Bond Duration

Bond duration is a measure of a bond’s price sensitivity to changes in interest rates. It tells you how much the price of a bond will change (in percentage terms) for every 1% change in interest rates. The higher the duration, the more sensitive the bond is to rate movements. Duration is one of the most important concepts in fixed income investing.

What Is Bond Duration?

Duration combines two ideas: the time to receive a bond’s cash flows and how much each cash flow is worth today. A bond that pays most of its value through a large maturity payment many years away has a high duration. A bond that pays large coupons every year returns more cash early and has a lower duration.

Mathematically, duration reflects the weighted average time to receive all of a bond’s cash flows, where each cash flow is weighted by its present value.

Two Types of Duration

**Macaulay Duration:**
The weighted average time (in years) until a bond’s cash flows are received. It is expressed in years.

**Modified Duration:**
Macaulay Duration adjusted by the yield. It directly tells you the percentage price change for a 1% change in yield.

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

Where n = number of coupon periods per year.

Practical Rule of Thumb

If a bond has a modified duration of 7, a 1% increase in interest rates will decrease the bond’s price by approximately 7%.

**Example:**
Bond price: Rs 100
Modified Duration: 7
Rates rise by 1%
Price falls to approximately Rs 93

Duration and Investment Strategy

– **Rising rate environment**: prefer low-duration bonds to minimise price loss
– **Falling rate environment**: prefer high-duration bonds to maximise price gains
– **Short-term investors**: low duration reduces mark-to-market risk
– **Long-term investors**: can tolerate higher duration for potentially higher returns

Duration in Mutual Funds

Debt mutual funds publish their portfolio duration (modified duration) in their fund factsheets. A liquid fund has a very low duration (a few days to weeks). A long-duration gilt fund may have a duration of 10 to 15 years.

Practical Example

Ratan holds a 10-year G-Sec bond with a modified duration of 7.5. The RBI raises the repo rate by 50 basis points (0.5%). The bond’s price falls by approximately 7.5% x 0.5% = 3.75%. His bond worth Rs 10 lakh falls in value to approximately Rs 9.625 lakh on a mark-to-market basis. If he holds to maturity, he still receives the full face value.

Key Takeaways

– Duration measures how sensitive a bond’s price is to interest rate changes
– Modified duration indicates the approximate % price change for a 1% rate change
– Higher duration = more price sensitivity; lower duration = less sensitivity
– In rising rate environments, shorter-duration bonds protect capital better
– Debt mutual fund factsheets publish portfolio duration; use it to assess interest rate risk