Modified & Macaulay duration in bonds: Know how they differ and their use in debt mutual funds

What is bond duration?

Bond duration is the time it takes for an investor to recover the bond price, including both interest and principal, through its cash ows. Duration should not be confused with the bond’s maturity term, which is the period from its issue date till the entire principal is repaid on maturity.

Duration also indicates how much a bond’s price may change with varying interest rates. Bond prices have an inverse relationship with interest rates, with a rise in rates leading to a fall in prices, and vice versa. Bonds with higher duration are more sensitive to interest rate changes and those with shorter duration are more stable.

Macaulay and modi ed durations are the two most widely used measures which serve different purposes.


Bond duration: How the two differ

Macaulay duration

This is the weighted average time it takes for investors to receive the bond’s cash ow, both coupon payment and principal amount. It is measured in years and has a direct correlation to the maturity term. The longer the maturity period, the longer the Macaulay duration. It also has an inverse relationship with coupon rate and yield. The higher the coupon payment and bond yield, the lower the Macaulay duration, and vice versa.

It is useful for investors in debt mutual funds as it helps assess the interest rate risk for a given duration. The longer the Macaulay duration, the higher the sensitivity to interest rate changes, and greater the price volatility in bonds.

ALSO READ | Invoice discounting: Know how this fund-raising option works, its types, benefits and drawbacks

Modified duration

It is derived from the Macaulay duration and measures the sensitivity of the bond’s price to changes in yield to maturity (expected return if you hold the bond till maturity), or more broadly, the changes in interest rates. It is expressed as a percentage change in the bond’s price for a 1% change in interest rates.

As in Macaulay duration, the longer the modi ed duration, the higher the price volatility that a debt security will be subjected to. Similarly, modi ed duration has an inverse relationship with coupon rate and yield. The lower the coupon and yield, the higher the duration.

Mutual fund portfolio managers can decide on investment strategies by assessing the risk linked to bonds in the portfolio depending on their modi ed duration. However, this is only one metric of risk assessment and does not indicate the overall risk associated with bond investment.