Fisher-Weil Duration
A duration measure that discounts each cash flow with the actual zero-coupon rate for its maturity, instead of pretending one flat yield applies to every payment date.
Ordinary duration measures assume a bond is discounted at a single yield-to-maturity, even though its coupons and principal actually land on different dates where the true zero-coupon curve may be higher or lower. Fisher-Weil duration fixes this by discounting each cash flow with the zero rate that actually applies to its own maturity, then computing the weighted-average time to payment from those present values.
Fisher-Weil duration is Macaulay duration done properly against the real term structure: each cash flow gets its own discount rate off the zero curve, not one shared yield-to-maturity.
Why it matters
Two bonds with identical Macaulay duration under a flat-yield assumption can behave differently when the curve twists, because Fisher-Weil duration is sensitive to the shape of the curve, not just its level. It is the more honest measure whenever the curve is steep or humped, which is most of the time.
Worked example
A 2-year bond pays a coupon at year 1 and a coupon-plus-principal at year 2. The 1-year zero rate is 3%, the 2-year zero rate is 4%. Discount the year-1 cash flow at 3% and the year-2 cash flow at 4%, rather than discounting both at a single blended yield of, say, 3.8%. The present values that come out of this are slightly different from the flat-yield case, which shifts the weighted-average maturity — the Fisher-Weil duration — away from what a standard duration calculation would report.
Risk managers use Fisher-Weil duration when comparing bonds or hedging portfolios against a curve that is not flat, since it reflects real reinvestment and discounting risk more accurately than a single-yield shortcut.
Practice in interviews
Further reading
- Fisher, L. and Weil, R., 'Coping with the Risk of Interest-Rate Fluctuations' (1971)