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 $1million of his inheritance to purchase 4 U.S. Treasury​ bonds:

1. An 8.62%​,​13-year bond​ that's priced at $1,094.61 to yield 7.47%.

2. A 7.771%​, ​15-year bond​ that's priced at $1017.84 to yield 7.57%.

3. A​ 20-year stripped Treasury​ (zero coupon)​ that's priced at $198.90 to yield 8.24%.

4. A​ 24-year, 7.47% bond​ that's priced at $955.08 to yield 7.89%.

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 $380,000 each into bonds 1 and 3 and $120,000each into bonds 2 and 4.

d. Which portfolio—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

Answers to parts (a), (b) & (c) are:

Formulas:

Part (d): If rates are about to increase and price volatility is to be avoided then the lower duration portfolio (i.e. portfolio of part (b)) should be chosen as shorter duration means price volatility is less.

Annual income from portfolio in part (b) = 58,327.66

Annual income from portfolio in part (c) = 48,472.09

(Calculations in the table above)

Portfolio in part (b) should be chosen as it has lower duration and also provides more annual interest income.