Question

Elliot Karlin is a​ 35-year-old bank executive who has just inherited a large sum of money. Having spent several years in the​ bank's investments​ department, he's well aware of the concept of duration and decides to apply it to his bond portfolio. In​ particular, Elliot intends to use $ 1 million of his inheritance to purchase 4 U.S. Treasury​ bonds: 1. An 8.64 % ​, ​13-year bond​ that's priced at $ 1 comma 094.51 to yield 7.49 % . 2. A 7.766 % ​, ​15-year bond​ that's priced at $ 1015.60 to yield 7.59 % . 3. A​ 20-year stripped Treasury​ (zero coupon)​ that's priced at $ 199.28 to yield 8.23 % . 4. A​ 24-year, 7.45 % bond​ that's priced at $ 958.11 to yield 7.84 % . Note that these bonds are semiannual compounding bonds.

a. Find the duration and the modified duration of each bond.

b. Find the duration of the whole bond portfolio if Elliot puts

$ 250,000 into each of the 4 U.S. Treasury bonds.

c. Find the duration of the portfolio if Elliot puts $ 330,000 each into bonds 1 and 3 and $ 170,000 each into bonds 2 and 4.

d. Which portfolio long b-or c should Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as​ possible? Explain. From which portfolio does he stand to make more in annual interest​ income? Which portfolio would you​ recommend, and​ why?

Answer 1

a. 1 - Duration - 8.505 ; Modified Duration - 7.912

2. Duration - 9.39 ; Modified Duration - 8.73

3. Duration - 20 ; Modified Duration - 18.479

4. Duration - 11.61 ; Modified Duration - 10.76

b. Duration of the entire portfolio with equal weights = 0.25* ( 8.505 +9.39+20+11.61) = 12.5

c. WIth unequal weights we have the duration as = 330/1160*( 28.505) + 170/1160*(21) = 11.186

d. Since Elliot wants to reduce his price volatility as much as possible and he speculates on interest going up, he should select portfolio 'b' with a greater duration since that would do both.

For a greater annual income he should put his in portfolio 'b' -

b = 0.25*(8.64+7.76+7.45) = $5.962

c = 330/1160*(8.64) + 170/1160*(11.61) = $4.159

Portfolio b hence would be more reccomended because of its higher duration in rising interest rate environment and gretaer interest income.