How to measure your portfolio’s interest rate risk with convexity

Why do portfolio durations and key rate durations differ?

Portfolio durations differ from key rate durations, as even though the durations of two portfolios may match, both portfolios may differ in the maturity profiles of the bonds they comprise, which will result in differing key rate durations.

What is convexity?

Another measure used to compute changes in bond value due to yield curve twists is convexity. While duration measures the change in bond value due to a change in yield, convexity measures the change in the duration of a bond due to a change in yields. Duration assumes that shifts in the yield curve are linear, whereas in fact, they often exhibit a curved or “convex” shape. Bonds can exhibit positive or negative convexity. A bond whose duration increases when the yield declines has positive convexity. These bonds will experience greater price increases due to falling yields than price falls when yields increase. Examples of bonds having positive convexity are non-callable bonds.

Examples of bonds exhibiting negative convexity are mortgage-backed securities since they can be prepaid. Popular ETFs investing in mortgage-backed securities include the iShares Barclays MBS Fixed-Rate Bond Fund (MBB) and the Vanguard Mortgage-Backed Securities ETF (VMBS) and the SPDR Barclays Capital Mortgage Backed Bond ETF (MBG).

Another example of negative convexity would be callable bonds, since the price of the bond stops increasing once the price is above the call value because investors don’t want to risk losing money if the bond is called at a price lower than what they have paid. Most municipal bonds are callable. An examples of an ETF investing in municipal bonds is the VanEck Vectors High Yield Municipal Index ETF (HYD). Another ETF, the State Street SPDR Barclays Municipal Bond Fund (TFI) also invests in municipal bonds. Bonds exhibiting higher positive convexity experience less adverse price movements when yields increase and higher price increases when yields decline.

To read about other popular measures of yield curve risk, please read on to the next part of this series.