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 four U.S. Treasury bonds:

An 8.5%, 13- year bond that's priced at $1,083.84 to yield 7.47%

A 7.875%, 15-year bond that's priced at $1,024.12 to yield 7.60%

A 20-year stripped Treasury that's priced at $205.99 to yield 8.22%

A 24-year, 7.5% bond that's priced at $957.53 to yield 7.90%

Find the duration and the modified duration of each bond. Assume that coupon payments are made annually.

Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the four U.S Treasury bonds.

Find the duration of the portfolio if Elliot puts $360,000 each into bonds a and c and $140,000 each into bonds b and d.

Which portfolio B or C should Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as possible? Explain.