Question

Your bond portfolio consists of $30 million worth of Treasury STRIPS with 7 years to maturity, and $10 million of Treasury notes with a Macaulay duration of 3 years. The term structure is flat, and all spot rates are 3%.
What is the modified (not Macaulay) duration of your portfolio?

a) 3 years
b) 4 years
c) Slightly less than 4 years
d) Slightly greater than 4 years
e) None of these

Answer 1

Answer:

d) Slightly greater than 4 years

Explanation:

The portfolio's Macaulay period (MaD) is the mean maturity of its retained earnings.

Fifty per cent of cash flows (in terms of PV) come after three years and another fifty per cent arrive after five years, so the MaD is 0.53 + 0.55 = 4.

We must divide the MaD by (1+ytm/2) to get Modified Duration (MoD).

Then portfolio MoD is 4/(1 + 0.02/2) = 3.96.