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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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Answer:

Amount of 5-Year bond is equal to 1.6 million

Amount 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 million

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

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