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 8.59%​, 13-year bond​ that's priced at $1,091.27 to yield7.48%.

2. A 7.795%​, 15-year bond​ that's priced at $1019.97 to yield7.57%.

3. A​ 20-year stripped Treasury​ (zero coupon)​ that's priced at$199.67 to yield 8.22%.

4. A​ 24-year, 7.46% bond​ that's priced at $958.15 to yield7.85%.

Note that these bonds are semiannual compounding bonds.

a. Find the duration and the modified durationof each bond.

b. Find the duration of the whole bondportfolio if Elliot puts $250,000 into each of the 4 U.S. Treasurybonds.

c. Find the duration of the portfolio if Elliotputs $300,000 each into bonds 1 and 3 and $200,000 each into bonds2 and 4.

d. Which portfolio dash—b orc —should Elliot select if he thinks rates areabout to head up and he wants to avoid as much price volatility as​possible? Explain. From which portfolio does he stand to make morein annual interest​ income? Which portfolio would you​ recommend,and​ why?

a. The duration and modified duration can becalculated using a​ spreadsheet, such as Excel. It gives theprecise duration measure because it avoids the​ rounding-offerrors, which are inevitable with manual calculations.

Bond​ 1: 13​ years, 8.59%​, priced to yield 7.48%.

The duration of this bond is __ years. Round to two decimal​places.)

The modified duration of this bond is __ years.​ (Round to twodecimal​ places.)

Bond​ 2: 15​ years, 7.795% priced to yield 7.57%.

The duration of this bond is ___ years.​(Round to two decimal​places.)

The modified duration of this bond is ___ years.(Round to twodecimal​ places.)

Bond​ 3: 20​ years, zero​ coupon, priced to yield 8.22%.

The duration of this bond is __ years.​(Round to two decimal​places.)

The modified duration of this bond is ___ years.​(Round to twodecimal​ places.)

Bond​ 4: 24​ years, 7.46%​, priced to yield 7.85%.

The duration of this bond is __ years.(Round to two decimal​places.)

The modified duration of this bond is ___ years.(Round to twodecimal​ places.)

b. Find the duration of the whole bondportfolio if Elliot puts $250,000 into each of the 4 U.S. Treasurybonds.

The duration of this portfolio is __ years.(Round to twodecimal​ places.)

c. Find the duration of the portfolio if Elliotputs $300,000 each into bonds 1 and 3 and $200,000 each into bonds2 and 4.

The duration of this portfolio is __ years.(Round to twodecimal​ places.)