You currently have a £100 million bond portfolio invested 30% in 5-year bonds with a modified...

You currently have a £100 million bond portfolio invested 30% in 5-year bonds with a modified duration of 4.05 years, 25% invested in 10-year bonds with a modified duration of 6.88 years and 45% in 20-year bonds with a modified duration of 10.09 years. The yield curve is currently flat at 8% across all maturities (5-year, 10-year and 20-year.)

Calculate the modified duration for your entire bond portfolio.
If the entire yield curve suddenly shifts down to yield 7.25%, what would you expect the portfolio to rise by in percentage terms? What is the new value of the portfolio?
What might you wish to do with the length of the duration of your portfolio in the light of a projected fall in bond yields from 8% to 7.25%? Suggest a new weighting for your portfolio to achieve this and what it would involve you doing?

Expert Solution

I. The formula for the modified duration of a portfolio is:

Modified Duration = Summation( n x PVn)/Summation (PVn)

So, the modified duration of the portfolio will be = (0.30 x 4.05 + 0.25 x 6.88 + 0.45 x 10.09)/1 (Here we have used just the percentages because after cancellation with the denominator, only the weights will remain)

So, modified duration = 7.4755 years.

II. Since this is a 0.75% decrease in yield, it will increase the portfolio value by 0.75 x 7.4755 = 5.6066%. The new value of the portfolio will be = 1.056066 x 100 = $105.6066 mn

III. We would wish that the duration had been more. This is because a higher duration would cause more increase in the value of the portfolio. To increase the duration, we would increase the weights of the bonds with the highest duration i.e. the 20-year bond. This would involve selling portions of the other two bonds (maybe get rid of them fully) and make the weight of 20-year bond as high as possible (preferably 100%).

jeff jeffy answered 1 year ago

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