Convexity is an important measure of risk for bond investors and portfolio managers and is an important tool for managing a portfolio’s exposure to market risk. To understand why this is important, let’s first look at what it is and how it’s used.

The term convexity refers to the curvature in the relationship between bond prices and bond yields. It's a measure of the rate of change in a bond's price in response to a change in interest rates. It is used to measure and manage a portfolio's exposure to market risk.

Convexity measures the sensitivity of a bond's price to changes in its yield. The more a bond’s price changes with interest rate changes, the higher its convexity. If a bond’s price rises more than expected when interest rates fall and drops less than expected when rates rise, the bond's duration is said to have positive convexity. Conversely, if a bond's price rises less or falls more than expected when interest rates change, its duration has negative convexity.

Bond investors and portfolio managers use convexity to measure how much risk is associated with a bond or portfolio of bonds. As bond prices rise and fall with changes in interest rates, portfolio investors can use convexity to anticipate how their portfolio's performance may be affected by market movements. Different types of bonds, depending on their terms and duration, will have different degrees of convexity, so investors can adjust their portfolios accordingly.

In particular, portfolio managers use convexity to hedge against market volatility. For instance, if the portfolio has a high degree of negative convexity, the manager might choose to invest in bonds with positive convexity in order to offset the risk in the portfolio. Similarly, if the bond's duration is highly positive, the manager might buy bonds with negative convexity to protect the portfolio.

Overall, convexity is an important measure of risk for bond investors. By using convexity to measure a bond's or portfolio's exposure to market risk, investors and portfolio managers can better anticipate how their investments may be affected by changes in the markets. They can use this information to adjust their portfolios accordingly, either hedging against market volatility or positioning themselves to take advantage of potential gains.