Resilience to the Financial Crisis in Customer

Transcription

Resilience to the Financial Crisis in
Customer-Supplier Networks
Xiao (Christy) Yu (with Ramazan Gen¸cay)
Simon Fraser University
March 30, 2015
Resilience to the Financial Crisis in Customer-Supplier Networks
Motivation and Objectives
I
Using data on North American public companies, we explore how a
company’s customer-supplier relations in the pre-crisis period help to
explain its resilience to the financial crisis of 2008-2009 as measured
by stock returns.
I
On average, stock returns are expected to be negatively affected by
the financial crisis.
I
If a firm’s stock return is less negatively affected by the crisis, this
firm is considered to be more resilient.
I
Inspired by the Sharpe (1964) & Lintner (1965) Capital Asset
Pricing Model (CAPM) beta, we construct two measures or indices
to capture the cross-sectional dependence contained in the
customer-supplier network: customer and supplier beta.
I
The two betas we construct summarize each company’s return
covariances with its customers and suppliers, respectively.
I
I
I
Our objectives are threefold.
First, customer and supplier relations could have different risk
characteristics.
Decomposing them into two different measures allows us to
separately analyze their characteristics and implications.
I
Second, if the importance of any one of the two betas is verified by
the regression results, it is useful tool when conducting risk or stress
analysis.
I
Third, our proposed techniques allow us to investigate effects from
higher-order linkages.
Adjacency Matrix in Customer-Supplier Network
I
In a customer-supplier network:
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I
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Each company i is represented by a node i;
A customer-supplier relationship between company i and j is
described by a link between them, where the supplier is the source
and the customer is the target.
The structure of the network can be characterized by an adjacency
matrix, G, which is a square matrix with dimension of the number of
companies (i.e., notes) in the network, such that
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(G )ij is 1 if and only if i (j) is the supplier (customer) of j (i); and
(G )ij is 0 otherwise.
Example
Customer-Supplier Network
v1
v2
v3
v4
v5
Adjacency Matrix

0 1 1 0 0
 0 0 0 1 0

G =
 0 0 0 1 1
 0 0 0 0 0
0 0 0 0 0






Transpose of Adjacency Matrix
Accordingly,
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(G T )ij is 1 if and only if i (j) is the customer (supplier) of j (i); and
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(G T )ij is 0 otherwise.
Example (cont’d)
v1
v2
v3
v4

G
T


=


0
1
1
0
0
v5
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0






Two Special Cases: Self-Loop and Bilateral Linkage
I
Suppose

a11
 a21

G = .
 ..
a12
a22
..
.
···
···
..
.
a1n
a2n
..
.






 and G T = 


an1 an2 · · · ann
where aij = 1 or 0 for any i and j.
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a11
a12
..
.
a21
a22
..
.
···
···
..
.
an1
an2
..
.
a1n
a2n
···
ann





First, aii = 1 for some i if company i is a customer (or supplier) of
itself, that is, node i has a self-loop.
Second, aij = aji = 1 for some i and j, where i 6= j, if company i is
both a supplier and a customer of company j, that is, the link
between node i and j is bilateral.
Two Special Cases: Self-Loop and Bilateral Linkage
Self-Loop
Bilateral Linkage
vi
vi
vj
The CAPM Beta
I
Our customer and supplier betas are inspired by the CAPM beta.
I
Let us recall: the CAPM beta of an asset (or portfolio) i is
βi =
cov (ri , rm )
2
σm
(1)
where cov (ri , rm ) is the covariance of the return on asset i with the
2
return on the market portfolio, and σm
is the variance of the return
on the market portfolio.
The CAPM Beta
I
Suppose that there are n assets in the market, an n × 1 vector β,
where βi , i = 1, ..., n, is the ith entry of β, can be expressed as


β1
 β2  Σ X


m m
β= . =
(2)
2
σm
 .. 
βn

I
σ11
 σ21

where Σm = 
 .
 .
σn1
In principle, Σm and
in the market.



σ12 . . σ1n
x1
 x2 
σ22 . . σ2n 



 . 
.
. .
. 
and
X
=
m



 . 
.
. .
. 
σn2 . . σnn
xn
Xm in the CAPM beta should contain all assets
Customer and Supplier Beta
I
Suppose that there are n companies in the network, define the
customer and supplier beta respectively as,
βc = (G ◦ Σ) X
βs = G T ◦ Σ X
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(3)
(4)
where
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◦ denotes the element-wise product of two matrices;
Σ is the n × n return variance-covariance matrix;
X is the n × 1 vector containing the relative weight of market
capitalization of each company;
In practice, Σ and X would only contain the companies that are
identified from the customer-supplier network. Hence, in general,
Σ 6= Σm and X 6= Xm .
βc = (G ◦ Σ) X
βs = G T ◦ Σ X
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βc and βs are n × 1 vectors
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I
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The ith entry in βc , βci , is the weighted average of company i’s
return covariances with its customers;
The ith entry in βs , βsi , is the weighted average of company i’s
return covariances with its suppliers;
The weights applied are the relative market capitalizations of its
customers and suppliers, respectively.
Example (cont’d)
I
G extracts each company’s return covariances with its
customers


0 σ12 σ13 0
0
 0 0
0 σ24 0 



0 σ34 σ35 
G ◦Σ= 0 0

 0 0
0
0
0 
0 0
0
0
0
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G T extracts each company’s return covariances with its
suppliers


0
0
0 0 0
 σ21 0
0 0 0 


T

0 0 0 
G ◦ Σ =  σ31 0

 0 σ42 σ43 0 0 
0
0 σ53 0 0
Example (cont’d)
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Hence the customer and supplier betas in this network are
σ12 x2 + σ13 x3
σ24 x4


βc = [G ◦ Σ] X =  σ34 x4 + σ35 x5

0

0
0
σ21 x1

h
i

T
σ31 x1
βs = G ◦ Σ X = 
 σ x +σ x
42 2
43 3
σ53 x3


βc1
  βc2
 
 =  βc3
  β
c4
βc5


βs1
  βs2
 
 =  βs3
  β
s4
βs5











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Other things being equal (assuming positive return covariances), for
company i, there are three aspects that contribute to higher βci (or
βsi ):
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it has more customers (or suppliers);
its customers (or suppliers) have larger market capitalizations;
it has larger return covariances with its customers (or suppliers).
Hence, customer and supplier betas can be considered the summary
of a company’s overall status of customer and supplier relations,
respectively.
Customer and Supplier Beta vs. CAPM Beta
I
The CAPM beta indicates an asset’s return covariance with the
entire market regardless of whether there are connections between
this asset and other assets in the market;
I
Our betas are supported by real customer-supplier relations – they
summarize each company’s return covariances with its trading
partners only.
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Under two assumptions, the relationship between the CAPM beta
and our betas can be demonstrated by a decomposition.
I
First, assume that there are n companies in the network and their
stocks are the only assets in the market. Thus, Σm = Σ and
Xm = X .
I
Second, assume that there is no self-loop or bilateral linkage in the
network.
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Under these two assumptions, the CAPM beta can be decomposed
into several components, including the customer and supplier betas:
β =ΣX
1
2
σm
= (G ∗ ◦ Σ) X
1
2
σm
1
G + G T + G u + In ◦ Σ X 2
σm
1
= (G ◦ Σ) X + G T ◦ Σ X + (G u ◦ Σ) X + (In ◦ Σ) X 2
σm
*
1
= βc + βs + βu + Var
2
σm
=
where

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

G∗ = 

1
1
..
.
1
1
..
.
···
···
..
.
1
1
..
.



 is an n × n matrix of 1;

1 1 ··· 1
In is the identity matrix of size n;
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G u = G ∗ − G − G T − In captures the lack of a customer-supplier
relationship between companies, that is, companies that are
unconnected;
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βu captures each company’s weighted average return covariances
with companies that are neither its customers nor suppliers, and the
weights applied are the relative market capitalization of the
companies that are neither its customers nor suppliers; and
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Var captures each company’s weighted return variance, and the
weight applied to each company is the relative market capitalization
of that company.
*
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Implicitly, the CAPM beta contains an “adjacency matrix” with all
the entries being one.
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In this sense, the CAPM beta does not utilize the specific structure
of the customer-supplier network.
By performing this decomposition, we observe that the return
covariance between a company and the market portfolio captured by
the CAPM beta originates from several sources: a company’s return
covariances with its customers, suppliers, and unconnected
companies and its own return variance.
Resilience to the Financial Crisis in Customer-Supplier
Networks
I
Using data on North American public companies, we explore how a
company’s βc and βs in the pre-crisis period help to explain its
resilience to financial crisis as measured by stock returns.
I
We study the financial crisis of 2008-2009.
Resilience to the Financial Crisis in Customer-Supplier
Networks
I
The main cross-sectional regression is
r¯icr
− r¯ipr = δ0 + δ1 βci + δ2 βsi
pr
pr
pr
cr
cr
cr
+ δ3 bˆmi
+ δ4 bˆSMBi
+ δ5 bˆHMLi
+ δ6 bˆmi
+ δ7 bˆSMBi
+ δ8 bˆHMLi
+ i
I
(5)
Where
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r¯icr is the time-series average of monthly excess returns for company
i during the crisis period (i.e., year 2008-2009), r¯ipr is the time-series
average of monthly excess returns for company i during the
pre-crisis period, r¯icr − r¯ipr is hence the difference between these two
averages for company i.
one βc and one βs are constructed for the pre-crisis period; βci and
βsi are the ith entry from the n × 1 vector βc and βs , respectively.
Fama-French Three-Factor Model - Rationale for the
Control Variables
I
The Fama-French three-factor model (Fama and French, 1992,
1996) postulates that the expected return on an asset is explained
by the sensitivity of its return to three factors:
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(i) the excess return on the market portfolio (m);
(ii) the difference between the returns on two portfolios – a portfolio
of small stocks and a portfolio of large stocks (SMB portfolio); and
(iii) the difference between the returns on two portfolios – a portfolio
of high book-to-market stocks and a portfolio of low book-to-market
stocks (HML portfolio).
Fama-French Three-Factor Model – Rationale for the
Control Variables
I
Specifically, the three factor sensitivities of asset i, bmi , bSMBi , and
bHMLi , are the slope coefficients in the time-series regression
rit − rft = αi + bmi (rmt − rft ) + bSMBi rSMBt + bHMLi rHMLt + it (6)
where rit is the rate of return on asset i at time t, rft is the risk-free
rate of interest at time t, rmt is the rate of return on the market
portfolio at time t, rSMBt and rHMLt are the rates of return at time t
on the SMB and HML portfolios, respectively.
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Their main result states that the sensitivity of an asset’s return
to the three factors provides a simple but powerful
characterization of the cross-section of average stock returns.
Fama-French Three-Factor Model - Rationale for the
Control Variables
I
Recall the main cross-sectional regression
r¯icr − r¯ipr = δ0 + δ1 βci + δ2 βsi
pr
pr
pr
cr
cr
cr
+ δ3 bˆmi
+ δ4 bˆSMBi
+ δ5 bˆHMLi
+ δ6 bˆmi
+ δ7 bˆSMBi
+ δ8 bˆHMLi
+ i
I
pr ˆpr
Using monthly data from the pre-crisis period, bˆmi
, bSMBi and
pr
ˆ
bHMLi for each company i are estimated from Equation (6).
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pr ˆpr
According to the Fama-French three-factor model, bˆmi
, bSMBi and
pr
bˆHMLi explain part of the cross-sectional variation in average stock
returns during the pre-crisis period.
cr ˆcr
cr
Similarly, bˆmi
, bSMBi and bˆHMLi
are constructed using crisis period
data – they would capture part of the cross-sectional variation in
average stock returns in the crisis period.
Data
I
We use data on the North American public companies; our full
sample is from January 2003 to December 2009.
I
According to the U.S. Statement of Financial Accounting Standards
(SFAS) No.131, public companies are required to report those
customers that account for at least 10% of their total yearly sales.
This information is contained in the Compustat Customer Segment
files, which are used to construct the G matrices.
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Companies’ monthly total returns and annual total market values are
the Compustat item TRT1M and mkvalt, respectively.
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The monthly returns on risk-free assets and the Fama-French three
factors are obtained from Kenneth French’s Data Library.
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The returns are all in percentages.
Summary Statistics
Mean
Std. Dev.
Min.
Max.
N
r¯cr − r¯pr
-1.452
2.054
-11.011
3.882
714
βc
0.057
0.156
-0.235
1.351
714
βs
0.005
0.039
-0.013
0.817
714
pr
bˆm
0.965
0.579
-0.830
3.475
714
pr
bˆSMB
pr
bˆHML
0.562
0.789
-1.955
5.138
714
0.122
0.846
-4.72
2.647
714
cr
bˆm
1.022
0.566
-0.656
3.084
714
cr
bˆSMB
0.506
0.98
-2.691
4.755
714
cr
bˆHML
-0.104
0.905
-3.264
5.016
714
Histogram of the Dependent Variable
150
100
r7ipr : 2003-2007
50
0
-10
-8
-6
-4
-2
0
2
4
6
8
10
Return in Percentage
150
100
r7icr : 2008-2009
50
0
-10
-8
-6
-4
-2
0
2
4
6
-4
-2
0
2
4
6
8
10
8
10
80
60
r7icr ! r7ipr
40
20
0
-10
-8
-6
Figure 1: Histogram of average monthly excess returns. r¯icr − r¯ipr is the
regressand in the main cross-sectional regression. The returns are in percentages. The
upper, middle and lower figure depict the histogram of r¯ipr , r¯icr and r¯icr − r¯ipr ,
respectively. The sample size is 714 companies.
Table 1: Resilience to the Financial Crisis as Measured by Stock Returns
(1)
βc
(2)
1.0396∗
(0.0904)
4.1774∗∗
(0.0148)
βs
pr
bˆm
0.2378
(0.1685)
−0.0055
(0.9597)
−0.1789
(0.1016)
−0.4978∗∗∗
(0.0027)
0.0659
(0.5003)
0.2586∗∗
(0.0103)
−1.1543∗∗∗
(0.0000)
pr
bˆSMB
pr
bˆHML
cr
bˆm
cr
bˆSMB
cr
bˆHML
−2.6265∗∗∗
(0.0000)
Intercept
R¯ 2
n
∗
0.00
1048
p < 0.1;
∗∗
p < 0.05;
0.05
714
∗∗∗
(3)
1.8886∗∗∗
(0.0001)
0.4504
(0.4097)
0.1074
(0.5389)
−0.0838
(0.4474)
−0.1730
(0.1084)
−0.5588∗∗∗
(0.0007)
0.0770
(0.4277)
0.2664∗∗∗
(0.0089)
−1.0371∗∗∗
(0.0000)
0.06
714
p < 0.01
Regression Results
I
We observe asymmetric effects of relations on the customer and
supplier side – in column (3) (main regression with full set of control
variables), the coefficient on βc is positive and statistically
significant, but the coefficient on βs is not statistically significant.
I
This result is generally robust to different choices of pre-crisis
period, which are consecutive subsets of the years 2003 to 2007.
Regression Results
I
Recall that customer and supplier beta are a summary of the overall
status of a company’s customer and supplier relations, respectively.
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“Stronger” and more “robust” relations with customer (or suppliers)
is characterized by having more customers (or suppliers) that are
larger companies and stronger cross-sectional dependence (i.e.,
larger positive return covariance) with the customers (or suppliers).
I
The regression results imply that, from the perspective of an
individual company, relations with downstream customers have more
significant implications than relation with upstream suppliers.
Regression Results
I
During a financial crisis, it becomes difficult to retain customers.
Hence a “robust” customer relationship in the pre-crisis period is
important for a company to survive a crisis, which explains the
positive sign and the statistical significance of the coefficient on βc .
I
However, in a crisis, it is relatively easy to retain suppliers, because
“willingness to buy” is always welcomed. Hence a “robust”
relationship with suppliers in the pre-crisis period is not crucial for a
company to survive a crisis, which explains the statistical
insignificance of the coefficient on βs .
Application of the Customer Beta
I
Customer beta can explain a company’s resilience to the financial
crisis 2008-2009, as measured by stock returns.
I
Investors or portfolio managers could construct customer beta when
conducting risk or stress analysis to gain insights into the relative
negative impact of a potential financial crisis on a stock’s
performance.
I
Specifically, the customer betas of stocks of interest should be
constructed and ranked from high to low by magnitude, with a
higher rank indicating more resilience to a crisis as measured by
stock returns.
I
This is an innovative way of conducting stress analysis in the sense
that it utilizes information contained in the customer-supplier
network.
I
Moreover, the application of customer beta can be incorporated into
existing approaches to portfolio selection as an additional dimension
or perspective.
I
For example, consider the single-period mean-variance (MV) model
of Markowitz (1952) with no risk-free asset, to find a portfolio on
the MV-efficient frontier, solve
N
N X
X
min
x1 ,x2, ...,xN
xi xj σij
i=1 j=1
subject to
N
X
xi µi = a
i=1
N
X
xi = 1
i=1
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The customer beta, which captures a stock’s relative resilience to a
crisis, can be incorporated into the above problem as an additional
constraint.
I
For instance, after stocks are ranked by the magnitude of customer
beta, only stocks that are above a certain threshold (e.g., 25-percent
quantile) can be included in the portfolio.
I
By enforcing such a constraint, only securities that are relatively
more resilient to potential crisis are used to construct the
MV-efficient frontier.
Higher-Order Linkages – Powers of Adjacency Matrix
I
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G captures the first-order customer linkages.
G k captures the kth-order customer linkages.
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G k ij is equal to the number of walks of length k from node i to
node j.
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a walk from node i to node j of length k is a succession of k links
beginning at i and ending at j.
A similar interpretation applies to the transpose of G , that is, (G T )k
captures kth-order supplier linkages.
Example (cont’d)
v1
v2
v3
v4



G =


2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
v5




 3 
G =




0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0






Effects from Higher-Order Linkages
I
To investigate the effects from higher-order linkages, we construct
βc and βs that correspond to each order of linkages:
βck = G k ◦ Σ X
βsk = (G T )k ◦ Σ X
(7)
(8)
where k = 1, 2, ..., K .
Effects from Higher-Order Linkages
I
The following cross-sectional regression is conducted:
cr
pr
r¯i − r¯i
=
δ0 + δ1 βc1i + δ2 βc2i + δ3 βc3i + δ4 βc4i + δ5 βs1i + δ6 βs2i + δ7 βs3i + δ8 βs4i
pr
pr
pr
+δ9 bˆmi + δ10 bˆSMBi + δ11 bˆHMLi
cr
cr
cr
+δ12 bˆmi + δ13 bˆSMBi + δ14 bˆHMLi + i
(9)
Table 2: Effects from Higher-Order Linkages
βc1
βc2
βc3
βc4
βs1
βs2
βs3
βs4
pr
bˆm
pr
bˆSMB
pr
ˆ
bHML
cr
bˆm
cr
bˆSMB
bˆcr
1.0717∗
−0.9546
5.5600∗
7.7537∗∗∗
10.5179∗∗∗
−24.0929
−408.1975
32210.1572
HML
−2.6286∗∗∗
Intercept
¯2
R
n
∗
0.2378
−0.0055
−0.1789
−0.4978∗∗∗
0.0659
0.2586∗∗
−1.1543∗∗∗
0.00
1048
p < 0.1;
∗∗
p < 0.05;
0.05
714
∗∗∗
1.9800∗∗∗
−1.1802
4.2785
2.6617
1.9461
−6.4654
−35.5332
3162.1340
0.1103
−0.0736
−0.1778
−0.5766∗∗∗
0.0705
0.2603∗∗
−1.0198∗∗∗
0.06
714
p < 0.01
Effects from Higher-Order Linkages – Regression Results
I
The coefficient on βc1 is the only one that is consistently positive
and statistically significant in the main regression with the full set of
control variables (i.e. column (3)).
I
This result is robust to different choices of pre-crisis period that are
consecutive subsets of 2003-2007.
I
This implies that a company’s weighted average return covariances
with its higher-order or indirect trading partners are not important in
explaining this company’s resilience to the financial crisis of
2008-2009 as measured by stock returns.
Conclusions
I
Under certain assumptions, the CAPM beta can be decomposed into
several components, including the customer and supplier betas.
I
We find asymmetric effects on the customer and supplier sides – for
a company to survive a financial crisis, relations with suppliers
during the pre-crisis period are not as important as having “robust”
relations with customers.
I
This result provides firms with useful guidelines on managing
relations with trading partners; that is, more attention should be
devoted to downstream customers.
Conclusions
I
Investors or portfolio managers could construct customer beta when
conducting risk or stress analysis to gain insights into the relative
negative impact of a potential financial crisis on a stock’s
performance.
I
Moreover, the application of customer beta can be incorporated into
existing approaches to portfolio selection as an additional dimension
or perspective.
I
As measures or “indices” containing useful information of the
customer-supplier network, our betas could potentially be applied in
other areas as well, which should be explored in future studies.
References
I Acemoglu, D., V. M. Carvalho, A. Ozdaglar, and A. Tahbaz-Salehi (2012). The
network origins of aggregate fluctuations. Econometrica 80 (5), 1977-2016.
I Allen, F. and A. Babus (2009). Networks in finance. Networks in finance,
Chapter 21, Network-based Strategies and Competencies, Edited by Paul
Kleindorfer and Jerry Wind.
I Allen, F. and D. Gale (2000). Financial contagion. Journal of Political Economy
108 (1), 1-33.
I Fama, E. F. and K. R. French (1992). The cross-section of expected stock
returns. Journal of Finance 47 (2), 427-465.
I Fama, E. F. and K. R. French (1996). Multifactor explanations of asset pricing
anomalies. Journal of Finance 51 (1), 55-84.
I Freixas, X., B. Parigi, and J. C. Rochet (2000). Systemic risk, interbank
relations and liquidity provision by the central bank. Journal of Money, Credit
and Banking 32 (3), 611-638.
References
I Hertzel, M. G., Z. Li, M. S. Officer, and K. J. Rodgers (2008). Inter-firm
linkages and the wealth effects of financial distress along the supply chain.
Journal of Financial Economics 87 (2), 374-387.
I Lintner, J. V. (1965). The valuation of risk assets and the selection of risky
investments in stock portfolios and capital budgets. Review of Economics and
Statistics 47, 13-47.
I Markowitz, H. (1952). Portfolio selection. Journal of Finance 7, 77–91.
I Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under
conditions of risk. Journal of Finance 19, 425-442.
I Van Mieghem P. (2010). Graph spectra for complex networks. Cambridge
University Press, Cambridge.

Resilience to the Financial Crisis in Customer

Transcription

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