Page 16 - FINAL CFA SLIDES DECEMBER 2018 DAY 15

LOS 54.f: Calculate the duration of a portfolio and Session Unit 16:
explain the limitations of portfolio duration., p.109
54. Understanding Fixed Income Risk and Return

2 approaches:

1. Calculate the weighted average no. of periods until the portfolio’s cash flows will be received.
2. Take a weighted average of the durations of the individual bonds in the portfolio.

Approach 1:
• Theoretically correct but not often used in practice; yield measure is cash flow yield, the IRR of the bond
portfolio. This is inconsistent with duration capturing the relationship between YTM and price. Will not
work for a portfolio that contains bonds with embedded options because the future cash flows are not
tanties
known with certainty and depend on interest rate movements.

Approach 2:
• Typically used in practice; works easily for a portfolio that contains bonds with embedded options by

using their effective durations. The weights for the calculation of portfolio duration under this approach
are the full price of each bond as % of the total portfolio value (using full prices). These proportions of
total portfolio value are multiplied by the corresponding bond durations to get portfolio duration.

Limitation:
For portfolio duration to “make sense” the YTM of every bond in
the portfolio must change by the same amount. Only with this
assumption of a parallel shift in the yield curve is portfolio

duration calculated with this approach consistent with the idea of
the % change in portfolio value per 1% change in YTM. It is
however is less accurate when there is greater variation in yields
among portfolio bonds, but is the same as the portfolio duration
under the first approach when the yield curve is flat.