The importance of having an effective formula for estimating bond price volatility has been proven in various studies. In their work, Shirvani and Wilbratte (2005), evaluated and compared three alternative estimations. The three alternative measures, Macaulay duration, convexity-augmented Macaulay duration and a new alternative that they proposed were described and evaluated for relative performance. The authors basically provide a better method for computing bond price volatility than the two that are conventionally accepted and commonly used. The alternative is a method that is easier and faster to use, even for students.
In the introduction, Shirvani and Wilbratte (2005) suggest an earlier paper in which they performed a comparison of the convexity-augmented Macaulay formula to their proposed formula. Their proposed formula only requires the concept of bond duration (D). The previous work revealed greater benefits in the use of the proposed model as opposed to the conventional two. It was showed to resolve the Macaulay formula deficiency by offering a functional form reflecting the asymmetric effects of changes in interest rate on bond prices.
The current paper is basically an extension of their earlier work showing that, as opposed to their earlier perception, the proposed model provides better results in coupon bonds that could be similar in accuracy to computations using the convexity-augmented formula, and in most cases, even considerably better in accuracy. Their work revealed that though efficient in convexity-augmented Macaulay formula to estimate coupon bond price volatility, the benefits in terms of accuracy were not worth the complicated work in bond convexities' calculation. The alternative proposed is simpler and only requires a hand-held calculator.
In the section, Alternative Bond Price Volatility Approximation Formulas, Shirvani and Wilbratte (2005) use numerical examples and graphic analysis in proving the benefits of the proposed model over the conventional ones. The effectiveness of the alternative that the authors proposed is based on their argument that rather than an approximation scale for bond price volatility, the alternative is much more exact in anticipating any change in zero-coupon bond prices. This is as opposed to the convexity approach that simply gives an approximation. In comparison to the Macaulay approach, the proposed approach is consistently more precise in approximating changes in bond price relative to interest rate changes.
Another advantage revealed of the third alternative over the other two is that it achieves greater accuracy on the Macaulay formula as well as greater changes in interest rate for the convexity-augmented formula. However, for changes that are smaller, similar results are obtained in terms of the accuracy of convexity-augmented formula and the proposed formula.
The proposed formula is also revealed as providing greater computational efficiency in the calculation of price changes. Thus, in areas where the proposed formula and the convexity approach have the same level of accuracy, the proposed approach offers the benefit of computational efficiency. This has an advantage in that it can be easily utilized in demonstrations during learning and can be computed by students in exams.
The model can be applied as a measure of risk. Shirvani and Wilbratte (2005) suggest that in cases where there are abnormally low interest rates or where there are major uncertainties in the financial markets because of situations like high level of budget deficits or volatility in exchange rates, it is possible that the value of the model can be enhanced by the potential of huge changes in interest rate.
Reference
Shirvani, H. and Wilbratte, B. (2005). Duration and Bond Price Volatility: Some Further Results, JOURNAL OF ECONOMICS AND FINANCE EDUCATION, 4(1): 1-6
