Deriving the Modified Duration and Its Link to Macaulay Duration

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Macaulay duration and modified duration are two of the many measures used in the world of fixed income/bonds.

The Macaulay duration represents a weighted average of the time with the weights being the PV of the cash flows. If a bond manager holds the bond up to the Macaulay duration, the price risk offsets the reinvestment risk of the bond (given an instantaneous change in the yield to maturity).

The Modified duration is a measure of the bond's interest rate risk, measuring the percentage change in the bond's price given a change in the yield to maturity.

This video will be useful for those who encounter these two measures in their studies or line of work and are curious of the relationship between Modified Duration and Macaulay Duration.