# Duration and Convexity

9 Pages Posted: 21 Oct 2008

See all articles by Robert M. Conroy

## Robert M. Conroy

University of Virginia - Darden School of Business

### Abstract

The price of a bond is a function of the promised payments and the market-required rate of return. Because the promised payments are fixed, bond prices change in response to changes in the market-required rate of return. For investors who hold bonds, the issue of how sensitive a bond's price is to changes in the required rate of return is important. There are four measures of bond-price sensitivity that are commonly used: Simple Maturity, Macaulay Duration (effective maturity), Modified Duration, and Convexity. Each of these measures provides a more exact description of how a bond price changes relative to changes in the required rate of return.

Excerpt

UVA-F-1238

Rev. Sept. 11, 2014

The price of a bond is a function of the promised payments and the market-required rate of return. Because the promised payments are fixed, bond prices change in response to changes in the market-required rate of return. For investors who hold bonds, the issue of how sensitive a bond's price is to changes in the required rate of return is important. There are four measures of bond-price sensitivity that are commonly used: Simple Maturity, Macaulay Duration (effective maturity), Modified Duration, and Convexity. Each of these measures provides a more exact description of how a bond price changes relative to changes in the required rate of return.

Maturity

Simple maturity is just the time left to maturity on a bond. We generally think of 5-year bonds or 10-year bonds. It is straightforward and requires no calculation. The longer the time to maturity, the more sensitive a particular bond is to changes in the required rate of return. Consider two zero-coupon bonds, each with a face value of \$ 1,000. Bond A matures in 10 years, and has a required rate of return of 10%. The price of Bond A is \$ 376.89, where

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Keywords: Finance

Suggested Citation

Conroy, Robert M., Duration and Convexity. Darden Case No. UVA-F-1238, Available at SSRN: https://ssrn.com/abstract=1279274