The solution to this question has the duration of the porfolio A + B calculated as the average of the durations of the two assets A and B.
However in the text the duration of a portfolio of more than 1 asset is defined as the discounted mean term weighted by present value for all the cashflows for all assets.
For example, in 5.15 we have:
DMT(A) = 400/88.77 = 4.51
DMT(B) = (100*22*1.08^-22)/(100*1.08^-22) = 22
the average is 13.25, which is the solution given in the Q&A bank.
If we had calulated the DMT as per the text we would have:
DMT = (400+100*22*1.08^-22)/(88.77+100*1.08^-22) = 7.5
The solution to the Q&A bank is putting equal weight to both DMT(A) and DMT(B) whereas the value of asset A is much larger than asset B, 88.77 compared to 18.39. I believe the two individual durations should have been weighted by present value, rather than by amount. Am I missing something?
Cheers
Last edited by a moderator: Apr 12, 2012