Question

Your pension fund is invested in $40 million worth of bonds with a duration of 5.5 years and $60 million worth of bonds with a duration of 8 years. The "target date" (the date that the fund needs to pay its contributors) is 6.967 years from now. To become duration-matched, the fund needs to shift how much of its money from 8-year duration bonds into 5.5-year duration bonds? Round your answer to the nearest dollar.

Answer 1

Current duration of bond portfolio = weight of 5.5 year bond x duration + weight of 5.5 year bond x duration

Current duration = 0.4 * 5.5 + 0.6 * 8 = 7 Years

Since the required duration of 6.967 is less than the current duation of 7 years

we will have to sell 8 year bond and buy 5.5 year bond

Let the weight of 5.5 years duration bond be x

then weight of 8 years duration bond = (1-x)

to get the target duration of 6.967 years

(x*5) + (1-x)*8 = 6.967

5x + 8 - 8x = 6.967

3x = 1.033

x = 0.34433

1-x = 0.6557

Total Portfolio of 5.5 years and 8 year bond = 40+60 = 100 million

for targer duration of 6.967 years

Amount of 5.5 years duration bond = 100 * 0.34433 = 34.43 million

Amount of 8 years duration bond = 100 * 0.6557 = 65.57 million

Therefore amount of 8 year bond to be sold = (65.57-60) = 5.57 million

Therefore amount of 5.5 year bond to be bought = (40-34.43) = 5.57 million