e
EPS
Ret ent ion rat io is t he opposit e of dividend payout rat io and m easures t he percent age of net
incom e not paid t o t he shareholders in t he form of dividends. I t is not hing but ( 1- DPR) .
Ex a m p l e : Th e f o l l o w i n g i s t h e f i g u r e f o r A sh a I n t e r n a t i o n a l d u r i n g t h e y e a r
2008- 09:
Net I ncom e: Rs. 1,000,000
Num ber of equit y shares ( 2008) : 150,000
Num ber of equit y shares ( 2009) : 250,000
Dividend paid: Rs. 400,000
Calculat e t he earnings per share ( EPS) , dividend per share ( DPS) , dividend payout rat io and
50
ret ent ion rat io for Asha I nt ernat ional.
Answer:
Aver age num ber of shar es =
150 ,000 + 250 ,000
Opening + closing
=
= 200 , 000
2
2
EPS =
Net I ncom e
1, 000,0000
=
=5
Average Num ber of shares
200,000
DPS =
Dividends
4, 00,000
=
=2
Average Num ber of shares
200,000
DPR =
2
DPS
=
= 0 . 4 or 40 %
5
EPS
Ret ent ion Rat io = 1- DPR = 0.6 or 60%
5 .4 .2 .3
Pr ice - e a r n in gs r a t io ( P/ E Ra t io)
Price earning rat io for a com pany is calculat ed by dividing t he m arket price per share wit h t he
earnings per share ( EPS) .
Price Earnings Rat io =
Market price per share
Annual earning per share
The earning per share is usually calculat ed for t he last one year. Som et im es, we also calculat e
t he PE rat io using t he expect ed fut ure one-year ret urn. I n such case, we call forward PE or
est im at ed PE rat io.
Exam ple: St ock XYZ, whose earning per share is Rs. 50 is t rading in t he m arket at Rs. 2000.
What is t he price t o earnings rat io for XYZ?
Answer:
Price Earnings Rat io =
Market price per share
2000
=
= 40
Annual earning per share
50
We cannot draw any conclusion as t o whet her a st ock is undervalued or overvalued in t he
m arket by j ust considering t he PE rat io. A higher PE rat io im plies t hat t he invest ors are paying
m ore for each unit of net incom e, which im plies t hat t he invest ors are opt im ist ic about t he
fut ure perform ance ( or fut ure growt h rat e) of t he com pany. St ocks wit h higher PE rat io are
also called growt h firm s and st ocks wit h lower PE rat io are called as incom e firm s.
5 .4 .2 .4
Pr ice - Book Ra t io
The price- book rat io is widely used as a conservat ive m easure of relat ive valuat ion of an asset ,
where t he asset s of t he firm are valued at book. I nvest ors also widely use t he rat io t o j udge
whet her t he st ock is undervalued or overvalued, as it ’s less suscept ible t o fluct uat ions t han t he
51
PE rat io. The form ula t o calculat e t he rat io is:
Price- book rat io = Market price of t he share / Book Value per share.
5 .4 .2 .5
Re t u r n on Equ it y
Ret urn on equit y m easures profit abilit y from t he equit y shareholders point of view. I t is t he
ret urn t o t he equit y shareholders and is m easured by t he following form ula:
ROE =
Net I ncom e aft er Tax – Preferred Dividends
Average Shareholder Equit y Excluding Preferred Share Capit al
Exam ple: XYZ Com pany net incom e aft er t ax for t he financial year ending 31 st March, 2009
was Rs. 10 m illion and t he equit y share capit al as on 31 st March, 2008 and 31 st March 2009
w as Rs. 8 0 m illion an d Rs. 12 0 m illion respect ively. Calculat e t h e ret u rn on equit y of
XYZ com pany for t he year 2008- 09.
Answer:
Aver age Equit y =
80 + 120
Opening Equit y + Closing Equit y
=
= 100 m illion
2
2
Ret urn on Equit y =
5 .4 .2 .6
Net Profit aft er Tax
10
=
= 0 . 10 or 10 %
100
Average Equit y
Th e D u Pon t M ode l
The Du Pont m odel is widely used t o decide t he det erm inant s of ret urn profit abilit y of a com pany,
or a sect or of t he econom y. Ret urns on shareholder equit y are expressed in t erm s of a com pany’s
profit m argins, asset t urn, and it s financial leverage.
DuPont Model breaks t he Ret urn on equit y as under:
RoE = Ret urn on Equit y
= Net Profit s/ Equit y
= Net Profit s/ Sales * Sales/ Asset s * Asset s/ Equit y
= Profit Margin * Asset Turnover * Financial Leverage
The first com ponent m easures t he operat ional efficiency of t he firm t hrough it s net m argin
rat io. The second com ponent , called t he asset t urnover rat io, m easures t he efficiency in usage
of asset s by t he firm and t he t hird com ponent m easures t he financial leverage of t he firm
t hrough t he equit y m ult iplier. The analysis reflect s a firm s’ efficiency in different aspect s of
business and is widely used now for cont rol purpose. I t shows t hat t he firm could im prove it s
RoE by a com binat ion of profit abilit y ( higher profit m argins), raising leverage ( by raising debt ) ,
by using it s asset s bet t er ( higher asset t urn) or a com binat ion of all t hree.
52
The DuPont analysis could be easily ext ended t o ascert ain a sect or ’s profit abilit y m et rics for
com parabilit y, or, for t hat m at t er, an ent ire m arket .
5 .4 .2 .7
D ivide n d Yie ld
Dividend yield is t he rat io bet ween t he dividend paid during t he last 1-year period and t he
current price of t he share. The rat io could also be used wit h t he forward dividend yield inst ead—
expect ed dividends, for eit her t he next 12 m ont hs, or t he financial year.
Exam ple: ABC Com pany paid a dividend of Rs. 5 per share in 2009 and t he m arket price of
ABC share at t he end of 2009 was Rs. 25. Calculat e t he dividend yield for ABC st ock.
Answer:
Dividend Yield =
5 .4 .2 .8
Last year dividend
5
=
= 0 . 20 or 20 %
Current Price per share 25
Re t u r n t o I n ve st or
The ret urn what t he invest or earns during a year by holding t he share of a com pany is not
equal t o t he dividend per share or t he earnings per rat io. An invest or ’s earning is t he sum of
t he dividend am ount t hat he received from t he com pany and t he change in t he m arket price of
t he share. The invest m ent am ount is equal t o t he m arket price of t he share at t he beginning of
t he year. An invest or ’s ret urn can be calculat ed using t he following form ula:
Expect ed Ret urn( r) =
Dividends + Δ ( m arket price of t he share)
Opening Market Price
Exam ple: The share price of PQR Com pany on 1st April 2008 and 31st March 2009 is Rs. 80
and Rs. 84 respect ively. The com pany paid a dividend of Rs. 6 for t he year 2008- 09. Calculat e
t he ret urn for a shareholder of PQR Com pany in t he year 2008- 09.
Answer:
Expect ed Ret urn( r) =
Dividends + ∆ ( m arket price of t he share) 6 + ( 84 – 80 ) 10
=
=
= 12 . 5 %
Opening Market Price
80
80
I f we writ e t he dividends during t he year as Div 1 , t he price of t he share at t he beginning and
at t he end of t he year as P0 and P1 respect ively, we can writ e t he above form ula as:
r =
Div 1 + P1 – P0
P0
This can be re- writ t en as:
P0 =
Div 1 – P1
(1 + r )
53
This im plies t hat given t he expect ed rat e of ret urn for an invest or, t he price of a share can be
calculat ed based on t he invest or expect at ion of t he fut ure dividends and t he fut ure share
price. We have already learned in t he previous chapt er about t he fact ors t hat affect t he expect ed
rat e of ret urns and how one can calculat e t he expect ed rat e of ret urns ( e.g. using CAPM) . Now
t he quest ion arises what det erm ines t he next year price ( P1 ) of a share.
5 .5
Te ch n ica l An a ly sis
Our final approach t o valuat ion is also considered t he m ost cont roversial, wit h t he num bers of
believers balancing t hose who find fault wit h t he m et hodology. Technical analysis involves
m aking t rading decisions by st udying records or chart s of past st ock prices and volum e, and in
t he case of fut ures, open int erest .
The t echnical analyst s do not at t em pt t o m easure a securit y’s int rinsic value but believe in
m aking short - t erm profit by analyzing t he volum e and price pat t erns and t rends. Technical
analyst s use st at ist ical t ools like t im e series analysis ( in part icular t rend analysis) , relat ive
st rengt h index, m oving averages, regressions, price correlat ions, et c. The field of t echnical
analysis is based on t he following t hree assum pt ions.
a)
The m arket discount s everyt hing: Technical analyst s believe t hat t he m arket price
t akes int o considerat ion t he int rinsic value of t he st ocks along wit h broader econom ic
fact ors and t he m arket psychology. Therefore, what is im port ant is an analysis of t he
price m ovem ent t hat reflect s t he dem and and supply of a st ock in t he short run.
b)
Price m oves in t rends: Trends are of t hree t ypes, viz. upt rend, downt rend and horizont al
t rend. Technical analyst s believe t hat once t rends are est ablished in t he prices, t he
price m oves in t he sam e direct ion as t he t rends suggest s.
c)
Hist ory t ends t o repeat it self: This assum pt ion leads t o a belief t hat current invest ors
repeat t he behavior of t he invest ors t hat preceded t hem and t herefore recognizable
price pat t erns can be observed if a chart is drawn.
There are various concept s t hat are used by t echnical analyst s like support prices, resist ance
levels, breakout s, m om ent um , et c. These concept s can be heard very oft en in business channels
and business newspapers. Support s refer t o t he price level t hrough which a st ock price seldom
falls and resist ance is t he price level t hrough which a st ock seldom surpasses. Breakout refers
t o sit uat ion when t he price act ually falls below t he support level or rises above t he resist ance
level. Once a breakout occurs, t he role is reversed. I f t he price increases beyond t he resist ance
level, t he resist ance level becom es t he support level and when t he price falls below t he support
level, t he support level becom es t he new resist ance level for t he st ock. Mom ent um refers t o
t he rat e at which price of a st ock changes.
54
5 .5 .1
Ch a lle n ge s t o Te ch n ica l An a lysis
There are m any quest ions, prim arily raised by fundam ent al analyst s, about t he assum pt ions
of t echnical analysis. While it is underst andable t hat price m ovem ent s are caused by t he
int eract ion of supply and dem and of securit ies and t hat t he m arket assim ilat es t his inform at ion
( as m ent ioned in t he first assum pt ion) , t here is no consensus on t he speed of t his adj ust m ent
or it s ext ent . I n ot her words, while prices m ay react t o changes in dem and- supply and ot her
m arket dynam ics, t he response could easily differ across securit ies, bot h in t he t im e t aken,
and t he degree t o which prices change. Ot her obj ect ions t o t echnical analysis arise from
Efficient Market s Hypot hesis, which we have seen in Chapt er 4. Proponent s of t he EMH aver
t hat m arket efficiency would preclude any t echnical t rading pat t erns t o repeat wit h any
predict able accuracy, rendering t he profit abilit y of m ost such t rading rules subj ect t o chance.
Furt her, t he success of a t rading rule could also m ake it crowded, in t he sense t hat m ost
t echnical t raders follow a sm all set of rules ( albeit wit h possibly different param et erizat ions) ,
speeding up t he adj ust m ent of t he m arket , and t hus reducing t he pot ent ial gains. Finally,
t echnical analysis involves m eaningful levels of subj ect ivit y- int erpret at ions m ay vary widely
on t he sam e pat t ern of st ock, or index prices- which also hinders syst em at ic reasoning and
ext ensibilit y across different securit ies.
55
CH APTER 6 : M ode r n Por t folio The or y
6 .1
I n t r odu ct ion
Underst anding t he risky behaviour of asset and t heir pricing in t he m arket is crit ical t o various
invest m ent decisions, be it relat ed t o financial asset s or real asset s. This underst anding is
m ost ly developed t hrough t he analysis and generalizat ion of t he behaviour of individual invest ors
in t h e m ark et under cer t ain assu m pt ion s. The t w o buildin g blocks of t his analysis and
generalizat ion are (i) t heory about t he risk-ret urn charact erist ics of asset s in a port folio (port folio
t heory) and ( ii) generalizat ion about t he preferences of invest ors buying and selling risky
asset s ( equilibrium m odels) . Bot h t hese aspect s are discussed in det ail in t his chapt er, where
our aim is t o provide a brief overview of how finance t heory t reat s st ocks ( and ot her asset s)
individually, and at a port folio level. We first exam ine t he m odern approach t o underst anding
port folio m anagem ent using t he t rade- off bet ween risk and ret urn and t hen look at som e
equilibrium asset- pricing m odels. Such m odels help us underst and t he t heoret ical underpinning
and ( hopefully predict ) t he dynam ic m ovem ent of asset prices.
6 .2
D iv e r sifica t ion a n d Por t folio Risk s
The age- old wisdom about not put t ing “ all your eggs in one basket ” applies very m uch in t he
case of port folios. Port folio risk ( generally defined as t he st andard deviat ion of ret urns) is not
t he weight ed average of t he risk ( st andard deviat ion) of individual asset s in t he port folio. This
gives rise t o opport unit ies t o elim inat e t he risk of asset s, at least part ly, by com bining risky
asset s in a port folio. To give an exam ple, consider a hypot het ical port folio wit h say, t en st ocks.
Each of t hese st ocks has a risk profile, a sim ple and widely used indicat or of which is t he
st andard deviat ion of it s ret urns. I nt uit ively, t he overall risk of t he port folio sim ply ought t o be
an aggregat ion of individual port folio risks, in ot her words, port folio risk sim ply ought t o be a
weight ed average of individual st ock risks. Our assert ion here is t hat t he risk of t he port folio is
usually m uch lower. Why? As we shall see in t he discussion here, t his is largely due t o t he
int errelat ionships t hat exist bet ween st ock price m ovem ent s. These so- called covariances
bet ween st ocks, could be posit ive, negat ive, or zero. An exam ple of t wo I T services st ocks,
react ing favourably t o a depreciat ion in t he dom est ic currency—as t heir export realizat ions
would rise in t he dom est ic currency—is one of posit ive covariance. I f however, we com pare
one I T services com pany wit h anot her from t he m et als space, say st eel, which has high foreign
debt , t hen a drop in t he share price of t he st eel com pany ( as t he falling rupee would increase
t he debt - service paym ent s of t he st eel firm ) and rise in share price of t he I T services com pany,
would provide an exam ple of negat ive covariance. I t follows t hat we would expect t o have zero
covariance bet ween st ocks whose m ovem ent s are not relat ed.
56
Let us now exam ine why and how port folio risk is different from t he weight ed risk of const it uent
asset s. Assum e t hat we have t he following t wo st ocks, as given in t able 6.1 here, and t hen
assum e furt her t hat t he ret urns of t he t wo hypot het ical st ocks behave in opposit e direct ions.
When A gives high ret urns, B does not and vice versa. We know t his is quit e possible, as in our
earlier com parison of a soft ware com pany wit h a com m odit y play. For a port folio wit h 60%
invest ed in A, t he port folio st andard deviat ion becom es zero. Alt hough t he t wo st ocks involved
were risky ( indicat ed by t he st andard deviat ions) , a port folio of t he t wo st ocks wit h a cert ain
weight m ay becom e t ot ally risk- free. The t able below shows a port folio of t he t wo st ocks wit h
weight of St ock A ( W) being 0.6 and weight of st ock B being ( 1- 0.6) or 0.4. I t can be seen t hat
irrespect ive of t he m arket condit ion, t he port folio gives a ret urn of 10% .
Ta ble 6 .1 : Por t folio of Tw o Asse t s
M a r k e t Con dit ion
Re t u r n on A
Re t u r n on B
Re t u r n on por t folio
( W = 0 .6 )
Good
16%
1%
10%
Average
10%
10%
10%
Poor
4%
19%
10%
St andard deviat ion
5%
7%
0%
Correlat ion
- 1.0
Why does t he port folio st andard deviat ion go t o zero? I nt uit ively, t he negat ive deviat ion in t he
ret urns of one st ock is get t ing offset by t he posit ive deviat ion in t he ot her st ock. Let us
exam ine t his in a som ewhat m ore form al and general cont ext .
Let us assum e t hat you can form port folios wit h t wo st ocks, A & B, having t he following
charact erist ics:
Ret urn on St ock A = RA
Mean ret urn on st ock A = RA
St d. deviat ion of t he ret urn of st ock A = σ A
Ret urn on St ock B = RB
Mean ret urn on st ock B = RB
St d. deviat ion of t he ret urn of st ock B = σ B
The t ot al available am ount t hat can be invest ed, is Re. 1. The proport ional invest m ent s in each
of t he st ocks are as below,
57
St ock A = W
St ock B = ( 1 - W)
where W is bet ween 0 and 1.
Given t his inform at ion, we can show t hat
σ 2p = W 2 σ 2A + (1 – W ) 2 σ 2B + 2W (1 – W ) Cov ( A, B)
That is, we would show t hat t he variance of our port folio, as denot ed by t he left hand side of
t his equat ion, is dependent on t he variance of st ock A, t hat of st ock B, and a t hird t erm , called
Cov( A,B) . I t is t his t hird t erm t hat denot es t he int errelat ionship bet ween t he t wo st ocks. As
discussed before, such a relat ion could be posit ive, negat ive or zero. I n cases wit h negat ive
covariance, port folio variance would act ually be lower t han t he ( weight ed) sum of st ock
variances! I n ot her words, since variance ( or st andard deviat ion) is t he prim ary m et ric of risk
m easurem ent , t hen we can say t hat t he risk of t he port folio would be lower t han individual
st ocks considered separat ely.
So here is how we go about deriving t his expression:
Wit h t hese invest m ent s t he port folio ret urn is,
RP = W RA + (1 – W ) RB
( 1)
RP = W RA + (1 – W ) RB
( 2)
w h er e, RP = Ret u r n on t h e por t f ol io an d RP
= Mean r et u r n on t h e por t f ol io. Let ,
σ P = St d.deviat ion of port folio ret urns, t hen t he variance of t he port folio ret urns can be
derived as,
σ2P =
∑ (R
1
n
– RP )
2
p
( 3)
wit h a st raight forward rearrangem ent and subst it ut ion for RP = and RP = from t he expressions
( 1) and ( 2) , t he port folio variance is,
2
= W
1
n
∑ (R
A
– RA
)2
+ (1 – W )
2
1
n
∑ (R
B
– RB
)2
We know t hat ,
1
n
∑ (R
A
– RA
)2
= σ2A ,
1
n
∑ (R
B
– RB
)2
= σ 2B
58
+ 2W (1 – W )
1
n
∑ (R
A
)(
– RA RB – RB
)
1
n
∑ (R
A
)(
)
– RA RB – RB = Cov ( A, B)
The covariance can be regarded as a m easure of how m uch t wo variables change t oget her
from t heir m eans. I t can also be expressed as, Cov ( A, B) = ρ A, B σ A σ B , where ρ A, B
is t he
correlat ion bet ween ret urns of st ocks A and B. Therefore, if t he correlat ion is posit ive and t he
st ocks have high st andard deviat ions, t hen t he covariance would be posit ive and large. I t
would be negat ive if t he correlat ion is negat ive.
Subst it ut ing t hese, t he port folio variance can be expressed as,
σ2P = W 2 σ2A + (1 – W ) σ2B + 2W (1 – W ) Cov ( A, B) .
2
( 4)
Equat ion ( 4) suggest s t hat t he t ot al port folio variance com prises t he weight ed sum of variances
and weight ed sum of t he covariances t oo. Let us exam ine t he insight s from expression ( 4) for
t he variance of com binat ions of st ocks ( or any ot her asset ) wit h varying level of correlat ions.
Given t he nat ure of t he ret urn relat ionship bet ween t he A and B ( in Table 6.1) , it is easy t o see
t hat t heir correlat ion is - 1.0. For t he port folio of st ock A and B, t he risk becom es zero, when
weight of st ock A ( W) = 0.6.
Ta ble 6 .2 : D e com posit ion of t h e Tot a l Por t folio Va r ia n ce
Elem ent of variance
Proport ion
Sigm a
Var/ Covar
Var – A
0.6
0.05
0.000864
Var – B
0.4
0.07
0.000864
Covar
- 0.001728
Alt hough t he t wo st ocks involved were risky ( indicat ed by t he st andard deviat ions) , one of
t heir possible com binat ions becom es t ot ally risk- free. The variances of t he individual st ocks
are offset by t heir covariance in t he port folio ( as shown in Table 6.2) .
When t he correlat ion bet ween t he t wo st ocks is 1.0, t he st andard deviat ion of t he port folio
shall be j ust a weight ed average of t he st andard deviat ion of t he t wo st ocks involved. This
im plies t hat a port folio wit h t wo perfect ly posit ively correlat ed st ocks cannot reduce risk. The
m inim um port folio st andard deviat ion would always correspond t o t hat of t he st ock wit h t he
least st andard deviat ion.
The st andard deviat ion of t he port folio wit h t wo uncorrelat ed ( correlat ion = 0) st ocks would
always be lower t han t he case wit h correlat ion 1.0. I t is possible t o choose a value for W in
such a way, so t hat t he port folio risk can be brought down below t hat of t he least less risky
st ock involved in t he port folio.
59
However, in t he real world t he correlat ions alm ost always lie bet ween 0 and 1. I t is very
st raight forward t o underst and t hat t he variance of port folios wit h st ocks having correlat ion in
t he 0 t o 1 range would cert ainly be lower t han t hose wit h st ocks having correlat ion 1. At t he
sam e t im e, t he variance of t hese port folios shall be higher t han t hose wit h uncorrelat ed st ocks.
Let us exam ine if we can reduce t he port folio variance by com bining st ocks wit h correlat ion in
t he range of 0 t o 1. Consider t he t wo st ocks, ACC and Dr. Reddy’s Laborat ories ( DRL) wit h
correlat ion around 0.21. As given in t he following t able, for a unique com binat ion, t he t ot al
variance ( st andard deviat ion) of t he port folio is less t han t hat of ACC, t he least risky st ock.
The det ails of t he risk of t his port folio are provided in t he following t able.
Ta ble 6 .3 : Re t u r n a n d st a n da r d de via t ion of ACC, D RL a n d Por t folio
Year
ACC
DRL
Com binat ions
W= 0.25
W= 0.50
W= 0.75
2001
1.24
1.5
1.44
1.37
1.31
2002
0.98
0.84
0.88
0.91
0.95
2003
1.41
1.42
1.42
1.42
1.41
2004
1.37
0.49
0.71
0.93
1.15
2005
1.61
1.2
1.30
1.41
1.51
St d. deviat ion
0.23
0.42
0.33
0.26
0.22
1.322
1.09
1.148
1.206
1.264
Average Ret urn
Not e: W represent s t he invest m ent in ACC
This suggest s t hat for cert ain values of W, t he variance of t he port folio can be brought down by
com bining securit ies wit h correlat ion t he range of 0 t o 1.
A com parison of t he behaviour ( ret urn-variance) of port folios m ade wit h st ocks of varying
correlat ion is given in t he following figure:
60
Figu r e 6 .1 : Por t folio Risk a n d Re t u r n for Asse t s w it h D iffe r e n t Cor r e la t ion s
Not e: t he port folio sigm a is t he st andard deviat ion. The port folios are creat ed by using act ual
ret urn dat a and assum ed correlat ions, except 0.4, which is t he act ual correlat ion bet ween t he
t wo st ocks.
Wit h t hese insight s we can now exam ine t he behaviour of port folios wit h a larger num ber of
asset s.
6 .2 .1
Por t folio va r ia n ce - Ge n e r a l ca se
Let us assum e t hat t here are N st ocks available for generat ing port folios. Then, t he port folio
variance ( given by equat ion 4) can be expressed as,
σ2P =
∑W
2
i
σ2i +
∑∑W W σ
i
i
( 5)
ij
where W i is t he proport ional invest m ent in each of t he asset s and σij is t he covariance bet ween
t he pair of asset s i and j . The double sum m at ion sign in t he second part indicat es t hat t he
covariance would appear for all possible com binat ions of i and j , except wit h t hem selves. For
i n st an ce,
if
t h er e
ar e
3
st o c k s ,
t h er e
w ould
be
six
cov ar ian ce
t erm s
( 1- 2, 1- 3, 2- 1, 2- 3, 3- 1, 3- 2) .
To exam ine t he charact erist ics of including a large num ber of st ocks in t he port folio, assum e
t hat
Wi =
1
N
σ2P = ∑
1
N2
σ2i + ∑ ∑
1
N2
σ ij
61
=
1
1 2
N –1
1
∑
σi +
∑∑
σ ij
N
N
N
N( N – 1)
=
N–1
1 2
σi +
σ ij
N
N
=
1
1

( Avg. Variance) + 1 –  ( Avg. Covariance )
N
N

we creat e an equally weight ed port folio ( equal invest m ent in t he st ocks) of N asset s. Then,
The expression j ust above gives t he following insight s:
1.
As N becom es a large num ber, t he port folio variance would be dom inat ed by t he
covariances rat her t han variances. The variance of t he individual st ocks does not m at t er
m uch for t he t ot al port folio variance. This is one of t he m ost powerful argum ent s for
port folio diversificat ion.
2.
Even by including a large num ber of asset s, t he port folio variance cannot be reduced
t o zero ( except when t hey are perfect ly negat ively correlat ed) . The part of t he risk
t hat cannot be elim inat ed by diversifying t hrough invest m ent s across asset s is called
t he m arket risk ( also called t he syst em at ic risk or non- diversifiable risk) . This is
som et hing all of us com m only experience while invest ing in t he m arket . One can
reduce t he risk of exposure t o say HCL Technologies in t he I T indust ry, by including
ot her st ocks from t he I T indust ry, like I nfosys t echnologies, Tech Mahindra and so on.
I f you consider t he exposure t o I T indust ry alone is t roubling, you can also spread your
invest m ent t o ot her indust ries like Banking, Telecom , Consum er product s and so on.
Going furt her, you can even invest across different m arket s, if you do not like t o be
exposed t o anyone econom y alone. But even aft er int ernat ional diversificat ion a cert ain
am ount of risk would rem ain. ( int ernat ional m arket s in t he globalize world t end t o
m ove t oget her) . This is t he m arket risk or syst em at ic risk or non- diversifiable risk.
3.
Given t he above, it appears t hat t he relevant risk of an asset is what it cont ribut es t o
a widely- held port folio, in ot her words, it s covariance risk.
6 .3
Equ ilibr iu m M ode ls: Th e Ca pit a l Asse t Pr icin g M ode l
The m ost im port ant insight from t he analysis of port folio risk is t hat a part of t he port folio
variance can be diversified away ( unsyst em at ic or diversifiable risk) by select ing securit ies
wit h less t han perfect correlat ion. This along wit h t he ot her insight s obt ained from t he analysis
would help us t o underst and t he pricing of risky asset s in t he equilibrium for any asset in t he
capit al m arket , under cert ain assum pt ions.
62
These addit ional assum pt ions required are as follows:
•
All in vest or s ar e m ean - v ar iance opt im izers. Th is im plies t h at in vest or s ar e
concerned only about t he m ean and variance of asset ret urns. I nvest ors would
eit her prefer port folios which offer higher ret urn for t he sam e level of risk or
prefer port folios which offer m inim um risk for a given level of ret urn ( t he indirect
assum pt ion of m ean-variance invest ors is t hat all ot her charact erist ics of t he asset s
are capt ured by t he m ean and variance) .
•
I nvest ors have hom ogenous inform at ion about different asset s. The well-organized
f i n an cial m ar k et s h av e r em ar k ab l e ab i l i t y t o d i g est i n f or m at i on al m ost
inst ant aneously ( largely reflect ed as t he price variat ion in response t o sensit ive
inform at ion) .
•
Transact ion cost s are absent in t he m arket and securit ies can be bought and sold
wit hout significant price im pact .
•
I nvest ors have t he sam e invest m ent horizon.
Given t hese assum pt ions, it is not im possible t o see t hat subst ant ive arbit rage opport unit ies
would not exist in t he m arket . For inst ance, if t here is a port folio which gives a higher ret urn
for sam e level of risk, invest ors would prefer t hat port folio com pared t o t he exist ing one.
I n light of t he behaviour of port folio risk and t he above assum pt ions, let us t ry t o visualize
what would be t he relat ionship bet ween risk and ret urn of asset s in t he equilibrium .
6 .3 .1
M e a n - Va r ia n ce I n ve st or s a n d M a r k e t Be h a viou r
We can use a so- called m ean-variance space t o exam ine t he aggregat e behaviour of t he
m arket (as all invest ors are m ean-variance opt im izers, t hese are t he only variables t hat m at t er).
Evident ly, all t he asset s in t he m arket can be m apped on t o a ret urn- st andard deviat ion space
as follows.
Figu r e 6 .2 : Re t u r n a n d Risk of Som e of t h e N ift y st ock s
Source: NSE
63
All t hese st ocks ( in figure 6.2) have correlat ions bet ween 0 and 1. Therefore, t heir com binat ion
could t heoret ically be charact erized as given in figure 6.3.
Figu r e 6 .3 : Fe a sible Se t of Por t folios
All t he feasible port folio com binat ions can be represent ed by t he space enclosed by t he curved
line and t he st raight - line. The curved line represent s com binat ions of st ocks or port folios
where correlat ions are less t han 1, wher eas port folios along t he st raight - lin e represent
com binat ions of st ocks or port folios wit h t he m axim um correlat ion (+ 1.0) ( no port folios would
lie t o t he right of t he st raight - line) .
Obviously, a m ean-variance invest or would prefer port folio A t o B, given t hat it has lower risk
for t he sam e level of ret urn offered by B. Sim ilarly, port folio A would be preferred t o port folio
C, given t hat it offers higher ret urn for t he sam e level of risk. D is t he m inim um variance
port folio am ong t he ent ire feasible set . A close exam inat ion of t he feasible set of port folios
reveals t hat port folios t hat lie along D-E represent t he best available com binat ion of port folios.
I nv est ors w it h var iou s r isk t oleran ce lev els can ch oose on e of t h ese por t f olios. Th ese
port folios offer t he m axim um ret urn for any given level of risk. Therefore, t hese are called t he
efficient port folios ( and t he set of all such port folios, t he efficient front ier) , as represent ed in
Figure 6.4.
64
Figu r e 6 .4 : Efficie n t Fr on t ie r
Ordinarily, t he invest or also has t he opport unit y t o invest in a risk- free asset . Pract ically, t his
could be a bank deposit , t reasury bills, Governm ent securit ies or Governm ent guarant eed
bonds. Wit h t he availabilit y of a risk- free securit y, t he choice facing t he m ean-variance invest or
can be convenient ly charact erised as follows:
Figu r e 6 .5 : Efficie n t Por t folio in t h e Pr e se n ce of a Risk - Fr e e Asse t
As given in figure 6.5, wit h t he presence of t he risk-free asset , t hat has no correlat ion wit h any
ot her risky asset , t he invest or also get s an added opport unit y t o com bine port folios along t he
efficient front ier wit h t he risk- free asset . This would im ply t hat t he invest or could part ly put
t he m oney in t he risky securit y and t he rem aining in any of t he risky port folios.
Apparent ly, t he port folio choice of t he m ean-variance invest or is no m ore t he securit ies along
t he efficient front ier ( D- E) . I f an invest or prefers less risk, t hen rat her t han choosing D by
going down t he efficient front ier, he can choose G, a com binat ion of risky port folio M and t he
risk- free asset . G gives a higher ret urn for t he level of risk of D. I n fact , t he sam e applies for
65
all t he port folios along t he efficient front ier t hat lie bet ween D and M ( t hey offer only lower
ret urns com pared t o t hose which lie along t he st raight - line connect ing t he risk- free asset and
risky port folio M) .
This gives t he powerful insight t hat , wit h t he presence of t he risk- free securit y, t he m ost
preferred port folio along t he efficient front ier would be M ( port folios t o t he right of M along t he
st raight line indicat es borrowing at t he risk- free rat e and invest ing in M) .
An invest or who does not want t o t ake t he risk of M, would be bet t er off by com bining wit h t he
risk- free securit y rat her t han invest ing in risky port folios wit h lower st andard deviat ion ( t hat
lie along t he M- D) .
I dent ificat ion of M as t he opt im al port folio, com bined wit h t he assum pt ions ( 1) t hat all invest ors
have t he sam e inform at ion about m ean and variance of securit ies and ( 2) t hey all have t he
sam e invest m ent horizon, suggest t hat all t he invest ors would hold only t he following port folios
depending on t he risk appet it e.
1.
The port folio purely of risky asset s, which would be M.
2.
The port folio of risky asset s and risk- free asset , which would be a com binat ion of
M and RF.
All ot her port folios are inferior t o t hese choices, for any level of risk preferred by t he invest ors.
Let us exam ine what would be t he nat ure of t he port folio M. I f all invest ors are m ean-variance
opt im izers and have t he sam e inform at ion, t heir port folios would invariably be t he sam e.
Then, all of t hem would ident ify t he sam e port folio as M. Obviously, it should be a com binat ion
of all t he risky st ocks ( asset s) available in t he m arket ( som ebody should be willing t o hold all
t he asset s available on t he m arket ) . This port folio is referred t o as t he m arket port folio.
Pract ically, t he m a r k e t por t folio can be regarded as one represent ed by a very liquid index
like t he NI FTY. The line connect ing t he m arket port folio t o t he risk- free asset is called t he
Ca pit a l M ar k e t Lin e ( CM L) . All point s along t he CML have superior risk- ret urn profiles t o any
port folio on t he efficient front ier.
Wit h t he underst anding about t he aggregat e behaviour of t he invest ors in t he securit ies m arket ,
we can est im at e t he risk prem ium t hat is required for any asset . Underst anding t he risk
prem ium dram at ically solves t he asset pricing problem t hrough t he est im at ion of t he discount ing
fact or t o be applied t o t he expect ed cash flows from t he asset . Wit h t he expect ed cash flows
and t he discount ing rat e, t he price of any risky asset can be direct ly est im at ed.
Let RM be t he required rat e of ret urn on t he m arket ( m arket port folio, M) , RF be t he required
rat e of ret urn on t he risk free asset and σM be t he st andard deviat ion of t he m arket port folio..
Fr om Figur e 6 .5 , t h e rat e of r isk prem ium requ ir ed f or un it varian ce of t he m ar ket is
est im at ed as,
66
RM – RF
( 6)
σ 2M
I n a very liquid m arket ( where asset s can be bought and sold wit hout m uch hassles) , invest or
has t he opport unit y t o hold st ocks as a port folio rat her t han in isolat ion. I f invest ors have t he
opport unit y t o hold a well- diversified port folio, t he only risk t hat m at t ers in t he individual
securit y is t he increm ent al risk t hat it cont ribut es t o a well- diversified port folio. Therefore, t he
risk relevant t o t he prospect ive invest or (or firm ) is t he covariance risk. Then, one can com put e
t he risk prem ium required on t he securit y as follows
Risk prem ium on st ock =
RM – RF
σ 2M
× Cov ( i , M )
where, Cov( i,M) , is t he covariance bet ween t he ret urns of st ock i and t he m arket ret urns
Cov ( i , M )
( ret urns on port folio M) . The quant it y represent ed by
is popularly called t he bet a
σ2M
( β ) . This m easures t he sensit ivit y of t he securit y com pared t o t he m arket . A bet a of 2.0
indicat es t hat if t he m arket m oves down ( up) by 1% , t he securit y is expect ed t o m ove down
( up) 2% . Therefore, we would expect t wice t he risk prem ium as com pared t o t he m arket . This
im plies t hat t he m inim um expect ed ret urn on t his st ock is 2 x ( Rm – Rf ) . I n general, t he risk
prem ium on a securit y is β t im es ( Rm – Rf ) . Obviously, t he m arket port folio will have a bet a of
1.0 ( covariance of a st ock wit h it self is variance) .
Now by com bining t he risk- free rat e and t he risk prem ium as est im at ed above, t he t ot al
required rat e of ret urn on any risky asset is,
Ri = RF + ( RM – RF ) β i
( 7)
This approach t o t he est im at ion of t he required ret urn of asset s ( cost of equit y, in case of
equit y) is called t he Capit al Asset Pricing Model ( CAPM, pioneered by William Sharpe) .
I f CAPM holds in t he m arket , all t he st ocks would be priced according t o t heir bet a. This would
im ply t hat t he st ock prices are est im at ed by t he m arket by discount ing t he expect ed cash
flows by applying a discount ing rat e as est im at ed based on equat ion ( 7) .
Hence, all t he st ocks can be ident ified in t he m ean ret urn- bet a space, as shown below and
relat ionship bet ween bet a and ret urn can be est im at ed. The line present ed in t he following
figure is popularly called the Se cu r it ie s M a r k e t Lin e ( SM L) .
67
Figu r e 6 .6 : Se cu r it y M a r k e t Lin e
Not e: t his figure is not based on any real dat a.
Prices ( ret urns) which are not according t o CAPM shall be quickly ident ified by t he m arket and
brought back t o t he equilibrium . For inst ance, st ocks A and B given in t he following figure
( 6.7) shall be brought back t o t he equilibrium t hrough m arket dynam ics.
This works as follows. St ock A, current ly requires a lower risk prem ium ( required rat e of
ret urn) t han a specified by CAPM ( t he price is higher) . Sensing t his price of A as relat ively
expensive, t he m ean-variance invest ors would sell t his st ock. The decreased dem and for t he
st ock would push it s price downwards and rest ore t he ret urn back t o as specified by CAPM ( will
be on t he line) . The reverse happens in case of st ock B, wit h increased buying pressure.
Figu r e 6 .7 : Ar bit r a ge s a r ou n d SM L
6 .3 .2
Est im a t ion of Be t a
The bet a of a st ock can be est im at ed wit h t he form ula discussed above. Pract ically, t he bet a
68
of any st ock can be convenient ly est im at ed as a regression bet ween t he ret urn on st ock and
t hat of t he m arket , represent ed by a st ock index like NI FTY ( t he dependent variable is t he
st ock ret urn and t he independent variables is t he m arket ret urn) .
Accordingly, t he regression equat ion is,
Ri = α i + β i RM + e i ,
( 8)
where t he regression coefficient βi represent s t he slope of t he linear relat ionship bet ween t he
st ock ret urn and t he m arket ret urn and α i denot e t he risk- free rat e of ret urn. The SLOPE
funct ion in MS- Excel is a convenient way t o calculat e t his coefficient from t he m odel.
The bet a of an exist ing firm t raded in t he m arket can be derived direct ly from t he m arket
prices. However, on m any occasions, we m ight be int erest ed t o est im at e t he required rat e of
ret urn on an asset which is not t raded in t he m arket . For inst ances like, pricing of an I PO,
t akeover of anot her firm , valuat ion of cert ain specific asset s et c.. I n t hese inst ances, t he
required rat e of ret urn can be est im at ed by obt aining t he bet a est im at es from sim ilar firm s in
t he sam e indust ry.
The bet a can be relat ed t o t he nat ure of t he asset s held by a firm . I f t he firm holds m ore risky
asset s t he bet a shall also be higher. Now, it is not difficult t o see why invest ors like vent ure
capit alist s dem and higher ret urn for invest ing in st art - up firm s. A firm ’s bet a is t he weight ed
average of t he bet a of it s asset s ( j ust as t he bet a of a port folio is t he weight ed average of t he
bet a of it s const it uent asset s) .
6 .4
M u lt ifa ct or M ode ls: Th e Ar bit r a ge Pr icin g Th e or y ( APT)
The CAPM is founded on t he following t wo assum pt ions ( 1) in t he equilibrium every m ean
variance invest or holds t he sam e m arket port folio and ( 2) t he only risk t he invest or faces is
t he bet a. Evident ly, t hese are st rong assum pt ions about t he m arket st ruct ure and behaviour
of invest ors. A m ore general fram ework about asset pricing should allow for relaxat ion of
t hese st rong and som ewhat count erfact ual assum pt ions. A num ber of alt ernat ive equilibrium
asset pricing m odels, including t he general arbit rage pricing t heory ( APT) , at t em pt t o relax
t hese assum pt ions t o provide a bet t er underst anding about asset pricing.
The arbit rage pricing t heory assum es t hat t he invest or port folio is exposed t o a num ber of
syst em at ic risk fact ors. Arbit rage in t he m arket ensures t hat port folios wit h equal sensit ivit y t o
a fundam ent al risk fact or are equally priced. I t furt her assum es t hat t he risk fact ors which are
associat ed wit h any asset can be expressed as a linear com binat ion of t he fundam ent al risk
f act ors an d t h e f act or sen sit ivit ies ( bet as) . Ar bit rage is t hen assum ed t o elim in at e all
opport unit ies t o earn riskless profit by sim ult aneously selling and buying equivalent port folios
( in t erm s of risk) which are overpriced and underpriced.
69
Under t hese assum pt ions, all invest ors need not have t he sam e m arket port folio as under
CAPM. Hence, APT relaxes t he assum pt ion t hat all invest ors in t he m arket hold t he sam e
port folio. Again, as com pared t o CAPM, which has only one risk dim ension, under t he APT
charact erizat ion of t he asset s, t here will be as m any dim ensions as t here are fundam ent al
risks, which cannot be diversified by t he invest ors. The fundam ent al fact ors involved could
for inst ance be t he growt h rat e of t he econom y ( GDP growt h rat e) , inflat ion, int erest rat es
an d an y ot h er m acr oecon om ic f act or w h ich w ou l d ex pose t h e in v est or ’s p or t f olio t o
syst em at ic risk.
I n t he lines of t he assum pt ions of arbit rage pricing t heory, a num ber of m ult ifact or asset
pricing m odels have been proposed. One such em pirically successful m odel is t he so- called
Fam a- French t hree- fact or m odel. The Fam a- French m odel has t wo m ore risk fact ors, viz.,
size, and book- t o- m arket rat io as t he addit ional risk fact ors along wit h t he m arket risk as
specified by CAPM. The size risk fact or is t he difference bet ween t he expect ed ret urns on a
port folio of sm all st ocks and t hat of large st ocks. And t he book- t o- m arket rat io is t he difference
in t he expect ed ret urn of t he port folio of high book- t o m arket - rat io st ocks and t hat of low
book- t o m arket - rat io st ocks.
Theoret ical and em pirical evidence suggest s t hat in t he real m arket , expect ed ret urns are
probably det erm ined by a m ult ifact or m odel. Against t his evidence, t he m ost popular and
sim ple equilibrium m odel, CAPM, could be regarded as a special case where all invest ors hold
t he sam e port folio and t heir only risk exposure is t he m arket risk.
70
CH APTER 7 : Va lua t ion of D e r iva t ive s
7 .1
I n t r odu ct ion
Derivat ives are a wide group of financial securit ies defined on t he basis of ot her financial
securit ies, i.e., t he price of a derivat ive is dependent on t he price of anot her securit y, called
t he underlying. These underlying securit ies are usually shares or bonds, alt hough t hey can be
various ot her financial product s, even ot her derivat ives. As a quick exam ple, let ’s consider t he
derivat ive called a ‘call opt ion’, defined on a com m on share. The buyer of such a product get s
t he right t o buy t he com m on share by a fut ure dat e. But she m ight not want t o do so—t here’s
no obligat ion t o buy it , j ust t he choice, t he opt ion. Let ’s now flesh out som e of t he det ails. The
price at which she can buy t he underlying is called t he st rike price, and t he dat e aft er which
t his opt ion expires is called t he st rike dat e. I n ot her words, t he buyer of a call opt ion has t he
right , but not t he obligat ion t o t ake a long posit ion in t he underlying at t he st rike price on or
before t he st rike dat e. Call opt ions are furt her classified as being European, if t his right can
only be exercised on t he st rike dat e and Am erican, if it can be exercised any t im e up and unt il
t he st rike dat e.
Derivat ives are am ongst t he widely t raded financial securit ies in t he world. Turnover in t he
fut ures and opt ions m arket s are usually m any t im es t he cash ( underlying) m arket s. Our
t reat m ent of derivat ives in t his m odule is som ewhat lim it ed: we provide a short int roduct ion
about of t he m aj or t ypes of derivat ives t raded in t he m arket s and t heir pricing.
7 .2
For w a r ds a n d Fu t u r e s
Forward cont ract s are agreem ent s t o exchange an underlying securit y at an agreed rat e on a
specified fut ure dat e ( called expiry dat e) . The agreed rat e is called forward rat e and t he
difference bet ween t he spot rat e, t he rat e prevailing t oday, and t he forward rat e is called t he
forward m argin. The part y t hat agrees t o buy t he asset on a fut ure dat e is referred t o as a long
invest or and is said t o have a long posit ion. Sim ilarly, t he part y t hat agrees t o sell t he asset in
a fut ure dat e is referred t o as a short invest or and is said t o have a short posit ion.
Forward cont ract s are bilat eral ( privat ely negot iat ed bet ween t wo part ies) , t raded out side a
regulat ed st ock exchange ( t raded in t he OTC or ‘Over t he Count er ’ m arket ) and suffer from
count er- part y risks and liquidit y risks. Here count er- part y risk refers t o t he default risk t hat
arises when one part y in t he cont ract default s on fulfilling it s obligat ions t hereby causing loss
t o t he ot her part y.
Fut ures cont ract s are also agreem ent s t o buy or sell an asset for a cert ain price at a fut ure
t im e. Unlike forward cont ract s, which are t raded in t he over-t he-count er m arket wit h no st andard
cont ract size or delivery arrangem ent s, fut ures cont ract s are st andardized cont ract s and are
71
t raded on recognized and regulat ed st ock exchanges. They are st andardized in t erm s of cont ract
sizes, t rading param et ers and set t lem ent procedures, and t he cont ract or lot size ( no. of
shares/ unit s per cont ract ) is fixed.
Since fut ures cont ract s are t raded t hrough exchanges, t he set t lem ent of t he cont ract is
guarant eed by t he exchange or a clearing corporat ion ( t hrough t he process of novat ion) and
hence t here is no count er- part y risk. Exchanges guarant ee execut ion by holding a caut ion
am ount as securit y from bot h t he part ies ( buyers and sellers) . This am ount is called as t he
m argin m oney, and is adj ust ed daily based on price m ovem ent s of t he underlying t ill t he
cont ract expires.
Com pared t o forward cont ract s, fut ures also provide t he flexibilit y of closing out t he cont ract
prior t o t he m at urit y by squaring off t he t ransact ion in t he m arket . Occasionally t he fact
forward cont ract s are bilat eral com es in handy—t wo part ies could suit a cont ract according t o
t heir needs; such a fut ures m ay not be t raded in t he m arket . Prim ary exam ples are long- t erm
cont ract s—m ost fut ures cont ract s have short m at urit ies of less t han a few m ont hs.
The t able here draws a com parison bet ween a forward and a fut ures cont ract .
Ta ble 7 .1 : Com pa r ison of For w a r d a n d Fu t u r e s Con t r a ct s
Nat ure of Cont ract
For w a r d Con t r a ct
Fu t u r e s Con t r a ct
Non-st andardized/
St andardized cont ract
Cust om ized cont ract
Trading
Privat e cont ract bet ween
Traded on an exchange
part ies – I nform al,
Over- t he- Count er m arket
Set t lem ent
Set by t he part ies.
Final Set t lem ent dat e is
Pre- specified in t he
fixed by t he exchange. I n
cont ract .
addit ion, t here is a provision
of daily set t lem ent , known as
daily m ark t o m arket
set t lem ent .
Risk
Count erpart y risk exist s,
Exchange provides t he
no independent guarant ee.
guarant ee of set t lem ent and
hence no count er part y risk.
72
7 .3
Ca ll a n d Pu t Opt ion s
Like forwards and fut ures, opt ions are derivat ive inst rum ent s t hat provide t he opport unit y t o
buy or sell an underlying asset on a fut ure dat e. As explained in t he int roduct ion, an opt ion
cont ract is a cont ract writ t en by a seller t hat conveys t he buyers a right , but not an obligat ion
t o eit her sell ( put opt ion) or buy ( call opt ion) a part icular asset at a specified price in t he
fut ure. I n case of call opt ions, t he opt ion buyer has a right t o buy and in case of put opt ions,
t he opt ion buyer has a right t o sell t he securit y at t he agreed upon price ( called st rike rat e or
exercise price) . I n ret urn for grant ing t he opt ion, t he part y ( seller) grant ing t he opt ion collect s
a paym ent from t he ot her part y. This paym ent collect ed is called t he “ prem ium ” or price of
t he opt ion.
Opt ions are like insurance cont ract s. Unlike fut ures, where t he part ies are denied of any favorable
m ovem ent in t he m arket , in case of opt ions, t he buyers are prot ect ed from downside risks and
in t he sam e t im e, are able t o reap t he benefit s from any favorable m ovem ent in t he exchange
rat e. The buyer of t he opt ion has a right but no obligat ion t o enforce t he execut ion of t he
opt ion cont ract and hence, t he m axim um loss t hat t he opt ion buyer can suffer is lim it ed t o t he
prem ium am ount paid t o ent er int o t he cont ract . The buyer would exercise t he opt ion only
when she can m ake som e profit from t he exercise, ot herwise, t he opt ion would not be exercised,
and be allowed t o lapse. Recall t hat in case of Am erican opt ions, t he right can be exercised on
any day on or before t he expiry dat e but in case of a European opt ion, t he right can be
exercised only on t he expiry dat e.
Opt ions can be used for hedging as well as for speculat ion purposes. An opt ion is used as a
hedging t ool if t he invest or already has ( or is expect ed t o have) an open posit ion in t he spot
m arket . For exam ple, in case of currency opt ions, im port ers buy call opt ions t o hedge against
fut ure depreciat ion of t he local currency ( which would m ake t heir im port s m ore expensive)
and export ers could buy put opt ions t o hedge against currency appreciat ion. There are ot her
m et hds of hedging t oo—using forwards, fut ures, or com binat ions of all t hree—and t he choice
of hedging is det erm ined by t he cost s involved.
7 .4
For w a r d a n d Fu t u r e s Pr icin g
Forwards/ fut ures cont ract are priced using t he cost of carry m odel. The cost of carry m odel
calculat es t he fair value of fut ures cont ract based on t he current spot price of t he underlying
asset . The form ula used for pricing fut ures is given below:
F = Se rT Where :
F = Fut ures Price
S = Spot price of t he underlying asset
73
R = Cost of financing ( using a cont inuously com pounded int erest rat e)
T = Tim e t ill expirat ion in years
E = 2.71828 ( The base of nat ural logarit hm s)
Exam ple: Securit y of ABB Lt d t rades in t he spot m arket at Rs. 850. Money can be invest ed at
11% per annum . The fair value of a one- m ont h fut ures cont ract on ABB is calculat ed as
follows:
F = Se rT = 850 * e
0. 1 1
1
12
= 857 . 80
The presence of arbit rageurs would force t he price t o equal t he fair value of t he asset . I f t he
fut ures price is less t han t he fair value, one can profit by holding a long posit ion in t he fut ures
and a short posit ion in t he underlying. Alt ernat ively, if t he fut ures price is m ore t han t he fair
value, t here is a scope t o m ake a profit by holding a short posit ion in t he fut ures and a long
posit ion in t he underlying. The increase in dem and/ supply of t he fut ures ( and spot ) cont ract s
will force t he fut ures price t o equal t he fair value of t he asset .
7 .4 .1
Cost - of- ca r r y a n d con ve n ie n ce yie ld
The cost of carry is t he cost of holding a posit ion. I t is usually represent ed as a percent age of
t he spot price. Generally, for m ost invest m ent , we consider t he risk- free int erest rat e as t he
cost of carry. I n case of com m odit ies cont ract s, cost of carry also includes st orage cost s ( also
expressed as a percent age of t he spot price) of t he underlying asset unt il m at urit y.
Fut ures prices being lower t han spot price ( backwardat ion) is also explained by t he concept of
convenience yield. I t is t he opposit e of carrying charges and refers t o t he benefit accruing t o
t he holder of t he asset . For exam ple, one of t he benefit s t o t he invent ory holder is t he t im ely
availabilit y of t he underlying asset during a period when t he underlying asset is ot herwise
facing a st ringent supply sit uat ion in t he m arket . Convenience yield has a negat ive relat ionship
wit h invent ory st orage levels ( and st orage cost ) . High st orage cost / high invent ory levels lead
t o negat ive convenience yield and vice versa.
The cost of carry m odel expresses t he forward ( fut ure) price as a funct ion of t he spot price and
t he cost of carry and convenience yield.
F = [ S + PV ( st orage cost ) ] * e ( r
– c)t
Where F is t he forward price, S is t he spot price, r is t he risk- free int erest rat e, c is t he
convenience yield and t is t he t im e t o delivery of t he forward cont ract ( expressed as a fract ion
of 1 year) .
74
7 .4 .2
Ba ck w a r da t ion a n d Con t a n go
The t heory of norm al backwardat ion was first developed by J. M. Keynes in 1930. The t heory
suggest s t hat t he fut ures price is a biased est im at e of t he expect ed spot price at t he m at urit y.
The underlying principle for t he t heory is t hat hedgers use t he fut ure m arket t o avoid risks and
pay a significant am ount t o t he speculat ors for t his insurance. When t he fut ure price is lower
t han t he current spot price, t he m arket is said t o be backwarded and t he opposit e is called as
a cont ango m arket . Since fut ure and spot prices have t o converge on m at urit y (t his is som et im es
called t he law of one price) , in t he case of a backwarded m arket , t he fut ure price will increase
relat ive t o t he expect ed spot price wit h passage of t im e, t he process referred t o as backwardat ion.
I n case of cont ango, t he fut ure price decreases relat ive t o t he expect ed spot price.
Backwardat ion and cont ango is easily explained in t erm s of t he seasonal nat ure of com m odit ies.
Com m odit y fut ures wit h expirat ion dat es falling in post harvest m ont h would face backwardat ion,
as t he expect ed spot price would be lower. When hedgers are net short ( farm ers willing t o sell
t he produce im m ediat ely aft er harvest ) , or t he risk aversion is m ore for short hedgers t han t he
long hedgers, t he fut ures price would be a downward biased est im at e of t he expect ed spot
price, result ing int o a backwarded m arket .
7 .5
Opt ion Pr icin g
Our brief t reat m ent of opt ions in t his m odule init ially looks at pay- off diagram s, which chart
t he price of t he opt ion wit h changes in t he price of t he underlying and t hen describes how call
and opt ion prices are relat ed using put - call parit y. We t hen briefly describe t he celebrat ed
Black- Scholes form ula t o price a European opt ion.
7 .5 .1
Pa yoffs fr om opt ion con t r a ct s
Payoffs from an opt ion cont ract refer t o t he value of t he opt ion cont ract for t he part ies ( buyer
and seller) on t he dat e t he opt ion is exercised. For t he sake of sim plicit y, we do not consider
t he init ial prem ium am ount while calculat ing t he opt ion payoffs.
I n case of call opt ions, t he opt ion buyer would exercise t he opt ion only if t he m arket price on
t he dat e of exercise is m ore t han t he st rike price of t he opt ion cont ract . Ot herwise, t he opt ion
is wort hless since it will expire wit hout being exercised. Sim ilarly, a put opt ion buyer would
exercise her right if t he m arket price is lower t han t he exercise price.
The payoff of a call opt ion buyer at expirat ion is:
Max [ ( Market price of t he share – Exercise Price) , 0]
The following figures shows t he payoff diagram for call opt ions buyer and seller ( assum ed
exercise price is 100)
75
The payoff for a buyer of a put opt ion at expirat ion is:
Max [ ( Exercise price – Market price of t he share) , 0]
The payoff diagram for put opt ions buyer and seller ( assum ed exercise price is 100)
From t he pay- off diagram s it ’s apparent t hat a buyer of call opt ions would expect t he m arket
price of t he st ock t o rise, and buying t he call opt ion allows him t o lock in t he benefit s of such
a rise, and also cap t he downside in t he event of a fall. The price of course is t he prem ium . On
t he ot her side, a seller of call opt ions has a cont rarian view, and hopes t o profit from t he
prem ium of t he call opt ions sold t hat would expire unexercised. I t ’s clear from t he vert ical axis
of t he payoff diagram ( which provides t he payoff t he cont ract ) , t hat while t he downside of a
call opt ion buyer is lim it ed, it is not so for t he seller.
I n a sim ilar sense, a buyer of put opt ions would expect t he m arket t o fall, and profit from it ,
wit h an insurance, or a hedge ( in t he event of an unexpect ed rise in t he m arket ) , t o cap t he
downside. The price of t he hedge is t he put opt ion prem ium .
76
7 .5 .2
Pu t - ca ll pa r it y r e la t ion sh ip
The put - call parit y relat ionship gives us a fundam ent al relat ionship bet ween European call
opt ions and put opt ions. The relat ionship is derived by not icing t hat t he payoff from t he following
t wo st rat egies is t he sam e irrespect ive of t he st ock price at m at urit y. The t wo st rat egies are:
St rat egy 1: Buy a call opt ion and invest ing t he present value of exercise price in risk- free
asset .
St rat egy 2: Buy a put opt ion and buying a share.
This can be shown in t he form of t he following diagram :
St r a t e gy 1 :
St r a t e gy 2 :
Since t he payoff from t he t wo st rat egies is t he sam e t herefore:
(
)
Value of call opt ion ( C) + PV of exercise price Ke – rt = value of put opt ion ( P) + Current share
price (S0 ) , i.e.
C + Ke – rt = P + S0
77
7 .6
Bla ck - Sch ole s for m u la
The m ain quest ion t hat is st ill unanswered is t he price of a call opt ion for ent ering int o t he
opt ion cont ract , i.e. t he opt ion prem ium . The prem ium am ount is dependent on m any variables.
They are:
-
Share Price (S0 )
-
Exercise Price ( K)
-
The t im e t o expirat ion i.e. period for which t he opt ion is valid ( T)
-
Prevailing risk- free int erest rat e ( r)
-
The expect ed volat ilit y of t he underlying asset ( σ )
One of t he landm ark invent ions in t he financial world has been t he Black- Scholes form ula t o
price a European opt ion. Fischer Black and Myron Scholes2 in t heir sem inal paper in 1973 gave
t he world a m at hem at ical m odel t o value t he call opt ions and put opt ions. The form ula proved
t o be very useful not only t o t he academ ics but also t o pract it ioners in t he finance world. The
aut hors were lat er awarded The Sveriges Riksbank Prize in Econom ic Sciences in Mem ory of
Alfred Nobel in 1997. The Black- Scholes form ula for valuing call opt ions ( c) and value of put
opt ions ( p) is as under:
c( S, t ) = SN ( d1 ) – ke
– r (T – t )
N ( d 2 ) and
p( S, t ) = Ke – r ( T – t ) N( – d 2 ) – SN( – d1 )
Where

S
σ2
ln   +  r +
2
K  
d1 =
σ T –t

 ( T – t )

d 2 = d1 – σ T – t
Where,
N (.) is t he cum ulat ive dist ribut ion funct ion ( cdf ) of t he st andard norm al dist ribut ion
T- t is t he t im e t o m at urit y
S is t he spot price of t he underlying asset
K is t he st rike price
r is t he cont inuously com pounded annual risk- free rat e
σ is t he volat ilit y in t he log ret urns of t he underlying.
78
Exam ple: Calculat e t he value of a call opt ion and put opt ion for t he following cont ract :
St ock Price ( S) = 100
Exercise Price ( K) = 105
Risk- free, cont inuously com pounded int erest Rat e ( r) = 0.10 ( 10% )
Tim e t o expirat ion ( T- t ) = 3 m ont h = 0.25 years
St andard deviat ion ( σ ) = 0.30 per year

σ2
S
ln   +  r +
2
K  
d1 =
σ T –t

0 .32
100  
 (T – t )
ln 
 +  0 . 10 +
2
 105  

=
0 . 3 * 0 . 25

 ( 0 . 25)

= – 0 . 0836
d 2 = d1 – σ T – t = 0 . 0836 – 0 . 3 0 . 25 = – . 0236
N( d1 ) = N ( – 0 . 0836) = 0 . 4667
N( d 2 ) = N ( – 0 . 0236) = 0 . 4076
N( – d1 ) = N ( 0 . 0836) = 0 . 5333
N( – d 2 ) = N ( 0 . 0236) = 0 . 5924
Value of call opt ion ( c) =
c ( S, t ) = SN ( d1 ) – ke – r ( T − t ) N( d 2 ) = 100 * 0 . 4667 – 105 * e –. 10 * 0 . 25 * 0 . 4076 = 4 . 9225
Value of Put opt ion ( p) =
p( S, t ) = Ke – r ( T – t ) N( – d 2 ) – SN( – d1 ) = 105 * e – 0 . 10 * 0 . 25 * 0 . 5924 – 100 * 0 . 5333 = 7 . 33
2
Black , Fischer ; My ron Scholes ( 1 973 ) . "Th e Pricin g of Opt ions an d Corp orat e Liabilit ies" . Jour nal of Polit ical
Econom y 81 ( 3) : 637- 654
79
CH APTER 8 : I nve st m e nt M a na ge m e nt
8 .1
I n t r odu ct ion
I n t he final chapt er of t his m odule we t ake a brief look at t he professional asset m anagem ent
indust ry. Worldwide, t he last few decades have seen an increasing t rend away from direct
invest m ent in t he m arket s, wit h t he ret ail invest or now preferring t o invest in funds or t he
index, rat her t han direct exposure int o equit ies. This has nat urally led t o a sharp increase in
t he asset s under m anagem ent of such firm s.
The asset m anagem ent indust ry prim arily consist s of t wo kinds of com panies, t hose engaged
in in v est m en t adv isor y or w ealt h m an agem en t act iv it ies, an d t h ose in t o in v est m en t
m anagem ent . I n t he first cat egory, invest m ent advisory firm s recom m end t heir client s t o t ake
posit ions in various securit ies, and wealt h m anagem ent firm eit her recom m end, or have cust ody
of t heir client s’ funds, t o be invest ed according t o t heir discret ion. I n bot h cases, t he engagem ent
wit h client s is at an account level, i.e., funds are separat ely m anaged for each client . I n
cont rast , invest m ent m anagem ent com panies com bine t heir client s’ asset s t owards t aking
posit ions in a single port folio, usually called a fund ( or a m ut ual fund) . A unit of such a fund
t hen represent s posit ions in each of t he securit ies owned in t he port folio. I nst ead of t racking
ret urns on t heir own port folios, client s t rack ret urns on t he net asset value ( NAV) of t he fund.
I n addit ion t o t he perceived benefit s of professional fund m anagem ent , t he m aj or reason
of invest m ent int o funds is t he diversificat ion t hey afford t he invest or. For inst ance, inst ead
of own ing ever y lar ge- cap st ock in t he m ar k et , an in vest or cou ld j u st buy u nit s of a
large- cap fund.
I n t his chapt er, we shall exam ine t he various t ypes of such funds, different iat ed by t heir
invest m ent m andat es, choice of securit ies, and of course, invest m ent perform ance, where we
would out line a few of t he key m et rics used t o m easure invest m ent perform ance of funds.
8 .2
I n v e st m e n t Com pa n ie s
I nvest m ent com panies pool funds from various invest ors and invest t he accum ulat ed funds in
various financial inst rum ent s or ot her asset s. The profit s and losses from t he invest m ent
( aft er repaying t he m anagem ent expenses) are dist ribut ed t o t he invest ors in t he funds in
proport ion t o t he invest m ent am ount . Each invest m ent com pany is run by an asset m anagem ent
com pany who sim ult aneously operat e various funds wit hin t he invest m ent com pany. Each
fund is m anaged by a fund m anager who is responsible for m anagem ent of t he port folio.
I nvest m ent com panies are referred t o by different nam es in different count ries, such as m ut ual
funds, invest m ent funds, m anaged funds or sim ply funds. I n I ndia, t hey are called m ut ual
funds. Our t reat m ent would use t hese nam es int erchangeably, unless explicit ly st at ed.
80
8 .2 .1
Be n e fit s of in ve st m e n t s in m a n a ge d fu n ds
The m ain advant ages of invest ing t hrough collect ive invest m ent schem es are:
-
Ch oice of Sch e m e s: There are various schem es wit h different invest m ent t hem es.
Through each schem e an invest or has an opport unit y t o invest in a wide range of
invest able securit ies.
-
Pr ofe ssion a l M a n a ge m e n t : Professionally m anaged by t eam of expert s.
-
Dive rsifica tion : Scope for bet t er diversificat ion of invest m ent since m ut ual fund asset s
are invest ed across a wide range of securit ies.
-
Liqu idit y: Easy ent ry and exit of invest m ent : invest ors can wit h ease buy unit s from
m ut ual funds or redeem t heir unit s at t he net asset value eit her direct ly wit h t he
m ut ual fund or t hrough an advisor / st ock broker.
-
Tr a n spa r e n cy: The asset m anagem ent t eam has t o on a regular basis publish t he
NAV of t he asset s and broad break- up of t he inst rum ent s where t he invest m ent
is m ade.
-
Ta x be n e fit s: Dividends received on invest m ent s held in cert ain schem es, such as
equit y based m ut ual funds, are not subj ect t o t ax.
8 .3
Act iv e v s. Pa ssiv e Por t folio M a n a ge m e n t
I f asset prices always reflect t heir equilibrium values ( expect ed ret urns equal t o t he value
specified by an asset pricing m odel) , t hen an invest or is unlikely t o benefit from act ively
searching for m ispriced ( overpriced/ underpriced) opport unit ies in asset s. I n ot her words, t he
invest or is bet t er off by sim ply invest ing in t he m arket , or a represent at ive benchm ark. For
inst ance, under such assum pt ions, an I ndian equit y invest or would achieve t he best possible
out com e by t rying t o replicat e t he Nift y 50 by invest ing in t he const it uent st ocks in t he sam e
proport ion as t hey are in t he index.
Such invest m ent assum es t hat gains in t he m arket are t hose of t he benchm ark, and not in t he
choice of individual securit ies, as opport unit ies in t heir select ion, or t im ing of ent ry/ exit are
t oo short t o be t aken advant age of. This, passive approach t o invest m ent rest s upon t he
t heory of m arket efficiency, which we saw in chapt er 4. Recall t hat t he EMH post ulat es t hat
prices always fully reflect all t he available inform at ion and any deviat ion from t he full inform at ion
price would be quickly arbit raged away. I n an efficient m arket , inform at ion about fundam ent al
fact ors relat ed t o t he asset , or it s m arket price, volum e or any ot her relat ed t rading dat a
relat ed has lit t le value for t he invest or.
81
Passive fund m anagers t ry t o replicat e t he perform ance of a benchm ark index, by replicat ing
t he weight s of it s const it uent st ocks. Given daily price m ovem ent in st ock prices, t he challenge
for such m anagers is t o m inim ize t he so- called ‘t racking error ’ of t he fund, which is calculat ed
as t he deviat ion in it s ret urns from t hat of t he index. The choice of t he index furt her different iat es
bet ween t he funds, for exam ple, an equit y index fund would sim ply t ry t o m aint ain t he ret urn
profile of t he benchm ark index, say, t he NI FTY 50; but if invest m ent s are allowed across asset
classes, t hen t he ‘benchm ark’ could well consist of a com binat ion of a equit y and a debt index.
Recent evidence of syst em at ic depart ures of asset prices in t he from equilibrium values, as
envisaged under t he m arket efficiency, has renewed int erest in ‘act ive’ fund m anagem ent ,
which ent ails t hat opt im al select ion of st ocks, and t he t im ing of ent ry/ exit could lead t o ‘m arketbeat ing’ ret urns.
This represent s an opport unit y for invest ors t o engage in act ive st rat egies based on t heir
obj ect ive views about t he asset s. I n a generic sense, such views are about t he relat ive under
pricing or over pricing of an asset . Over pricing present s an opport unit y t o engage in short
selling, under pricing an opport unit y t o t ake a long posit ion, and com binat ions of t he t wo are
also possible, across st ocks, and port folios.
The obj ect ive of an act ive port folio m anager is t o m ake higher profit s from invest ing, wit h
sim ilar, or lower risks at t ached. The risk of a port folio, as not ed in an earlier chapt er, is usually
m easured wit h t he st andard deviat ion of it s asset s. A good port folio m anager should have
good forecast ing abilit y and should be able t o do t wo t hings bet t er t han his com pet it ors:
m arket t im ing and securit y select ion.
By m arket t im ing, we refer t o t he abilit y of t he port folio m anager t o gauge at t he beginning of
each period t he profit abilit y of t he m arket port folio vis-à-vis t he risk-free port folio of Governm ent
bonds. The st rengt h of such a signal would indicat e t he level of invest m ent required in t he
m arket .
By securit y select ion, we refer t o abilit y of a port folio m anager in ident ifying m ispricing in
individual securit ies and t hen invest ing in securit ies wit h t he m axim um m ispricing, which
m axim izes t he so- called alpha. The alpha of a securit y refers t o t he expect ed excess ret urn of
t he securit y over t he expect ed rat e of ret urn (for exam ple, est im at ed by an equilibrium asset pricing m odel like t he CAPM) . The m ispricing m ay be eit her way: I f t he port folio m anager
believes t hat a securit y is going t o generat e negat ive ret urn, his port folio should give a negat ive
weight for t he sam e i.e. short t he securit y and vice versa. The t radeoff for t he act ive invest or
is t he presence of nonsyst em at ic risk in t he port folio. Since t he port folio of an act ive invest or
is not fully diversified, t here is som e nonsyst em at ic ( firm - specific) risk t hat is not diversified
away. Act ive fund m anagem ent is a diverse business—t here are m any ways t o m ake m oney in
82
t he m arket —alm ost all t he invest m ent st yles we would exam ine furt her in t he chapt er are
illust rat ive exam ples.
Act ive and passive fund m anagem ent are not always chalk and cheese—t here are t echniques
t hat ut ilize bot h, like port folio t ilt ing. A t ilt ed port folio shift s t he weight s of it s const it uent s
t owards one or m ore of cert ain pre- specified m arket fact ors, like earnings, valuat ions, dividend
yields, or t owards one or m ore specific sect ors.
By t heir very nat ure of operat ions, act ive and passive invest m ent s differ m eaningfully in t erm s
of t heir cost s t o t he invest ors. Passive invest m ent is charact erized by low t ransact ion cost s
( given t heir low t urnover) , m anagem ent expenses, and t he risks at t ached.
Act ive fund
m anagem ent is underst andably m ore expensive, but has seen cost s falling over t he years on
com pet it ive pricing and increased liquidit y of t he m arket s, which reduced t ransact ion cost s.
8 .4
Cost s of M a n a ge m e n t : En t r y / Ex it Loa ds a n d Fe e s
Running a m ut ual fund involves cert ain cost s ( e.g. rem unerat ion t o t he m anagem ent t eam ,
advert ising expenses et c.) which m ay be recurring or non- recurring in nat ure. These cost s are
recovered by t he fund from t he invest ors ( e.g. from redem pt ion fees) or from charges on t he
asset s ( t ransact ion fees, m anagem ent fees and com m ission et c.) of t he funds.
Generally, t he m anagem ent t eam is paid a fixed percent age of t he asset under m anagem ent
as t heir fees.
I nvest m ent m anagem ent com panies can be broadly classified on t he basis of t he securit ies
t hey invest in and t heir invest m ent obj ect ives. Before we look at eit her, we define t he core
m easure of ret urn for a fund, t he NAV, and so- called open, and closed- ended funds.
8 .5
N e t Asse t Va lu e
Th e net asset value NAV is t he m ost im port an t and w idely f ollowed m et ric of a fund’s
perform ance. I t is calculat ed per share using t he following form ula:
NAV ( per share) =
Market Value of Asset s – Market Value of liabilit ies
Num ber of shares out s t an dign
Net asset value ( NAV) is a t erm used t o describe t he per unit value of t he fund’s net asset s
( asset s less t he value of it s liabilit ies) . Hence t he NAV for a fund is
Fund NAV = ( Market Value of t he fund port folio – Fund Expenses) / Fund Shares Out st anding
Just like t he share price of a com m on st ock, t he NAV of a fund would rise wit h t he value of t he
fund port folio, and is inst ant ly reflect ive of t he value of invest m ent .
83
8 .6
Cla ssifica t ion of fu n ds
8 .6 .1
Ope n e n de d a n d close d- e n de d fu n ds
Funds are usually open or closed- ended. I n an open- ended fund, t he unit s are issued and
redeem ed by t he fund, at any t im e, at t he NAV prevalent at t he t im e of issue / redem pt ion.
The fund discloses t he NAV on a daily basis t o facilit at e issue and redem pt ion of unit s. Unlike
open- ended funds, closed- ended funds sell unit s only at t he out set and do not redeem or sell
unit s once t hey are issued. The invest ors can sell or purchase unit s t o ( or from ) ot her invest ors
and t o facilit at e such t ransact ions, such unit s are t raded on st ock exchanges. Price of closed
ended schem es are det erm ined based on dem and and supply for t he unit s at t he st ock exchange
and can be m ore or less t han t he NAV of t he unit s.
We now exam ine t he different kind of funds on t he basis of t heir invest m ent s. While we had
earlier m ent ioned m ut ual fund invest m ent s represent ed as unit s in a single port folio, in real
life, fund houses float various schem es from t im e- t o- t im e, each a const it ut ing a port folio
where input s t ranslat e int o unit s. These schem es are different iat ed by t heir chart er which
m andat es t heir invest m ent int o asset classes.
Beyond t he t ype of inst rum ent s t hey invest in, fund houses are also different iat ed in t erm s of
t heir invest m ent st yles. The approaches t o equit y invest ing could be diversified or undiversified,
growt h, incom e, sect or rot at ors, value, or m arket - t im ing based.
Each m ut ual fund schem e has a part icular invest m ent policy and t he fund m anager has t o
ensure t hat t he invest m ent policy is not breached. The policy is laid right at t he out set when
t he fund is launched and is specified in t he prospect us, t he ‘Offer Docum ent ’ of t he schem e.
The invest m ent policy det erm ines t he inst rum ent s in which t he m oney from a specific schem e
will be prim arily invest ed. Based on t hese securit ies, m ut ual funds can be broadly classified
int o equit y funds ( growt h funds and incom e funds) , bond funds, m oney m arket funds, index
funds, et c. Generally, fund houses have dozens of schem es float ing in t he m arket at any given
t im e, wit h separat e invest m ent policies for each schem e.
8 .6 .2
Equ it y fu n ds
Equit y funds prim arily invest in com m on st ock of com panies. Equit y funds can be growt h
funds or incom e funds. Growt h funds focus on growt h st ocks, i.e., com panies wit h st rong
growt h pot ent ial, wit h capit al appreciat ion being t he m aj or driver, while incom e funds focus on
com panies t hat have high dividend yields. I ncom e funds focus on dividend incom e or coupon
paym ent s from bonds ( if t hey are not pure equit y) .
Equit y funds m ay also be sect or- specific wherein t he invest m ent is rest rict ed t o st ocks from a
specific indust ry. For exam ple, in I ndia we have m any funds focusing on com panies in power
sect or and infrast ruct ure sect or.
84
8 .6 .3
Bon d fu n ds
Bond funds invest prim arily in various bonds t hat were described in t he earlier segm ent . They
have a st able incom e st ream and relat ively lower risk. They could pot ent ially invest in corporat e
bonds, Governm ent . bonds, or bot h.
8 .6 .4
I n de x fu n ds
I ndex funds have a passive invest m ent st rat egy and t hey t ry t o replicat e a broad m arket
index. A schem e from such a fund invest s in com ponent s of a part icular index proport ionat e t o
t heir represent at ion in t he benchm ark. I t is possible t hat a schem e t racks m ore t han one index
( in som e pre- specified rat io) , in eit her equit y, or across asset classes.
8 .6 .5
M on e y m a r k e t fu n ds
Money m arket m ut ual funds invest in m oney m arket inst rum ent s, which are short-t erm securit ies
issu ed by ban ks, non - ban k cor porat ions and Govern m ent s. Th e var ious m oney m ark et
inst rum ent s have already been discussed earlier.
8 .6 .6
Fu n d of fu n ds
Fund of funds add anot her layer of diversificat ion bet ween t he invest or and securit ies in t he
m arket . I nst ead of individual st ocks, or bonds, t hese m ut ual funds invest in unit s of ot her
m ut ual funds, wit h t he fund m anagers’ m andat e being t he opt im al choice across m ut ual fund
schem es given ext ant m arket condit ions.
8 .7
Ot h e r I n v e st m e n t Com pa n ie s
I n addit ion t o t he broad cat egories m ent ioned here, t here are m any ot her kinds of funds,
depending on m ark et oppor t un it ies, and invest or appet it e. Tot al r et ur n fu nds look at a
com binat ion of capit al appreciat ion and dividend incom e. Hybrid funds invest in a com binat ion
of equit y, bonds, convert ibles, and derivat ive inst rum ent s. These funds could be furt her
dist ribut ed as ‘asset allocat ion’, ‘balanced’, or ‘flexible port folio’ funds, based on t he breadt h of
t heir invest m ent in different asset classes, and t he frequency of m odifying t he allocat ion.
Global, regional, or em erging m arket funds recognize invest m ent opport unit ies across t he
world, and accordingly base t heir invest m ent focus. Such funds could again com prise eit her, or
a com binat ion of equit y, debt , or hybrid inst rum ent s. We m ent ion som e ot her, specific t ypes of
invest m ent vehicles below.
8 .7 .1
Un it I n ve st m e n t Tr u st s ( UI T)
Sim ilar t o m ut ual funds, UI Ts also pool m oney from invest ors and have a fixed port folio of
asset s, which are not changed during t he life of t he fund. Alt hough t he port folio com posit ion is
act ively decided by t he sponsor of t he fund, once est ablished t he port folio com posit ion is not
changed ( hence called unm anaged funds) .
85
The way an UI T is est ablished is different from t hat of ot her m ut ual funds. UI Ts are usually
creat ed by sponsors, who first m ake invest m ent in t he port folio of securit ies. The ent ire port folio
is t hen t ransferred t o a t rust and t he t rust ees issue t rust cert ificat es t o t he public, which is
sim ilar t o shares. The t rust ees dist ribut e t he incom es from t he invest m ent and t he m at urit y
( capit al) am ount t o t he shareholders on m at urit y of t he schem e.
8 .7 .2
REI TS ( Re a l Est a t e I n ve st m e n t Tr u st s)
REI TS are also sim ilar t o m ut ual funds, but t hey invest prim arily in real est at es or loans
secured by real est at e. REI T can be of t hree t ypes – equit y, m ort gage or hybrid t rust s. Equit y
t rust s invest in real est at e asset s, m ort gage t rust s invest in loans backed by m ort gage and
hybrid t rust s invest in eit her.
8 .7 .3
H e dge Fu n ds
Hedge funds are generally creat ed by a lim it ed num ber of wealt hy invest ors who agree t o pool
t heir funds and hire experienced professionals ( fund m anagers) t o m anage t heir port folio.
Hedge funds are privat e agreem ent s and generally have lit t le or no regulat ions governing
t hem . This gives a lot of freedom t o t he fund m anagers. For exam ple, hedge funds can go
short ( borrow) funds and can invest in derivat ives inst rum ent s which m ut ual funds cannot do.
Hedge funds generally have higher m anagem ent fees t han m ut ual funds as well as perform ance
based fees. The m anagem ent fee ( paid t o t he fund m anagers) , in t he case of hedge funds is
dependent on t he asset s under m anagem ent ( generally 2 - 4% ) and t he fund perform ance
( generally 20% of t he excess ret urns over t he m arket ret urn generat ed by t he fund) .
8 .8
Pe r for m a n ce a sse ssm e n t of m a n a ge d fu n ds
Prior t o t he developm ent of t he m odern port folio t heory ( MPT) , port folio m anagers were
evaluat ed by com paring t he ret urn generat ed by t hem wit h som e broad yardst ick. The risk
borne by t he port folio m anagers or t he source of perform ance such as m arket t im ing, m arket
volat ilit y, t he securit y select ions and valuat ions were not considered. Wit h t he developm ent of
t he MPT, t he goal of perform ance evaluat ion is t o st udy whet her t he port folio has provided
superior ret urns com pared t o t he risks involved in t he port folio or com pared t o an equivalent
passive benchm ark.
The perform ance evaluat ion approach t ries t o at t ribut e t he perform ance t o t he following:
-
Risk
-
Tim ing: m arket or volat ilit y
-
Securit y select ion – of indust ry or individual st ocks
86
Therefore:
a)
The focus of evaluat ion should be on excess ret urns
b)
The port folio perform ance m ust account for t he difference in t he risk
c)
I t should be able t o dist inguish t he t im ing skills from t he securit y select ion skills.
The assessm ent of m anaged funds involves com parison wit h a benchm ark. The benchm ark
could be based on t he Capit al Market Line ( CML) or t he Securit y Market Line ( SML) . When it is
based on capit al Market Line, t he relevant m easure of t he port folio risk is σ and when based
on Securit y Market Line, t he relevant m easure is β . Various m easures are devised t o evaluat e
port folio perform ance, viz. Sharpe Rat io, Treynor Rat io and Jensen Alpha.
8 .8 .1
Sh a r pe Ra t io
Sharpe rat io or ‘excess ret urn t o variabilit y’ m easures t he port folio excess ret urn over t he
sam ple period by t he st andard deviat ion of ret urns over t hat period. This rat io m easures t he
effect iveness of a m anager in diversifying t he t ot al risk ( σ ) . This m easure is appropriat e if one
is evaluat ing t he t ot al port folio of an invest or or a fund, in which case t he Sharpe rat io of t he
port folio can be com pared wit h t hat of t he m arket . The form ula for m easuring t he Sharpe
rat io is:
Shar pe Rat io = ( r p – r f ) / σ p
This will be com pared t o t he Shape rat io of t he m arket port folio. A higher rat io is preferable
since it im plies t hat t he fund m anager is able t o generat e m ore ret urn per unit of t ot al risks.
However, m anagers who are operat ing specific port folios like a value t ilt ed or a st yle t ilt ed
port folio generally t akes a higher risks, and t herefore m ay not be willing t o be evaluat ed based
on t his m easure.
8 .8 .2
Tr e yn or Ra t io
Treynor ’s m easure evaluat es t he excess ret urn per unit of syst em at ic risks ( β ) and not t ot al
risks. I f a port folio is fully diversified, t hen β becom es t he relevant m easure of risk and t he
perform ance of a fund m anager m ay be evaluat ed against t he expect ed ret urn based on t he
SML ( which uses β t o calculat e t he expect ed ret urn) . The form ula for m easuring t he Treynor
Rat io is:
Theynor Rat io = ( r p – r f ) / β p
8 .8 .3
Je n se n m e a su r e or ( Por t folio Alph a )
The Jensen m easure, also called Jensen Alpha, or port folio alpha m easures t he average ret urn
on t he port folio over and above t hat predict ed by t he CAPM, given t he port folio’s bet a and t he
average m arket ret urns. I t is m easured using t he following form ula:
87
α p = r p – [ rf + β p ( rM – rf ) ]
The ret urns predict ed from t he CAPM m odel is t aken as t he benchm ark ret urns and is indicat ed
by t he form ula wit hin t he bracket s. The excess ret urn is at t ribut ed t o t he abilit y of t he m anagers
for m arket t im ing or st ock picking or bot h. This m easure invest igat es t he perform ance of
funds and especially t he abilit y of t he m anagers in st ock select ion in t erm s of t hese cont ribut ing
aspect s.
This m easure is widely used in evaluat ing m ut ual fund perform ance. I f α P is posit ive and
significant , it im plies t hat t he fund m anagers are able t o ident ify st ocks wit h high pot ent ial for
excess ret urns. Market t im ing would refer t o t he adj ust m ent in t he bet a of t he port folio in
t andem wit h m arket m ovem ent s. Specifically, t im ing skills call for increasing t he bet a when
t he m arket is rising and reducing t he bet a, when t he m arket declines, for exam ple t hrough
fut ures posit ion. I f t he fund m anager has poor m arket t im ing abilit y, t hen t he bet a of t he
port folio would not have been significant ly different during a m arket decline com pared t o t hat
during a m arket increase.
Exam ple: The dat a relat ing t o m arket port folio and an invest or ‘P’ port folio is as under:
Average Ret urn
I nvest or P’s Port folio
Market Port folio ( M)
28%
18%
1.4
1
30%
20%
Bet a ( β )
St andard Deviat ion ( σ )
Assu m i n g t h at t h e r isk- f r ee r at e f or t h e m ar k et i s 8 % , cal cu lat e ( a) Sh ar pe Rat i o
( b) Treynor Rat io and ( c) Jensen Alpha for t he invest or P and t he m arket .
Answer:
I nvest or P Port folio
Market Port folio ( M)
Shar pe Rat io = ( r p – r f ) / σ p
( 28% - 8% ) / 30% = 0.67
( 18% - 8% ) / 20% = 0.5
Tr eynor Rat io = ( r p – r f ) / β p
( 28% - 8% ) / 1.4 = 5
( 18% - 8% ) / 1 = 10
Jensen Alpha
28% - [ 8% + 1.4* ( 18% - 8% ) ]
18% - [ 8% + 1
( α p ) = r p – [ rf + β p ( rM – rf ) ]
= 28% - 22% = 6%
( 18% - 8% ) ] = 0
***
88
M OD EL TEST
I N VESTM EN T AN ALYSI S AN D PORTFOLI O
M AN AGEM EN T M OD ULE
Q: 1.
__________ would m ean t hat no invest or would be able t o out perform t he m arket
wit h t rading st rat egies based on publicly available inform at ion.
Q: 2.
( a)
Sem i st rong form efficiency
( b)
Weak-form efficiency
( c)
St rong form efficiency
A com pany's __________ provide t he m ost accurat e inform at ion t o it s m anagem ent
and shareholders about it s operat ions.
Q: 3.
( a)
advert isem ent s
( b)
financial st at em ent s
( c)
product s
( d)
vision st at em ent
( a)
Act ive
( b)
Passive
Q: 6.
[ 2 Marks]
Unlike t erm insurance, __________ ensure a ret urn of capit al t o t he policyholder on
m at urit y, along wit h t he deat h benefit s.
Q: 5.
[ 1 Mark]
______ fund m anagers t ry t o replicat e t he perform ance of a benchm ark index, by
replicat ing t he weight s of it s const it uent st ocks.
Q: 4.
[ 1 Mark]
( a)
high prem ium or low prem ium policies
( b)
fixed or variable policies
( c)
assurance or endowm ent policies
( d)
growt h or value policies
Gross Profit Margin = Gross Profit / Net Sales
( a)
FALSE
( b)
TRUE
[ 1 Mark]
[ 2 Marks]
Securit y of ABC Lt d. t rades in t he spot m arket at Rs. 595. Money can be invest ed at
10% per annum . The fair value of a one- m ont h fut ures cont ract on ABC Lt d. is ( using
cont inuously com pounded m et hod) :
( a)
630.05
( b)
620.05
( c)
600.05
( d)
610.05
[ 2 Marks]
89
Q: 7.
Q: 8.
Account s payable appears in t he Balance Sheet of com panies.
( a)
TRUE
( b)
FALSE
[ 2 Marks]
A port folio com prises of t wo st ocks A and B. St ock A gives a ret urn of 8% and st ock B
gives a ret urn of 7% . St ock A has a weight of 60% in t he port folio. What is t he
port folio ret urn?
Q: 9.
( a)
9%
( b)
11%
( c)
10%
( d)
8%
[ 2 Marks]
Evidence accum ulat ed t hrough research over t he past t wo decades suggest s t hat
du r i n g m an y episodes t h e m ar k et s ar e n ot ef f icien t ev en in t h e w eak f or m .
[ 2 Marks]
Q: 10.
( a)
FALSE
( b)
TRUE
Mr. A buys a Put Opt ion at a st rike price of Rs. 100 for a prem ium of Rs. 5. On expiry
of t he cont ract t he underlying shares are t rading at Rs. 106. Will Mr. A exercise his
opt ion?
Q: 11.
( a)
No
( b)
Yes
[ 3 Marks]
Price m ovem ent bet ween t wo I nform at ion Technology st ocks would generally have a
______ co-variance.
Q: 12.
( a)
zero
( b)
posit ive
( c)
negat ive
[ 1 Mark]
I n t he case of callable bonds, t he callable price ( redem pt ion price) m ay be different
from t he face value.
Q: 13.
( a)
FALSE
( b)
TRUE
[ 2 Marks]
Term st ruct ure of int erest rat es is also called as t he ______.
( a)
t erm curve
( b)
yield curve
( c)
int erest rat e curve
( d)
m at urit y curve
90
[ 2 Marks]
Q: 14.
Q: 15.
Q: 16.
Each invest m ent com pany is run by an _______.
( a)
asset deploym ent com pany
( b)
revenue m anagem ent com pany
( c)
asset m anagem ent com pany
( d)
asset reconst ruct ion com pany
A ________, is a t im e deposit wit h a bank wit h a specified int erest rat e.
( a)
cert ificat e of deposit ( CD)
( b)
com m ercial paper ( CP)
( c)
T- Not e
( d)
T- Bill
[ 1 Mark]
Prices ( ret urns) which are not according t o CAPM shall be quickly ident ified by t he
m arket and brought back t o t he __________.
Q: 17.
[ 1 Mark]
( a)
average
( b)
st andard deviat ion
( c)
m ean
( d)
equilibrium
[ 1 Mark]
Net acquisit ions / disposals appears in t he Cash Flow St at em ent of Com panies.
[ 3 Marks]
Q: 18.
Q: 19.
( a)
TRUE
( b)
FALSE
______ are a fixed incom e securit y.
( a)
Equit ies
( b)
Forex
( c)
Derivat ives
( d)
Bonds
[ 1 Mark]
I nvest m ent advisory firm s m anage ______.
( a)
each client 's account seperat ely
( b)
all client s account s in a com bined m anner
( c)
only t heir own m oney and not client 's m oney
91
[ 1 Mark]
Q: 20.
_______ m easures t he percent age of net incom e not paid t o t he shareholders in t he
form of dividends.
Q: 21.
Q: 22.
( a)
Wit hholding rat io
( b)
Ret ent ion rat io
( c)
Preservat ion rat io
( d)
Maint enance rat io
[ 1 Mark]
I n a Bond t he ____ is paid at t he m at urit y dat e.
( a)
face value
( b)
discount ed value
( c)
com pounded value
( d)
present value
Banks and ot her financial inst it ut ions generally creat e a port folio of fixed incom e
securit ies t o fund known _______ .
Q: 23.
( a)
asset s
( b)
liabilit ies
[ 2 Marks]
Which of t he following account ing st at em ent s form t he backbone of financial analysis
of a com pany?
Q: 24.
[ 1 Mark]
( a)
t he incom e st at em ent ( profit & loss) ,
( b)
t he balance sheet
( c)
st at em ent of cash flows
( d)
All of t he above
The balance sheet of a com pany is a snapshot of t he ______ of t he firm at a point in
t im e.
Q: 25.
[ 1 Mark]
[ 2 Marks]
( a)
t he sources and applicat ions of funds of t he com pany.
( b)
expendit ure st ruct ure
( c)
profit st ruct ure
( d)
incom e st ruct ure
The need t o have an underst anding about t he abilit y of t he m arket t o im bibe inform at ion
int o t he prices has led t o count less at t em pt s t o st udy and charact erize t he levels of
efficiency of different segm ent s of t he financial m arket s.
( a)
TRUE
( b)
FALSE
92
[ 1 Mark]
Q: 26.
I n invest m ent decisions, _______ refers t o t he m arket abilit y of t he asset .
[ 2 Marks]
Q: 27.
( a)
value
( b)
profit abilit y
( c)
price
( d)
liquidit y
Mr. A buys a Call Opt ion at a st rike price of Rs. 700 for a prem ium of Rs. 5. Mr. A
expect s t he price of t he underlying shares t o rise above Rs. ______ on expiry dat e in
order t o m ake a profit .
Q: 28.
( a)
740
( b)
700
( c)
720
( d)
760
[ 3 Marks]
The ______ refers t o t he lengt h of t im e for which an invest or expect s t o rem ain
invest ed in a part icular securit y or port folio, before realizing t he ret urns. [ 2 Marks]
Q: 29.
( a)
invest m ent horizon
( b)
credit cycle horizon
( c)
durat ion horizon
( d)
const raint horizon
A ________ provides an account of t he t ot al revenue generat ed by a firm during a
period ( usually a financial year, or a quart er) .
Q: 30.
( a)
Account ing analysis st at em ent
( b)
financial re-engineering st at em ent
( c)
prom ot ional expenses st at em ent
( d)
profit & loss st at em ent
New st ocks/ bonds are sold by t he issuer t o t he public in t he ________ .
( a)
fixed incom e m arket
( b)
secondary m arket
( c)
m oney m arket
( d)
prim ary m arket
93
[ 1 Mark]
[ 1 Mark]
Q: 31.
Securit y of ABC Lt d. t rades in t he spot m arket at Rs. 525. Money can be invest ed at
10% per annum . The fair value of a one- m ont h fut ures cont ract on ABC Lt d. is ( using
cont inously com pounded m et hod) :
Q: 32.
( a)
559.46
( b)
549.46
( c)
539.46
( d)
529.46
[ 2 Marks]
I f t he m arket is _______, t he period aft er a favorable ( unfavorable) event would not
generat e ret urns beyond ( less t han) what is suggest ed by an equilibrium m odel such
as CAPM.
Q: 33.
( a)
weak- form efficient
( b)
st rong form efficient
( c)
sem i- st rong form efficient
[ 1 Mark]
A sell order com es int o t he t rading syst em at a Lim it Price of Rs. 120. The order will
get execut ed at a price of _______.
Q: 34.
( a)
Rs. 120 or m ore
( b)
Rs. 120 or less
[ 2 Marks]
__________ have precedence over com m on st ock in t erm s of dividend paym ent s,
and t he residual claim t o it s asset s in t he event of liquidat ion.
Q: 35.
( a)
Preferred shares
( b)
Equit y shares
[ 1 Mark]
One needs t o average out t he t im e t o m at urit y and t im e t o various coupon paym ent s
t o find t he effect ive m at urit y for a bond. The m easure is called as _____ of a bond.
[ 2 Marks]
Q: 36.
( a)
durat ion
( b)
I RR
( c)
YTM
( d)
yield
I n case of com pou n d in t er est rat e, w e n eed t o k n ow t h e _ _ _ _ _ _ _ f or w h ich
com pounding is done.
( a)
period
( b)
frequency
( c)
t im e
( d)
durat ion
[ 1 Mark]
94
Q: 37.
Net change in Working Capit al appears in t he Cash Flow St at em ent of Com panies.
[ 3 Marks]
Q: 38.
( a)
FALSE
( b)
TRUE
A com pany's net incom e for a period is Rs. 15,00,00,000 and t he average shareholder's
fund during t he period is Rs. 1,00,00,00,000. The Ret urn on Average Equit y is :
[ 3 Marks]
Q: 39.
( a)
13%
( b)
12%
( c)
15%
( d)
16%
A port folio com prises of t wo st ocks A and B. St ock A gives a ret urn of 14% and st ock
B gives a ret urn of 1% . St ock A has a weight of 60% in t he port folio. What is t he
port folio ret urn?
Q: 40.
( a)
10%
( b)
9%
( c)
12%
( d)
11%
[ 2 Marks]
Average Ret urn of an invest or's port folio is 10% . The risk free ret urn for t he m arket is
8% . The Bet a of t he invest or's port folio is 1.2. Calculat e t he Treynor Rat io.
Q: 41.
( a)
4
( b)
8
( c)
2
( d)
6
[ 3 Marks]
The share price of PQR Com pany on 1st April 2009 and 31st March 2010 is Rs. 20 and
Rs. 24 respect ively. The com pany paid a dividend of Rs. 5 for t he year 2009- 10.
Calcu lat e t h e r et u r n f or a sh ar eh older of PQR Com pan y in t h e y ear 2 00 9 - 10 .
[ 1 Mark]
( a)
45%
( b)
65%
( c)
75%
( d)
55%
95
Q: 42.
Port folio m anagem ent is t he art of m anaging t he expect ed _______ requirem ent for
t he corresponding ________.
Q: 43.
( a)
incom e, expendit ure
( b)
gain, losses
( c)
profit , loss t olerance
( d)
ret urn, risk t olerance
[ 1 Mark]
Average Ret urn of an invest or's port folio is 55% . The risk free ret urn for t he m arket is
8% . The Bet a of t he invest or's port folio is 1.2. Calculat e t he Treynor Rat io.
[ 3 Marks]
Q: 44.
( a)
41
( b)
39
( c)
43
( d)
45
I n addit ion t o t he perceived benefit s of professional fund m anagem ent , t he m aj or
reason of invest m ent int o funds is t he ______ t hey afford t he invest or.
Q: 45.
( a)
specialisat ion
( b)
diversificat ion
( c)
variet y
( d)
expansion
[ 1 Mark]
ABC Lt d. has paid a dividend of Rs. 10 per share last year and it is expect ed t o grow
at 5% every year. I f an invest or's expect ed rat e of ret urn from ABC Lt d. share is 7% ,
calcu l at e t h e m ar k et pr ice of t h e sh ar e as per t h e div iden d discou n t m odel.
[ 2 Marks]
Q: 46.
( a)
540
( b)
530
( c)
525
( d)
535
The CAPM is founded on t he following t wo assum pt ions ( 1) in t he equilibrium every
m ean variance invest or holds t he sam e m arket port folio and ( 2) t he only risk t he
invest or faces is t he bet a.
( a)
TRUE
( b)
FALSE
[ 1 Mark]
96
Q: 47.
Market s are inefficient when prices of securit ies assim ilat e and reflect inform at ion
about t hem .
Q: 48.
( a)
TRUE
( b)
FALSE
[ 1 Mark]
St ock ret urns are generally expect ed t o be independent across weekdays, but a num ber
of st udies have found ret urns on Monday t o be lower t han in t he rest of t he week. This
depart ure from m arket efficiency is also som et im es called t he _____ effect . [ 2 Marks]
Q: 49.
( a)
Monday- Friday
( b)
weekday
( c)
Monday
( d)
weekend
Over pr icing in a st ock presen t s an opport u nit y t o engage in ____ _ t he st ock.
[ 2 Marks]
Q: 50.
( a)
short covering
( b)
short selling
( c)
act ive buying
( d)
going long
What is t he am ount an invest or will get on a 1-year fixed deposit of Rs. 10000 t hat
pays 8% int erest com pounded quart erly?
Q: 51.
Q: 52.
Q: 53.
( a)
12824.32
( b)
13824.32
( c)
10824.32
( d)
11824.32
For longer invest m ent horizons invest ors look at ______ .
( a)
riskier asset s like equit ies.
( b)
low risk asset s like governm ent securit ies.
Dividend Per Share = Tot al Dividend / Num ber of Shares in issue
( a)
TRUE
( b)
FALSE
[ 1 Mark]
[ 2 Marks]
[ 1 Mark]
Price m ovem ent bet ween t wo St eel com pany st ocks would generally have a ______
co-variance.
( a)
posit ive
( b)
negat ive
( c)
zero
[ 1 Mark]
97
Q: 54.
The price of a derivat ive is dependent on t he price of anot her securit y, called t he
_____ .
Q: 55.
Q: 56.
Q: 57.
Q: 58.
( a)
basis
( b)
variable
( c)
underlying
( d)
opt ions
[ 1 Mark]
Call Opt ions can be classified as :
( a)
European
( b)
Am erican
( c)
All of t he above
[ 1 Mark]
I n I ndia, Com m ercial Papers ( CPs) can be issued by _____.
( a)
Mut ual Fund Agent s
( b)
I nsurance Agent s
( c)
Prim ary Dealers
( d)
Sub- Brokers
An endowm ent fund is an inst it ut ional invest or.
( a)
FALSE
( b)
TRUE
[ 1 Mark]
______ orders are act ivat ed only when t he m arket price of t he relevant securit y
reaches a t hreshold price.
Q: 59.
[ 3 Marks]
( a)
Lim it
( b)
Market - loss
( c)
St op- loss
( d)
I OC
[ 2 Marks]
A port folio com prises of t wo st ocks A and B. St ock A gives a ret urn of 9% and st ock B
gives a ret urn of 6% . St ock A has a weight of 60% in t he port folio. What is t he
port folio ret urn?
( a)
11%
( b)
9%
( c)
10%
( d)
8%
[ 2 Marks]
98
Q: 60.
The issue price of T- bills is generally decided at an ______ .
( a)
OTC m arket
( b)
int er- bank m arket
( c)
exchange
( d)
auct ion
[ 3 Marks]
________________________________________
Cor r e ct An sw e r s :
Qu e st ion N o.
Answ er s
Qu e st ion N o.
Answ er s
1
( a)
31
( d)
2
( b)
32
( c)
3
( b)
33
( a)
4
( c)
34
( a)
5
( b)
35
( a)
6
( c)
36
( b)
7
( a)
37
( b)
8
( d)
38
( c)
9
( b)
39
( b)
10
( a)
40
( c)
11
( b)
41
( a)
12
( b)
42
( d)
13
( b)
43
( b)
14
( c)
44
( b)
15
( a)
45
( c)
16
( d)
46
( a)
17
( a)
47
( b)
18
( d)
48
( d)
19
( a)
49
( b)
20
( b)
50
( c)
21
( a)
51
( a)
22
( b)
52
( a)
23
( d)
53
( a)
24
( a)
54
( c)
25
( a)
55
( a)
26
( d)
56
( c)
27
( b)
57
( b)
28
( a)
58
( c)
29
( d)
59
( d)
30
( d)
60
________________________________________
99
( d)