Meaning of Duration
Duration is the number of years for which the bond’s sensitivity to the changes in the interest rates is measured. Specifically, it measures the changes in the market value of security due to 1% change in interest rates. Simply understood, it is an approximation of how long it would take for one to recoup his or her initial investment in the bond. The relationship between duration and volatility in prices is direct i.e. the longer the duration, the more volatility in prices.
Types of Durations
Macaulay Duration
The Macaulay duration of a bond is the weighted average term to maturity of the cash flows from a bond. It is used by portfolio or debt managers who use an immunization strategy. It is calculated as follows – Macaulay Duration=Current bond price (∑t=1n (1+y) tt ∗ C +(1+y) nn ∗ M) Where, C=periodic coupon payment y=periodic yield M=the bond’s maturity value n=duration of bond in periods
Modified Duration
The modified duration of a bond is an adjusted version of the Macaulay duration. It is used to calculate the changes in a bond's duration and price for each percentage change in the yield to maturity. Modified duration is more commonly used. For larger changes in yield, both the modified duration and convexity are used for better estimation of changes in bond prices with changes in yield. It is calculated as follows - Modified Duration=(1+nYTM) * Macaulay Duration Where, YTM=yield to maturity n=number of coupon periods per year
