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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 topurchase 4 U.S. Treasury? bonds:
1. An 8.69 %?, ?13-year bond? that's priced at $ 1 comma 100.37 toyield 7.47 %.
2. A 7.821 %?, ?15-year bond? that's priced at $ 1024.08 to yield7.55 %.
3. A? 20-year stripped Treasury? (zero coupon)? that's priced at $198.52 to yield 8.25 %.
4. A? 24-year, 7.46 % bond? that's priced at $ 957.11 to yield 7.86%.
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 comma 000 into each of the 4 U.S. Treasury bonds.
c. Find the duration of the portfolio if Elliot puts $ 380 comma000 each into bonds 1 and 3 and $ 120 comma 000 each into bonds 2and 4.
d. Which portfoliolong dashb or clong dashshould Elliot select ifhe thinks rates are about to head up and he wants to avoid as muchprice volatility as? possible? Explain. From which portfolio doeshe stand to make more in annual interest? income? Which portfoliowould you? recommend, and? why?