# 2. Macaulay, Modified and Effective Durations

## b. define, calculate, and interpret Macaulay, modified, and effective durations;

## c. explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options;

## d. define key rate duration and describe the use of key rate durations in measuring the sensitivity of bonds to changes in the shape of the benchmark yield curve;

What are Yield duration statistics?

Yield duration statistics measure the sensitivity of a bond's full price to the bond's own yield-to-maturity.

What are curve duration statistics?

Curve duration statistics measure the sensitivity of a bond's full price to the benchmark yield curve, e.g., effective duration.

What is Macaulay Duration?

Macaulay duration is defined as the weighted average time to full recovery of principal and interest payments. The weights are the shares of the full price corresponding to each coupon and principal payment.

What is Modified Duration?

Modified duration shows how bond prices move proportionally with small changes in yields. Specifically, modified duration estimates the percentage change in bond price with a change in yield.

What is Effective Duration?

Effective duration measures interest rate risk in terms of a change in the benchmark yield curve. It is very similar to approximate modified duration.

##### Source:

- CFA