The Relative Importance of Duration and Yield Volatility on Bond Price Volatility: Comment

The purpose of this paper is to investigate the relative importance of yield volatility and durationl in determining a bond's price volatility. Although our analysis is confined to default-free government securities, the basic result can be generalized to any fixed income financial asset. The concept of duration was first introduced by Frederick Macaulay 5 in his 1938 study of railroad bond prices. Macaulay demonstrated that duration and not maturity was the proper measure of a bond's time dimension. Much of the theoretical research in the area since Macaulay's contribution has concentrated on the relationship between price change and duration for a given change in all yields. In a 1945 article, Samuelson 9 employed duration to assess the effect of a general change in interest rates on the value of a portfolio containing both asset and liability positions. Specifically, he considered the effects of a flat 1 percent increase in rates along the entire yield curve. Samuelson then proved the following theorem for just such a change in yields: