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?

Question

Kian Shah

Business

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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Answers (1)

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Meadow Bright · Answer 1

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.