Elliot Karl is a 35-year old bank executive who has just inherit a large amount of money. Having spent several years in the bank's investment department, he is well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, he intends to use $1 million of his inheritance to purchase four US Treasury bonds:
1) An 8.5%, 13-year bond that is priced at $1,045 to yield 7.47%.
2) A 7.875%, 15-year bond that is priced at $1,020 to yield 7.60%.
3) A 20-year zero-coupon stripped treasury that is priced at 202 to yield 8.22%.
4) A 24-year, 7.5% bond that is priced at $955 to yield 7.90%.
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 four U.S. Treasury bonds.
c. Find the duration of the portfolio if Elliot puts $360,000 each into bonds 1 and 3 and $140,000 each into bonds 2 and 4.
d. Which portfolio in b or c question should he 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 make more in annual interest income? Which portfolio would you recommend, and why?