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13 February, 07:39

If the duration of 5-year maturity bonds with coupon rates of 12.2% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 5% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?

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  1. 13 February, 08:08
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    Amount of 5-Year bond is equal to 1.6 millionAmount of 20-Year bond is equal to 22.2 million.

    Explanation:

    Step 1. Given information.

    Amount of perpetual obligation = D/r = $ 2,500,000/0.105 = $23,809,524

    Duration of perpetuity = (1+y) / y = (1+0.105) / 0.105 = 1.105/0.105 = 10.5238 years

    Let w be the weight of 5-year bond and (1-w) is the weight of 20-year bond in the bond portfolio.

    Portfolio duration = weighted average duration of holdings

    10.5238 = w*4 + (1-w) * 11

    10.5238 = 4w + 11 - 11w

    7w = 0.4762

    w=0.0680

    Step 2. Formulas needed to solve the exercise, and

    Step 3. Calculation.

    Amount of 5-Year bond = 0.068x23,809,524 = 1.6 million Amount of 20-Year bond = 0.932x23,809,524 = 22.2 million

    Step 4. Solution.

    Amount of 5-Year bond is equal to 1.6 millionAmount of 20-Year bond is equal to 22.2 million.
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