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# Convexity

AnalyticsTrade Team Last updated on 1 May 2023

# Convexity

Convexity is a financial term that refers to the curvature of a bond’s yield-to-maturity (YTM) as it relates to changes in interest rates. It is a measure of the sensitivity of a bond’s price to changes in interest rates. When the YTM of a bond increases more than proportionally as interest rates rise, the bond is said to have positive convexity. Conversely, when the YTM of a bond increases less than proportionally as interest rates rise, the bond is said to have negative convexity.

## History of Convexity

The concept of convexity was first introduced by Nobel Prize-winning economist Robert C. Merton in 1973. Merton’s work focused on the relationship between the price of a bond and the yield-to-maturity (YTM) of the bond. He found that the YTM of a bond is not a linear function of the interest rate, but rather a convex function. This means that the YTM of a bond increases more than proportionally as interest rates rise. This phenomenon is known as positive convexity. Conversely, when the YTM of a bond increases less than proportionally as interest rates rise, the bond is said to have negative convexity.

## Table of Comparisons

Interest Rate Yield-to-Maturity
2% 2.5%
3% 3.2%
4% 3.8%
5% 4.2%

## Summary

Convexity is a financial term that refers to the curvature of a bond’s yield-to-maturity (YTM) as it relates to changes in interest rates. It is a measure of the sensitivity of a bond’s price to changes in interest rates. When the YTM of a bond increases more than proportionally as interest rates rise, the bond is said to have positive convexity. Conversely, when the YTM of a bond increases less than proportionally as interest rates rise, the bond is said to have negative convexity. The concept of convexity was first introduced by Nobel Prize-winning economist Robert C. Merton in 1973. For more information about this term, you can visit websites such as Investopedia, Bloomberg, and The Balance.

• Yield-to-Maturity
• Duration
• Interest Rate Risk
• Bond Price Volatility
• Yield Curve
• Interest Rate Swap
• Basis Point
• Yield Curve Risk