God I hate CFAI right now! There’s a question on the CFAI website which is confusing the h**l out of me (Akron, last question).
Firstly, in the textbook it says “…because the bonds [in the portfolio] are zero coupon bonds, the effective duration of each bond is the same as the maturity of the bonds. The portfolio’s effective duration is the weighted sum of the efective duration of each bond position.”
So, if I have three zero coupon bonds of 5, 10, and 30 years maturity (as in the question) the portfolio effective duration is 0.333(5+10+30) = 15 right? However, the question states that the portfolio has equal weightings in each key rate duration and has an effective duration of 4.7. Eh?
Then, in the textbook it says that the sum of the key rate durations is the same as the effective duration of the portfolio.
The key rate durations in the question are 1.8, 3.6 and 8.7, which equal 14.1!
Thanks.