Investment Management

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  • Topic: Bond, Zero-coupon bond, Yield curve
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  • Published : March 23, 2013
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UNIVERSITY OF TEXAS AT DALLAS SCHOOL OF MANAGEMENT FIN6310: INVESTMENT MANAGEMENT SOLUTIONS TO PROBLEM SET #1 PROF. ARZU OZOGUZ SPRING 2013

1. Calculate the value of the following two bonds. Assume that coupon payments are made semi-annually and that par value is $1,000 for both bonds. Coupon rate Time to maturity Yield-to-maturity Bond A 5% 5 yrs 7.2% Bond B 5% 25 yrs 7.2%

Recalculate the bonds’ values if the yield to maturity changes to 9.4%. Which bond is more sensitive to the changes in the yield? Will this always be the case? When the yield-to-maturity is 7.2%, the bond prices are, respectively, 1 1 1.036 0.036 1 1.036 0.036 1 1.047 0.047 1 1.047 0.047 25 1000 1.036 1000 1.036 908.98

1

25

746.58

When the yield-to-maturity is 9.4%, the bond prices are, respectively, 1 25 1000 1.036 1000 1.047 827.62

1

25

579.01

Price of bond A decreases by 8.95%, while price of bond B drops by 22.45%. The longer term bond is more sensitive to a given change in the discount rate. This will always be the case. Mathematically, there are more terms in the equation for the longer-term bond that are influenced by the discount rate. Practically speaking, your money is tied up longer with a longer term bond and so you will experience greater capital losses and gains when interest rates change. 2. A bond with a coupon rate of 4.7% is priced to yield 6.30%. Coupon is paid is semi-annually; the par value is $1,000. The bond has 5 years remaining until maturity. Assuming that market rates stay the same over the next five years, calculate the value of the bond at the beginning of

each year and the amount of change in the bond’s value from year to year. Describe the behavior of the bond’s value over time. At t = 0, at issue the price will be 1 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 1 1.0315 0.0315 23.5 1000 1.0315 932.28

At the end of year 1, the price becomes 1 23.5 1000 1.0315 1000 1.0315 1000 1.0315 1000 1.0315 944.20

1

23.5

956.88

1

23.5

970.37

1

23.5 1000

984.73

The price change from year to year is ∆ ∆ ∆ ∆ ∆ 11.92 12.68 13.49 14.36 15.27

The bond is selling at a discount today; its price will rise to move toward par value at maturity. The change in price increases as it gets closer to maturity. 3. Suppose that you purchased a 20-year bond that pays an annual coupon of $40 and is selling at par. Calculate the one –year holding period return for each of these three cases. a. The yield-to-maturity is 5.5% one year from now. If the yield-to-maturity is 5.5% one year from now, the bond will be selling for 1 1 1000 1.055 40 825.89 1.055 0.055 Hence, the holding-period-return (HPR) is: 825.89 40 1000 13.41% 1000

b. The yield-to-maturity is the same one year from today as it is today.

In this case, the bond price will remain at par and therefore the holding period return equals to coupon rate 4% c. The yield-to-maturity is 2.5% one year from now. 1 1000 1.025 40 1224.68 1.025 0.025 Hence, the holding-period-return (HPR) is: 1224.68 40 1000 26.47% 1000 1 4. Plot the yield curve implied by the data in the following table. Time to maturity 3 months 6 months 1 year 2 years 5 years 10 years 15 years 20 years Yield-tomaturity 2.40% 2.60% 3.00% 4.30% 4.80% 5.70% 6.40% 5.20%

Based on the Expectations Hypothesis, what does the yield curve tell us about short-term rates 5 years from now? What does it tell us about short rates 15 years from now and 20 years from now?

Since the yield curve is upward sloping through the fifth year, investors expect that short term rates will be higher during that period than they are today. That is, they expect the 3-month rate to be higher than 2.4% when five years have passed.

They also expect short term rates to be higher than current rates in 15 years. This is reflected in the slope of the yield curve which is positive through year 15. However, the expectation is that after 15 years, short term rates will begin to...
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