Effective Duration Calculator
From a bond's initial price and its repriced values when yield rises and falls, compute the effective duration — the bond's interest-rate sensitivity.
Input Data
Results
At a glance:Effective Duration measures how much a bond's price moves when the market yield changes — its interest-rate risk. It uses price revaluation: effective duration = (P− − P+) ÷ (2 × P0 × Δy). Unlike modified duration (fixed cash flows only), it handles bonds with embedded options (callable, puttable, MBS). Intuition: for every 1% change in yield, price moves about 'duration' percent in the opposite direction.
Formula
Effective duration = (P− − P+) ÷ (2 × P0 × Δy).
P0 = initial price, P− = price if yield falls, P+ = price if yield rises, Δy = yield change (decimal).
$$$D_{eff} = \\dfrac{P_- - P_+}{2 \\times P_0 \\times \\Delta y}$$$$$$\\Delta y$ (0.5\\% = 0.005)$$$$$\\dfrac{1032 - 971}{2 \\times 1000 \\times 0.005}=6.1$$$How to Use
- Enter the bond's current initial price (P0).
- Enter the repriced value when yield falls (P−).
- Enter the repriced value when yield rises (P+).
- Enter the symmetric yield change (Δy).
- Read the effective duration.
Effective duration by price revaluation
| Initial P0 | P− (yield↓) | P+ (yield↑) | Δy | Effective duration |
|---|---|---|---|---|
| 1,000 | 1,032 | 971 | ±0.5% | 6.10 |
| 1,000 | 1,050 | 955 | ±1.0% | 4.75 |
| 980 | 1,000 | 962 | ±0.25% | 7.76 |
Case Studies
Case 1: Computing effective duration
Bond initial price P0 = HK$1,000. When yield falls 0.5%, repriced to P− = HK$1,032; when yield rises 0.5%, repriced to P+ = HK$971. Δy = 0.5% = 0.005.
Effective duration = (1,032 − 971) ÷ (2 × 1,000 × 0.005) = 61 ÷ 10 = 6.1.
Interpretation: duration 6.1 means for every 1% yield change, price moves about 6.1% opposite. Using actual repriced reaction, it works for option-bearing bonds.
Case 2: Larger duration = higher rate risk
Compare two bonds when yield rises 1%. A duration 6.1, B duration 2.0. Yield +1%: A price ≈ −6.1%, B ≈ −2.0%. On HK$1M each, A loses ≈ HK$61,000, B ≈ HK$20,000.
Same rate move, long-duration A swings over 3× the short-duration B.
Interpretation: duration quantifies rate risk. In a hiking-rate environment long-duration bonds fall more; in a cutting environment they gain more. Long maturity, low coupon, low yield → larger duration. Manage portfolio duration by rate outlook. Duration covers only rate risk, not credit/liquidity; and it is a linear approximation — add convexity for large moves.
FAQ
How does effective duration differ from modified duration?
Both measure price sensitivity to rate moves, but the methods and scope differ. Modified duration is derived from the weighted average cash-flow timing (Macaulay) assuming cash flows never change — fine for plain fixed-rate bonds, but not for bonds with embedded options (callable, puttable, MBS) where cash flows themselves shift when rates move. Effective duration revalues the price at a small up and down yield shift and reads the actual reaction, so it captures embedded-option effects and applies more broadly. For plain bonds the two are close; for option-bearing bonds only effective duration is accurate. This calculator uses the revaluation method.
Why also consider convexity?
Duration is a linear approximation — it assumes price-yield is a straight line, but the true relationship is a convex curve, accurate only for small moves. Full estimate: price change % ≈ −duration × Δy + 0.5 × convexity × (Δy)². The first term dominates small moves; the second (convexity) matters for large moves and favours the holder (positive convexity). Pair with a bond-convexity calculator.
Does a larger effective duration mean higher risk?
For interest-rate risk, yes: larger duration means price is more sensitive. Duration 6.1 means price moves about 6.1% per 1% yield change; duration 2 moves only about 2%. So in a rising-rate environment long-duration bonds fall more; in a falling-rate environment they gain more. Longer maturity, lower coupon and lower yield give longer duration. But duration covers only rate risk, not credit or liquidity risk — a short-duration high-yield bond may still be riskier overall.
Is a larger effective duration 'more dangerous'?
For rate risk, yes — more sensitive, higher rate risk — but 'dangerous' depends on the dimension. Duration quantifies 'how many percent price moves per 1% yield change'. Long duration is a risk when rates rise, an opportunity when rates fall. Bonds with longer maturity, lower coupon, lower yield have larger duration (zero-coupon ≈ its maturity). But duration measures only rate risk, not credit risk or liquidity risk; a short-duration low-rated high-yield bond may be far riskier overall. Investors use duration to manage a portfolio's rate exposure — shorten it when hikes are expected, lengthen when cuts are expected.
Why duration alone is not enough, and how convexity fits?
Duration is a linear approximation valid only for small moves. The true price-yield curve is convex, so its slope changes: price rises faster as yield falls, slows as yield rises. Convexity measures that curvature and is good for holders (positive convexity). Full estimate: price change % ≈ −duration × Δy + 0.5 × convexity × (Δy)². Duration gives the first-order slope, convexity the second-order correction; together they estimate large moves better. Use duration for small shifts; add convexity when rates may swing sharply or when comparing two bonds with similar duration but different convexity.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.