posted on 06-06-2019

Negative Convexity

Updated October 1, 2019

What is Negative Convexity?

Negative convexity refers to the shape of a bond's yield curve and the extent to which a bond's price is sensitive to changing interest rates.

How Does Negative Convexity Work?

The degree to which a bond's price changes when interest rates change is called duration, which often is represented visually by a yield curve. Convexity describes how much a bond's duration changes when interest rates change, meaning that investors can learn a lot not just from the direction of the yield curve but the curviness of the yield curve. Accordingly, convexity helps investors anticipate what will happen to the price of a particular bond if market interest rates change.

Generally, when interest rates fall, bond prices rise. But a bond with negative convexity loses value when interest rates fall. This is often the case for mortgage-backed securities (MBS) because they rely on underlying mortgage loans, which are typically refinanced (and thus paid off early) when interest rates fall.  Prepayment repays principal early, leaving investors stuck with reinvesting their money at the market's current lower rates.

Why Does Negative Convexity Matter?

Convexity is a price-predicting tool for bonds. It also reveals the interest rate risk of a bond and helps investors consider whether a bond's yield is worth the underlying risk.

Most mortgage bonds are negatively convex, largely because they can be prepaid. Callable bonds can also exhibit negative convexity at certain prices and yields. This is because an issuer's incentive to call a bond at par increases as interest rates decrease. In fact, the price might actually drop as it becomes more obvious that the bond will be called.