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 $1 million of his inheritance to purchase 4 U.S. Treasury bonds: 1. An 8.55%, 13-year bond that's priced at $1,088.85 to yield 7.47%. 2. A 7.899%, 15-year bond that's priced at $1031.92 to yield 7.54%. 3. A 20-year stripped Treasury (zero coupon) that's priced at $200.05 to yield 8.21%. 4. A 24-year, 7.41% bond that's priced at $956.93 to yield 7.81%. 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 $350,000 each into bonds 1 and 3 and $150,000 each into bonds 2 and 4. d. Which portfoliob or 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? Bond 1: 13 years, 8.55%, priced to yield 7.47%. The duration of this bond is years. (Round to two decimal places.) The modified duration of this bond is years. (Round to two decimal places.) Bond 2: 15 years, 7.899% priced to yield 7.54%. The duration of this bond is years. (Round to two decimal places.) The modified duration of this bond is years. (Round to two decimal places.) Bond 3: 20 years, zero coupon, priced to yield 8.21% The duration of this bond is years. (Round to two decimal places.) The modified duration of this bond is years. (Round to two decimal places.) Bond 4: 24 years, 7.41%, priced to yield 7.81%. The duration of this bond is years. (Round to two decimal places.) The modified duration of this bond is years. (Round to two decimal places.) b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds. The duration of this portfolio is years. (Round to two decimal places.) c. Find the duration of the portfolio if Elliot puts $350,000 each into bonds 1 and 3 and $150,000 each into bonds 2 and 4. The duration of this portfolio is years. (Round to two decimal places.)

Answer 1

If rates are going to go up, the portfolio with lesser duration, ie first portfolio should be selected

Settlement date Maturity date Coupon Yield Duration K M Bond1 Bond2 Bond3 Bond4 12-Apr-20 12-Apr-20 12-Apr-20 12-Apr-20 12-Apr-33 12-Apr-35 12-Apr-40 12-Apr-44 8.55% 7.9% 0.0% 7.4% 7.47% 7.54% 8.21% 7.81% 8.53 9.38 20.00 11.64 =DURATION(12,13,14,15,1,0) =DURATION(K2,K3,K4,K5,1,0) =DURATION(L2,L3,L4,L5,1,0) =DURATION(M2,M3, M4, M5,1,0) 13 15 20 24 8.48 9.34 19.92 11.61 =J6/(1+J5/J8) =K6/(1+K5/8) L6/(1+L5/L8) =M6/(1+M5/M8) 250,000 250,000 250,000 250,000 12.39 =SUMPRODUCT(J6:M6, 11:M11)/SUM(J11:M11) 350,000 150,000 350,000 150,000 13.14 =SUMPRODUCT(16:M6, 13:M13)/SUM(J13:M13) Time to maturity (years) Modified duration Amount invested Duration of Portfolio Amount invested Duration of Portfolio