Problem Set No. 2

Economics 330 – Money and Banking
Problem Set No. 2 (Risk and Return)
Spring 2015
Neri
Dr. John
Due at the beginning of class on February 26, 2015
1) Congratulations! You just won the lottery! You can elect to receive your prize in one
of four payment streams:
(i) $1,000,000 now
(ii) $1,500,000 at the end of five years
(iii) $60,000 per year in perpetuity, with payments made at the end of each year (so your
first payment comes one year from today)
(iv) $150,000 per year for the next ten years, with payments made at the end of each year
(so your first payment comes one year from today)
Suppose the annual interest rate is 5%, calculate the present value of each of the four
payment options (i.e., in today’s dollars). Rank for four options from most to least
valuable. You can use Excel or a calculator to solve this, but you must show the formulas
you use.
2) Suppose you buy four assets on February 1, 2011, hold them for one year, and then
resell them on February 1, 2012 if they have not matured. The four assets are:
i. a one year discount bond with face value of $1,000.
ii. a two year discount bond with face value of $1,000.
iii. a ten year coupon bond with a face value of $1,000 and a coupon
rate of 10%.
iv. A consol bond with an annual coupon of $100.
(a) Calculate the price for each of the four assets on February 1, 2011 if the initial
interest rate on that date is 10 %. [Hint about coupon bond: Think about the price
of the coupon bond if the interest rate is equal to the coupon rate]
(b) Calculate the price for each of the four assets after one year on February 1, 2012
assuming that the interest rate has changed to 7.13 %. Do the same for 8.48%,
10%, 11.75% and 13.81% (Look familiar?) [Hint: After one year, the 2 year and
10 year bonds have one year less time remaining to maturity. And, the one-year
bond has no price because it matured]
[You do not have to use the following table, but its a good way to think about
how to present your results for parts (b) and (c)]
Interest Rate
7.13%
8.48%
10%
11.75
13.81%
1-Yr Discount
Bond
2-Yr Discount
Bond
10-Yr Coupon
Bond
Consol
(c) Compute the rate of return from holding each of the four assets for one year,
under each of the five interest rate scenarios. [Remember to include capital
gains/losses and coupon payments]
(d) Which asset's rate of return is most sensitive to shocks to interest rates? Which
asset is least sensitive to interest rate risk? Rank the four assets in terms of
exposure to interest rate risk.
3) Three zero-coupon bonds with face values of $10,000 are currently selling for the
following amounts:
Bond
Years to
Price
Maturity
A
1
$9804
B
2
$9427
C
3
$8978
Calculate the yield to maturity for each of the three bonds.
4) Describe how the following shocks would affect BOTH BOND PRICES AND
INTEREST RATES, using the supply and demand framework. You will need to figure
out which curve shifts, and in which direction. Use properly labeled graphs to illustrate
your answers. Don't just say "such and such a curve shifts"; explain why the curve shifts.
(a) Technological advances make it easier to match buyers and sellers in the
corporate bond market, making corporate bonds more liquid. Describe the impact
on both the corporate bond market and the Treasury bond market, assuming that
treasuries were already extremely liquid and thus did not benefit from the
technological advance. (Have a different picture for each market)
(b) President Obama proposes in March 2015 cutting Social Security benefits for
future retirees, while leaving benefits for current retirees and payroll tax rates
alone. If adopted, this proposal will not reduce the current budget deficit, but will
reduce expected future budget deficits. Describe the effect of this announcement
in March 2015 on the market for short-term treasury bills; the market for longterm treasury bonds; and the market for long-term corporate bonds. (Assume that
the markets believe that this proposal will be adopted).
5) Suppose the interest rate for a 1-year $1000 Treasury bond is 1%.
a. What will be the price and yield for a 1-year BB-rated corporate bond if the probability
of default is 6 percent.
b. What is the yield spread between the two bonds.