One (Portfilio A) will require a payment of $100,000,000 at the end of 5 years (

Question

One (Portfilio A) will require a payment of $100,000,000 at the end of 5 years (target date) while the other (Portfolio B) will require a payment of $100,000,000 at the end of 10 years (target date). You will assume the following information:

Portfolio A: Funded by a collection of corporate bonds with an 8% coupon rate.

Portfolio B: Funded by a collection of corporate bonds with a 6% coupon rate.

The goal is to develop an immunized dedicated portfolio by using duration matching and employing dynamic immunization techniques, rebalancing at the end of 2 years for portfolio A and 4 years for portfolio B.

Explanation / Answer

Answer:

Part A is starting with $ 100,000,000 and the required return is 8.00%, the required terminal value must equal P1(1+s/2)2T, where:

P1 = initial portfolio value

s = safety net rate of return

T = years in the investment horizon

= (100,000,000) x (1+.08/2)(2x2) = $ 65,610,000

Part A immunized rate of return:

Required initial portfolio value = (Required terminal value) / (1+i/2)2T where i is the immunized rate of return

= $ 65,610,000 / (1 + 0.08/2)2x2 = $ 43,046,721

therefore Part A has an initial safety margin of $100,000,000 – $ 387,793,112 = $56,953,279.

Part B is starting with $ 100,000,000 and the required return is 6.00%, the required terminal value must equal P1(1+s/2)2T, where:

P1 = initial portfolio value

s = safety net rate of return

T = years in the investment horizon

= (100,000,000) x (1+.06/2)(4x2) = $ 16,777,216

Part A immunized rate of return:

Required initial portfolio value = (Required terminal value) / (1+i/2)2T where i is the immunized rate of return

= $ $ 16,777,216  / (1 + 0.06/2)4x2 = $ 2,814,750

therefore Part A has an initial safety margin of $100,000,000 – $ 2,814,750 = $97,185,250.

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