Elliot Karlin is a? 35-year-old bank executive who has justinherited a large sum of money. Having spent several years in the?bank's investments? department, he's well aware of the concept ofduration 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 8.68%?,?13-year bond? that's priced at $1,099.55 to yield7.47%.

2. A 7.852%?,?15-year bond? that's priced at $ 1028.65$to yield7.53 %.

3. A? 20-year stripped Treasury? (zero coupon)? that's priced at$198.52 to yield 8.25%.

4. A? 24-year, 7.43%bond? that's priced at $955.96 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 $350,000each into bonds 1 and 3 and $150,000

each into bonds 2 and 4.

d. Which portfolio —b or c—should Elliot select if he thinksrates are about to head up and he wants to avoid as much pricevolatility as? possible? Explain. From which portfolio does hestand to make more in annual interest? income? Which portfoliowould you? recommend, and? why?

a. The duration and modified duration can be calculated using a?spreadsheet, such as Excel. It gives the precise duration measurebecause it avoids the? rounding-off errors, which are inevitablewith manual calculations.