Modified Duration

Modified Duration is a measure of a bond’s price sensitivity to changes in interest rates. It tells you by what percentage a bond’s price will change for every 1% (100 basis point) change in yield. Modified Duration is derived from Macaulay Duration and is the more actionable measure used by portfolio managers and risk analysts.

What Is Modified Duration?

While Macaulay Duration is the weighted average time to receive cash flows, Modified Duration adjusts it to directly express price sensitivity. The relationship is:

Modified Duration = Macaulay Duration / (1 + YTM/n)

Where YTM is the yield to maturity and n is the number of coupon periods per year.

How to Use Modified Duration

If a bond has a Modified Duration of 6:
– Rates rise by 1%: bond price falls by approximately 6%
– Rates fall by 1%: bond price rises by approximately 6%
– Rates rise by 0.5%: bond price falls by approximately 3%

This is an approximation. The actual price change is also affected by convexity (which captures the curvature in the price-yield relationship). Modified Duration + Convexity gives a better estimate for large rate changes.

Key Drivers of Modified Duration

– **Longer maturity**: increases duration (more future cash flows)
– **Lower coupon rate**: increases duration (more weight on distant principal)
– **Lower yield**: increases duration (distant cash flows are discounted less)
– **More frequent coupons**: reduces duration (faster cash flow return)

Modified Duration in Practice

Portfolio managers use Modified Duration to manage interest rate risk:

– When expecting rising rates: reduce portfolio duration (buy short-dated bonds, sell long-dated ones)
– When expecting falling rates: increase portfolio duration (buy long-dated bonds to profit from price appreciation)

Debt mutual fund factsheets publish “Modified Duration” of the portfolio. A fund with duration 0.2 is much less sensitive to rate changes than a fund with duration 8.

Price Change Approximation

Price change (%) ≈ -Modified Duration x change in yield (%)

The negative sign shows the inverse relationship: rising yields lead to falling prices.

Practical Example

Kavita holds a Rs 10 lakh bond with Modified Duration of 5. The RBI cuts the repo rate by 0.75%. Her bond price rises by approximately 5 x 0.75% = 3.75%. Her holding is now worth Rs 10,37,500 on a mark-to-market basis. If she holds to maturity, the price gain is unrealised, but she can sell in the secondary market to lock in the profit.

Key Takeaways

– Modified Duration measures the % price change of a bond for a 1% change in yield
– Higher duration = more sensitivity to rate changes; lower duration = less sensitivity
– Derived from Macaulay Duration adjusted for the bond’s yield
– Portfolio managers use duration to position for expected rate movements
– Debt mutual fund duration is published in factsheets; use it to assess the fund’s interest rate risk profile