Calculate the duration for each of following bonds or portfolio in (1)-4) and answer question (5)....

Calculate the duration for each of following bonds or portfolio in (1)-4) and answer question (5). A 10-year bond with 8% annual coupon and 8% yield to maturity. PLEASE EXPLAIN HOW YOU GOT EACH
A 30-year bond with 2% annual coupon and 8% yield to maturity.
100-year bond with 9% annual coupon and 8% yield to maturity
portfolio of bond (1) and (2), with 30.71% invested in bond (1) and 69.29% in bond (2). (Hint: Duration of a portfolio equals the weighted average duration of all bonds in the portfolio)
An insurance company holds a $100 million asset. The asset stands to lose if interest rate drops. The company estimates the duration of its assets to be 13.49 years and considers one of the above bonds (or portfolio of bonds) in (1)-(4) to hedge the potential loss from the asset. Which one would be the best choice of the insurance company?

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Expert Solution

I have used excel to calculate the duration of the indiviual bonds and portfolio. I have added the image of one calculation for your understanding.

Assuming face value to be 1000 $.

10-year bond with 8% annual coupon and 8% yield to maturity. Duration is 7.2469

Like wise the duration of other bonds and portfolios is :

A 30-year bond with 2% annual coupon and 8% yield to maturity. Duration is 16.2559 years.

100-year bond with 9% annual coupon and 8% yield to maturity. Duration is 13.4895 years.

Portfolio of bond (1) and (2), with 30.71% invested in bond (1) and 69.29% in bond (2).

Portfolio Duration = w1D1 + w2D2 + w3D3 + ... + wkDk

Bond 1 Duration = 7.2469. Bond 2 Duration = 16.2559 Bond 1 Weight = 30.71 % or 0.3071 Bond 2 Weight = 69.29/100 = 0.6929

Portfolio Duration = 7.2469 * 0.3071 + 16.2559 * 0.6929 = 13.4892 years

So Bond 3 and portfolio have the same duration as the insurance company's asset. Using the duration matching concept, one can choose either of the above. However as there are risks associated with holding a bond with longer maturity, it would be better to choose the portfolio of bonds to hedge the potential loss from the asset.

jeff jeffy answered 1 year ago

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