In: Finance
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.