Contents
Definition
Modified Duration (MD) measures the percentage change in a bond's price for a 1 percentage-point (100 basis-point) change in its yield to maturity. It is derived from Macaulay Duration — the weighted-average time (in years) to receive the bond's cash flows, where each weight is the present value of that cash flow divided by the bond's total present value:
Macaulay Duration (D_mac) = [Σ t · PV(CF_t)] / P
Modified Duration (MD) = D_mac / (1 + y/m)
where y is the annual YTM and m is the number of coupon periods per year (2 for semi-annual). The resulting MD approximates: %ΔP ≈ −MD × Δy. A bond with MD = 7 will lose approximately 7% in price if yields rise 100 bps, and gain ~7% if yields fall 100 bps. Modified Duration is the workhorse risk metric for Indian debt mutual funds — SEBI requires fund factsheets to disclose portfolio MD monthly.
How it is computed
Step 1 — Compute PV of each cash flow: PV(CF_t) = CF_t / (1 + y/m)^t using the bond's YTM. Step 2 — Macaulay Duration: weight each period t by its PV fraction and sum. Step 3 — Divide by (1 + y/m). For zero-coupon bonds, Macaulay Duration equals time to maturity exactly, making MD = n / (1 + y/m). For plain-vanilla coupon bonds, MD < maturity because earlier coupon payments pull the weighted average forward in time. Portfolio MD is the market-value-weighted average of individual bond MDs — additive and therefore easy to compute for large portfolios. Indian convention: most corporate bond MD calculations use Actual/365 day-count; G-Sec MD calculations use Actual/Actual per RBI's NDS-OM methodology.
Why it matters for investors
Modified Duration answers the question: "How much rupee value will my bond or bond-fund portfolio gain or lose if interest rates move by X basis points?" It is the primary tool for: (1) Interest-rate risk management — a pension fund matching a 15-year liability should hold a portfolio with MD ≈ 15 to immunise against rate moves; (2) Debt fund category selection — SEBI's fund categorisation mandates MD ranges (e.g., Overnight Funds MD < 1 day; Long Duration Funds MD > 7 years); (3) Duration positioning — if a portfolio manager expects RBI rate cuts, lengthening MD (buying longer-tenor bonds) amplifies capital gains. MD is a first-order linear approximation; for large yield moves, Convexity (the second-order term) must be added: %ΔP ≈ −MD·Δy + ½·Convexity·(Δy)².
Worked example
A 5-year NABARD AAA bond issued at ₹100 face value, 7.50% annual coupon (paid semi-annually), YTM = 7.50% (priced at par). Semi-annual coupon = ₹3.75; 10 periods, y/m = 3.75%.
PV of each cash flow at 3.75% per period:
- Periods 1–9: ₹3.75 discounted; Period 10: ₹103.75
- Sum of PVs = ₹100 (at-par bond)
Macaulay Duration = [Σ t·PV(CF_t)] / 100 ≈ 8.54 semi-annual periods = 4.27 years.
Modified Duration = 4.27 / (1 + 0.075/2) = 4.27 / 1.0375 = 4.12 years.
Interpretation: If RBI cuts the policy repo rate by 50 bps and the 5-year AAA yield falls 50 bps, price appreciation ≈ 4.12 × 0.50% = ~2.06%. A long-duration gilt fund with MD = 9 would gain ~4.50% on the same rate move.
Caveats
Linearity limit: MD is accurate only for small yield changes (±50–100 bps). For larger moves, convexity materially improves the estimate. Embedded options: Callable bonds have effective duration (option-adjusted) that is lower than standard MD because the call option truncates price upside. Floating-rate bonds: MD resets at each coupon date to roughly the time until the next reset, making MD very low regardless of maturity. Credit events: Duration measures rate risk, not credit risk — a bond whose spread widens 200 bps due to a downgrade will fall in price in ways not captured by MD alone.
See also
- Yield to Maturity (YTM)
- Yield Curve
- Floating-Rate Bond
- Debt Funds in India — Complete Guide
- Tax on Investments in India
Primary source
- SEBI Mutual Fund Regulations, Sixth Schedule (portfolio disclosure): sebi.gov.in
- RBI — Government Securities Market in India (primer): rbi.org.in
- Finance Act 2023, Section 50AA
MintByte is registered with AMFI (ARN-314872) and APMI (APRN-01658). This glossary entry is for educational purposes only and does not constitute investment advice or a recommendation to buy or sell any security.