Modified Duration is a formula that expresses the measurable change in the value of a security in response to change in interest rates. It illustrates the effect of a 100-basis point (1%) change in interest rates on the price of a bond. Modified duration illustrates the concept that bond prices and interest rates move in opposite directions – higher interest rates lower bond prices, and lower interest rates raise bond prices. The formula provides investors and portfolio managers with valuable insights into the potential impact of interest rate movements on bond prices, aiding in informed decision-making and risk management strategies. Investors can use modified duration to adjust the maturity of their bond portfolio in order to better match their risk tolerance and investment objectives.

MODIFIED DURATION FORMULA

MODIFIED DURATION = Macaulay Duration / (1 + YTM/N)

Macaulay Duration. Weighted average number of years an investor must maintain his or her position in the bond.

YTM. Yield to Maturity and is the total return on a bond if held until maturity.

N. The number of coupon periods per year.

RELATION TO MACAULAY DURATION

Modified duration builds upon the concept of Macaulay duration, enabling investors to assess how sensitive a bond is to changes in interest rates.

Macaulay duration computes the average time it takes for a bondholder to receive the bond’s cash flows, considering their respective weights.

To calculate modified duration, one must first calculate the Macaulay duration, which involves multiplying the time period by the periodic coupon payment and dividing the result by 1 plus the periodic yield raised to the time to maturity.

APPLICATIONS

Managing Interest Rate Risk.

Modified duration is used to manage interest rate risk through strategies like portfolio immunization and asset-liability management.

Investors employ modified duration in designing bond portfolio strategies, such as active and passive management, duration matching, and convexity optimization.

Performance Evaluation.

It is used to evaluate bond performance by comparing it against benchmarks and conducting attribution analysis.