Question

a. A 10-year 5% coupon bond has a yield of 8% and a duration of 7.85 years. If the bond yield increases by 60 basis points, what is the percentage change in the bond price?

b. Alpha Insurance Company is obligated to make payments of $2 million, $3 million, and $4 million at the end of the next three years, respectively. The market interest rate is 8% per annum.

i. Determine the duration of the company’s payment obligations.

ii. Suppose the company’s payment obligations are fully funded and immunized using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds the company will hold in the portfolio.

Answer 1

a

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =10

Bond Price =∑ [(5*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^10

k=1

Bond Price = 798.7

New bond price @ YTM =8.6 using duration

Mod.duration prediction = -Mod. Duration*Yield_Change*Bond_Price

=-7.85*0.006*798.7

=-37.61877

New bond price = bond price+Modified duration prediction

=798.7+-37.61877

=761.08

%age change = (new price/old price)-1

=(761.08/798.7-1) = -4.71%