Duration and Bond Price Volatility: Some Further Results
In the introduction Shirvani and Wilbratte state that they presented a new approach for calculating bond price volatility. This formula represents an alternative to famous Macaulay formula. They both rely on the same concept of bond duration; however, the SW model resolves a deficiency in the Macaulay formula that allows more precise calculations depending on interest rate changes on bond prices. The SW formula is also compared to the convexity-augmented Macaulay formula. It provides better estimates of coupon bond price volatility but this is not too significant for calculating bond convexities. The SW approach allows quick and easy calculations what makes it very useful for classroom work.
The Macaulay approximation becomes increasingly inaccurate as the percentage change in the bond yield becomes larger in absolute value, and especially so for positive changes in the yield;
The convexity-augmented Macaulay formula takes the form of parabola. It improves the previous research but still the result is at odds with the inverse relationship between the percentage change in the bond price and the percentage change in the bond yield.
The convexity approximation deteriorates as changes in the market interest rates become significant.
The result of the SW approach is built on the duration of the bond that is in the center of attention. The authors suggested gravitation as an effective tool to deal with these deficiencies and introduced a “sister” zero-coupon bond with the same duration and price for every coupon bond. Any bond must have a center of gravity which is located in its duration. Any bond now should be considered as a single point. “Thus, any coupon bond can be treated as a zero-coupon bond, with the maturity and hence duration of the zero-coupon bond being equal to the coupon bond’s duration” (Shirvani and Wilbratte 2005). This leads to the fact that small changes in bond yield will not have a significant impact. The calculations based on the new approach clearly demonstrate that the bond price changes are not symmetric. The equation of the new formula allows gaining better estimates of the actual price changes. Moreover, the equation provides a measure for the risk of capital loss for investors “by indicating the extent to which various bonds’ prices change for a given change in bond yields” and can be used to calculate the percentage gains or losses that the investors can realize in case the bond yield rises or falls (Shirvani and Wilbratte 2005).
Shirvani Hassan and Barry Wilbratte. “Duration and Bond Price Volatility: Some Further Results.” Jourmal of Economics and Finance Education 4.1 (2005): 18-23.