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:

a. An 8.5%, 13-year bond that’s priced at $1,045 to yield 7.47%

b. A 7.875%, 15-year bond that’s priced at $1,020 to yield 7.60%

c. A 20-year stripped Treasury that’s priced at $202 to yield 8.22%

d. A 24-year, 7.5% bond that’s priced at $955 to yield 7.90%

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

2. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds.

3. Find the duration of the portfolio if Elliot puts $360,000 each into bonds a and c and $140,000 each into bonds b and d.

4. 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?