Effective Duration Calculator

What effective duration measures

Effective duration captures the first-order sensitivity of a bond's price to a parallel shift in the yield curve. A bond with an effective duration of 5 is expected to lose approximately 5% of its market value for every 1 percentage point increase in yields, and gain approximately 5% for every 1 percentage point decrease.

The metric is essential for portfolio managers, risk analysts, and fixed-income traders who need to quantify interest rate risk across instruments that may not follow simple present-value discounting — particularly callable bonds whose cash flows change when issuers exercise early redemption options.

Effective duration formula

The calculation requires three price observations: the bond's current price (P₀), the price when yields decrease by a small amount (P−), and the price when yields increase by the same amount (P+). The yield shift (Δy) must be expressed as a decimal.

By averaging the upward and downward price responses and normalising by the initial price and the size of the yield shock, effective duration provides a symmetric, unitless sensitivity measure.

Effective duration vs modified duration

Modified duration assumes that cash flows do not change when yields shift. This is valid for plain-vanilla fixed-rate bonds but breaks down for callable bonds, where the issuer may redeem the bond early if rates fall, truncating future coupon payments and capping price appreciation.

Effective duration accounts for these cash-flow changes because it is computed from repriced models or observed market prices under different yield scenarios, not from a closed-form derivative of the price–yield function. For option-free bonds, effective duration and modified duration converge to the same value.

Worked example

A callable corporate bond is currently priced at 100. An analyst shifts the benchmark yield curve down by 50 basis points and reprices the bond at 102.10 using an option-adjusted spread model. Shifting yields up by 50 basis points gives a repriced value of 97.80.

Effective Duration = (102.10 − 97.80) / (2 × 100 × 0.005) = 4.30 / 1.00 = 4.30. The bond has an effective duration of 4.30, meaning its price is expected to change by approximately 4.30% for every 1% parallel shift in the yield curve.

Convexity and second-order effects

Duration is a linear approximation. For large yield changes, the actual price change diverges from the duration estimate because of convexity — the curvature of the price–yield relationship. Positive convexity (typical of non-callable bonds) means the bond gains more when rates fall than it loses when rates rise. Negative convexity (typical of callable bonds when rates are near the call strike) flattens the upside.

For more precise risk management, analysts combine effective duration with effective convexity to build a second-order Taylor approximation of price change: ΔP/P ≈ −Duration × Δy + 0.5 × Convexity × (Δy)².

Limitations of this calculator

This tool requires the user to supply pre-computed prices under shifted yield scenarios. It does not perform bond valuation, option-adjusted pricing, or yield-curve construction. The accuracy of the result depends entirely on the quality of the input prices. For bonds with embedded options, those prices should come from an appropriate valuation model (binomial tree, Monte Carlo, OAS model) rather than simple present-value discounting.