Effective Duration

The calculation is a controlled experiment on a valuation model. Start from the current price consistent with the benchmark curve and the bond's option-adjusted spread. Shift the entire curve up by a small amount, hold the OAS constant, let the model re-derive the cash flows and discount them, and record the lower price. Repeat with the curve shifted down by the same amount to obtain the higher price. Effective duration equals the price at the lower curve minus the price at the higher curve, divided by twice the size of the shift in decimal form, all divided by the initial price.

Two modelling choices matter. The shift must be small enough that convexity does not distort the symmetric difference, yet large enough that the model's numerical noise does not dominate. Holding the OAS fixed is what isolates interest rate sensitivity from credit and liquidity repricing; if the spread is allowed to move, the result blends two distinct risks.

When a bond's cash flows are fixed, yield duration measures are internally consistent: there is one yield, one set of payments, and a clean analytical derivative. Introduce a call, a put, a prepayment option or a coupon reset and the payment stream becomes a function of the rate path, so no single yield summarises the bond.

The economic consequences are visible in the numbers. A callable bond's effective duration is lower than the duration of an otherwise identical straight bond, because rate declines push the price toward the call price rather than toward the higher present value of remaining coupons. That price compression is negative convexity. A putable bond is similarly damped on the downside, since the put floors the price as rates rise. A floating-rate note has very small effective duration, because the coupon reset restores value near par at each date. Mortgage pass-throughs combine these effects, with duration that lengthens as rates rise and shortens as they fall.

Effective duration is the standard risk statistic in fixed income index and fund reporting, precisely because broad benchmarks contain callable corporates, agency debt, securitised product and floating-rate paper. A portfolio's effective duration is the market-value-weighted average of its holdings' effective durations, which lets managers state an active duration position relative to a benchmark in a single number.

It also feeds practical hedging arithmetic. Multiplying effective duration by market value gives money duration, the currency change in value per one percentage point move; scaling that to one basis point gives the price value of a basis point used to size futures and swap hedges. In liability-driven investing, asset and liability effective durations are matched so that a small parallel move leaves surplus roughly unchanged. Because the measure assumes a parallel shift, desks supplement it with key rate durations to capture curve reshaping, and with one-sided durations for instruments whose sensitivity is asymmetric.

Expect to compute effective duration from two model prices and a stated curve shift, and to reverse the relationship: given effective duration and convexity, estimate a percentage price change for a specified yield move, adding the convexity term for larger shocks. You should be able to rank the durations of a straight bond, an otherwise identical callable bond and an identical putable bond, and to explain how the ranking depends on where rates stand relative to the exercise triggers.

Equally testable are the limits. Effective duration is model-dependent, so different prepayment or interest rate volatility assumptions produce different answers for the same security. It captures only parallel shifts, so it says nothing about steepening or flattening exposure. It holds the spread constant, so it excludes spread duration risk. Recognising which of these limitations a question is probing is usually the difference between the right and the plausible answer.