An insurance company must make a payment of $16,105 in five years. The market interest rate...

An insurance company must make a payment of $16,105 in five years. The market interest rate is 10%, so the present value of the obligation is $10,000. The company's portfolio manager wishes to fund the obligation using three-year zero-coupon bonds and perpetuities paying annual coupons. What's the percentage weight for perpetuities in the hedging portfolio?

75%

50%

25%

Can't be calculated.

Solutions

Expert Solution

The duration of perpetuity is 1.1/0.1 = 11 years

Let the weight of ZCB be W, thus

(W*3)+ [(1-W)*11] = 5

3W +[(11-11W] =5

3W +11 - 11W =5

-8W = -6

W = 6/8 = 75%

Thus weight of perpetuity = 25%

jeff jeffy answered 2 years ago

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