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When we talk about bond duration analysis we are talking about the bonds term to maturity and its coupon rate. There is a duration formula that is used to calculate weighted average of the times at which a fixed income security ends up giving cash flows. Duration increases with maturity but the funniest thing is that it decreases with coupon. It is usually shorter than maturity unless the type of bond is a zero coupon bond. The reason behind this is very simple -- a bond with a higher coupon rate gives a better percentage of its value before maturity.
After Macaulay, there have been different versions of calculating and doing bond duration analysis. However, Macaulay’s formula and method is the simplest and most commonly used even today. Macaulay’s formula makes bond duration analysis very simple by using the yield to maturity to calculate the bond’s present value.
If you want to find out the sensitivity of a bond’s price to interest rate movements, you will need duration analysis. This analysis will reveal that the sensitivity is approximately proportionate to the percentage price change for a given change in yield. This was the method put forth by Hicks in 1939 and it represents the elasticity of a bond price if we take into account the discount factor. In contrast, Macaulay’s duration formula did not forecast the bond’s precise reaction to a change in the interest rate.
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