Question

URGENT!! You are managing a fund with obligations to make payments of $1.3 million, $2.3 million, and $1.3 million at the end of each of the next three years, respectively. The annual interest rate is 12%. You wish to immunize your position by investing in one-year zero-coupon bonds and perpetuities. How much you should allocate to the one-year zero-coupon bonds and perpetuities to fund your plan?

Answer 1

Present Value of obligations =

=

= 3,919,574.53  

Duration of Payments =

= 7603749.09 /  3,919,574.53

= 1.94 years _ _ _ (A)

let the weight in ZCB be x, weight in perpetuity will be 1-x

Duration of Zero coupon Bond 1

Duration of perpetuity = 1.12 / 0/12 = 9.33333333333

Equating Equation A with WEighted duration of ZCB and Perpetuity

1.94 = Duration of ZCB * Weight of ZCB + Duration of perpetuity * Weight of perpetuity

1.94 = 1 * x + 9.33333333333 * (1-x)

1.94 = 1 * x + 9.33333333333 - 9.33333333333 * x

1.94 = 9.33333333333 - 8.33333333333 * x

x = (9.33333333333 - 1.94) / 8.33333333333

x = 0.8871 OR 88.72%

Weight of ZCB = 88.71%

Weight of Perpetuity = 100% - 88.71%

= 11.28%