COMM 324
INVESTMENTS AND PORTFOLIO MANAGEMENT
ASSIGNMENT 3
Due: November 14
1. A newly issued bond pays its coupons annually. Its coupon rate is 5%, its maturity is 20
years, and its yield to maturity is 8%
a. Find the holding period return for a one year investment period if the bond is
selling at a yield to maturity of 7% by the end of the year.
b. If you sell the bond after one year, what taxes will you owe if the tax rate on
interest income is 40%, and the tax rate on capital gain income is 30%. The bond
is subject to original issue discount (OID) tax treatment.
c. What is the after tax holding period return on the bond?
d. Find the realized compound yield before taxes for a two-year holding period
return, assuming that (1) you sell the bond after two years; (2) the bond yield is
7% at the end of the second year; and (3) the coupon can be reinvested for one
year at a 3% interest rate.
e. Use tax rates in part (b) to compute the after-tax two-year realized compound
yield. Remember to take account of OID tax rules.
2. A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five
years at a call price of $1,100. The bond sells at a yield to maturity of 7%, or 3.5% per
half-year.
a. What is the yield to call? At what yield to maturity would you expect the bond to
be called after five years?
b. What is the yield to call if the call price is only $1,050?
c. What is the yield to maturity if the call price is $1,100, but the bond can be called
in two years instead of five years?
3. You observe the following term structure
Effective Annual Yield
1-year Zero
6.1%
2-year Zero
6.2%
3-year Zero
6.3%
4-year Zero
6.4%
a. If you believe that the term structure next year will be the same as today’s, will
the one-year or the four-year zeros provide a greater expected one-year return?
b. What if you believe in the expectation hypothesis?
4. Suppose that a one-year zero-coupon bond with a face value of $100 currently sells at
$94.34, while a two-year zero sells at $84.99. You are considering the purchase of a twoyear maturity bond making annual coupon payments. The face value of the bond is $100,
and the coupon rate is 12% per year.
a. What is the yield to maturity of the two year zero? The two-year coupon bond?
b. What is the forward rate for the second year?
c. If the expectation hypothesis is accepted, what are (1) the expected price of the
coupon bond at the end of the first year and (2) the expected holding period
return on the coupon bond over the first year (ignore taxes)?
d. Will the expected rate of return be higher or lower if you accept the liquidity
preference hypothesis?
5. A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon
payments coming once annually). The bond sells at par.
a. What are the duration and convexity of the bond?
b. Find the actual price of the bond assuming that its yield to maturity immediately
increases from 7% to 8% (with maturity still 10 years)
c. What price would be predicted by the price-duration formula?
d. What price would be predicted by the duration-with-convexity formula?
6. A 30-year bond has a 7% coupon rate, paid annually. It sells today for $867.42. A 20year bond has 6.5% coupon rate, also paid annually. It sells today for $879.50. A bond
market analyst forecasts that in 5 years, 25-year bond will sell at YTM of 8%, and 15year bond will sell at YTM of 7.5%. Because the yield curve is upward sloping, the
analyst believes that coupon will be reinvested in short term securities at a rate of 6%.
What bond offers the higher expected rate of return over the five year period?
7. Assume liabilities of $250, $300, and $450 must be met at the end of year 1, 2, and 3,
respectively. Find a portfolio of bonds listed below that meets these cash outflows.
CF
Bond
A
B
C
Price
950
1000
920
1
50
100
1000
2
1050
100
3
1100