Chapter 3: 10-4B (page 329)
A coupon bond paying semi-annual interest is reported as having an ask price of 117% of its $1,000 par value. If the last interest payment was made one month ago and the coupon rate is 6%, what is the invoice price of the bond?
$11, 174.95
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Frank Meyers, CFA, is a fixed-income portfolio manager for a large pension fund. A member of the Investment Committee, Fred Spice, is very interested in learning about the management of fixed-income portfolios. Spice has approached Meyers with several questions. Specifically, Spice would like to know how fixed-income managers position portfolios to capitalize on their expectations of future interest rates.
Meyers decides to illustrate fixed-income trading strategies to Spice using a fixed rate bond and note. Both bonds have semi-annual coupon periods. All interest rate (yield curve) changes are parallel unless otherwise stated. The characteristics of these securities are shown in the following table. He also considers a nine-year floating-rate bond (floater) that pays a floating rate semi-annually and is currently yielding 5%.
Spice asks Meyers about how a fixed-income manager would position his portfolio to capitalize on expectations of increasing interest rates. Which of the following would be the most appropriate strategy?
a. Shorten his portfolio duration.
b. Buy fixed-rate bonds.
c. Lengthen his portfolio duration.
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has a convexity of 150.3 and a modified duration of 11.81 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has a nearly identical modified duration—11.79 years—but considerably higher convexity of 231.2.
a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage of capital loss on each bond? What percentage of capital loss would be predicted by the duration-with-convexity rule?
b. Repeat part ( a ), but this time assume the yield to maturity decreases to 7%.
c. Compare the performance of the two bonds in the two scenarios, one involving an increase in rates, the other a decrease. Based on their comparative investment performance, explain the attraction of convexity.
d. In view of your answer to ( c ), do you think it would be possible for two bonds with equal duration, but different convexity, to be priced initially at the same yield to maturity if the yields on both bonds always increased or decreased by equal amounts, as in this example? Would anyone be willing to buy the bond with lower convexity under these circumstances?
Question: A newly issued bond pays its coupons once a year. 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 when its yield is 7%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains 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, assuming that (i) you sell the bond after two years, (ii) the bond yield is 7% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 3% interest rate.
e. Use the tax rates in part ( b ) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules.
Question: Now suppose the bond in the previous question is selling for 102. What is the bond’s yield to maturity? What would the yield to maturity be at a price of 102 if the bond paid its coupons only once per year?
A member of a firm’s investment committee is very interested in learning about the management of fixed-income portfolios. He would like to know how fixed-income managers position portfolios to capitalize on their expectations concerning three factors influencing interest rates. Assuming that no investment policy limitations apply, formulate and describe a fixed-income portfolio management strategy for each of the following interest rate factors that could be used to exploit a portfolio manager’s expectations about that factor.
( Note: Three strategies are required, one for each listed factor.)
a. Changes in the level of interest rates.
b. Changes in yield spreads across/between sectors.
c. Changes in yield spreads as to a particular instrument.
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