An insurance company has invested in the following fixed-income securities:

(a) $10,000,000 of 5-year Treasury notes paying 5 percent interest and selling at par value,

(b) $5,800,000 of 10-year bonds paying 7 percent interest with a par value of $6,000,000, and

(c) $6,200,000 of 20-year subordinated debentures paying 9 percent interest with a par value of $6,000,000.

a. What is the weighted-average maturity of this portfolio of assets?

b. If interest rates change so that the yields on all the securities decrease 1 percent, how does the weighted-average maturity of the portfolio change?

c. Explain the change in the weighted-average maturity of the portfolio if the yields increase 1 percent.

d. Assume that the insurance company has no other assets. What will be the effect on the market value of the company’s equity if the interest rate changes in

(b) and

(c) occur?