"If two portfolios have the same duration, the change in their value when interest rates change will be the same." Explain why you agree or disagree with this statement

Question

What will be an ideal response?

Answer 1

While not the sole or best measure, duration attempts to measure an asset's price sensitivity to yield changes. Duration does a good job of estimating an asset's percentage price change for a small change in yield. However, it does not do as good a job for a large change in yield. The percentage price change due to convexity can be used to supplement the approximate price change using duration. For a portfolio, its duration is the weighted average of the duration for each asset. If the two portfolios with the same duration have the same weighted average it does not imply that it has the same assets and/or the same proportion of assets and/or assets with the same maturities. Thus, if there is a change in interest rate it can affect the duration of each portfolio's assets differently. This is particularly true if the change in interest rates is different for different maturities. Thus, there is certainly no guarantee that a change in interest rates (when all is said and done) will produce the same duration for each portfolio.

To further understand why two portfolios with the same duration can be differently influenced by change in interest rates consider the derivation of duration. In the derivation of the relationship between modified duration (which is the approximate percentage change in price for a 100-basis-point change in yield) and bond price volatility, we started with the bond price equation. This price equation assumes that all cash flows for the bond are discounted at the same discount rate. Essentially, the derivation assumes that the yield curve is flat and all shifts are parallel. There are limitations of applying duration when this assumption does not hold, and the yield curve does not shift in a parallel fashion. This is extremely important when we try to use a portfolio's duration to quantify the responsiveness of a portfolio's value to a change in interest rates. If a portfolio has bonds with different maturities, the duration measure may not provide a good estimate for unequal changes in interest rates of different maturities. Thus, if two portfolios have the same duration, the change in their value when interest rates change will not necessarily be the same.