Elliot Karlin is a35-year-old bank executive who has just inherited a large sum of money. Having spent several years in thebank's investmentsdepartment, he's well aware of the concept of duration and decides to apply it to his bond portfolio. Inparticular, Elliot intends to use $1 million of his inheritance to purchase 4 U.S. Treasurybonds:

1. An 8.53%, 13-year bondthat's priced at $1,086.34 to yield 7.48%.

2. A 7.855%, 15-year bondthat's priced at $1026.20 to yield 7.56%.

3. A20-year stripped Treasury(zero coupon)that's priced at $200.05 to yield 8.21%.

4. A24-year, 7.41% bondthat's priced at $954.85 to yield 7.83%.

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 $300,000 each into bonds 1 and 3 and $200,000 each into bonds 2 and 4.

d. Which portfoliob or cshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility aspossible? Explain. From which portfolio does he stand to make more in annual interestincome? Which portfolio would yourecommend, andwhy?

a. The duration and modified duration can be calculated using aspreadsheet, such as Excel. It gives the precise duration measure because it avoids therounding-off errors, which are inevitable with manual calculations.

Bond1: 13years, 8.53%, priced to yield 7.48%.

The duration of this bond is years.(Round to two decimalplaces.)

The modified duration of this bond is years.(Round to two decimalplaces.)

Bond2: 15years, 7.855% priced to yield 7.56%.

The duration of this bond is years.(Round to two decimalplaces.)

The modified duration of this bond is years.(Round to two decimalplaces.)

Bond3: 20years, zerocoupon, priced to yield 8.21%.

The duration of this bond is years.(Round to two decimalplaces.)

The modified duration of this bond is years.(Round to two decimalplaces.)

Bond4: 24years, 7.41%, priced to yield 7.83%.

The duration of this bond is years.(Round to two decimalplaces.)

The modified duration of this bond is years.(Round to two decimalplaces.)

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 decimalplaces.)

c. Find the duration of the portfolio if Elliot puts $300,000 each into bonds 1 and 3 and $200,000 each into bonds 2 and 4.

The duration of this portfolio is years.(Round to two decimalplaces.)

d. Which portfoliothe portfolio in part b or the portfolio in part cshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility aspossible?(Choose the best answerbelow.)

A.

He should invest in the portfolio in part c. The portfolio in part c has a higher duration than the portfolio in part b. If rates are about torise, then it is riskier to invest in the portfolio in part b, because it would be more price volatile than the other portfolio.

B.

He should invest in the portfolio in part c. The portfolio in part b has a higher duration than the portfolio in part c. If rates are about torise, then it is safer to invest in the portfolio in part c, because it would be less price volatile than the other portfolio.

C.

He should invest in the portfolio in part b. The portfolio in part c has a higher duration than the portfolio in part b. If rates are about torise, then it is safer to invest in the portfolio in part b, because it would be less price volatile than the other portfolio.

D.

He should invest in either portfolio. The portfolio in part c has a higher duration than the portfolio part b. If rates are about torise, then it is equally safe to invest in eitherportfolio, because both portfolios would be equally price volatile.