Duration measures how much a bond's price changes when interest rates move. A bond with a modified duration of 8.0 years loses approximately 8.0% in price for every 100 basis point rise in yield, and gains approximately 8.0% for every 100 bp decline. Portfolio managers use duration as the primary tool for expressing and hedging interest rate views.
Two duration concepts matter most in practice. Macaulay duration is the weighted average time to receive a bond's cash flows, expressed in years. Modified duration converts that figure into a direct price sensitivity measure.
The relationship is:
Modified Duration = Macaulay Duration / (1 + y/k)
where y is the yield to maturity and k is the number of coupon payments per year. For a semiannual-pay bond yielding 4.0%, the divisor is 1.02.
The price change approximation is:
% Price Change ≈ -Modified Duration × Δy
For larger yield moves, adding the convexity correction improves accuracy:
% Price Change ≈ -ModDur × Δy + 0.5 × Convexity × (Δy)²
Convexity is always positive for standard non-callable bonds, so the correction always works in the investor's favor.
Consider a 10-year Treasury note with a 4.0% coupon, priced at par (yield = 4.0%, semiannual payments). The Macaulay duration for this bond is approximately 8.35 years. Applying the formula:
Modified Duration = 8.35 / (1 + 0.04/2) = 8.35 / 1.02 = 8.19 years
A 50 bp rise in yield (Δy = 0.005) produces an estimated price change of:
-8.19 × 0.005 = -4.1%
On a 1,000,000 position, that is a mark-to-market loss of approximately 41,000.
For comparison, a 30-year 4.0% coupon bond at par carries a modified duration of approximately 17.5 years, meaning the same 50 bp move produces roughly a -8.75% price change. Extending maturity more than doubles the interest rate risk in this example.
The YCP /duration page displays live modified duration estimates across all Treasury tenors, updated daily after each market close.
Four rules govern how duration responds to bond characteristics:
These relationships explain why long-duration zero-coupon bonds are the most interest rate sensitive instruments, and why floating-rate notes, which reset frequently, carry near-zero duration.
Portfolio duration is the market-value-weighted average of the individual bond durations:
Portfolio Duration = Σ (Market Value Weight × Bond Duration)
Consider a 10 million portfolio: 5 million in 2-year notes (modified duration 1.9 years) and 5 million in 10-year notes (modified duration 8.2 years).
Portfolio Duration = 0.5 × 1.9 + 0.5 × 8.2 = 5.05 years
A 100 bp parallel shift would produce an estimated loss of approximately 505,000. A manager who wants to reduce that sensitivity can sell 10-year notes and buy 2-year notes, lowering the weighted average. One who wants to extend risk adds to the long end.
The YCP /duration page shows current modified duration by tenor, making it straightforward to estimate the duration impact of shifting allocations across the curve.
Macaulay duration is the weighted average time (in years) to receive all cash flows. Modified duration divides Macaulay duration by (1 + y/k) and gives a direct price sensitivity measure: the percentage price change per 1% change in yield.
DV01 (dollar value of a basis point) is modified duration expressed in dollar terms per basis point move. For a $1,000,000 position with modified duration of 8.19 years, DV01 = 1,000,000 × 0.0819 × 0.0001 = 819.
The call option gives the issuer the right to redeem the bond early, typically when rates fall. When rates decline, the bond's price appreciation is capped because the issuer will likely call. This cap on upside reduces the effective (option-adjusted) duration relative to an equivalent non-callable bond.
The linear approximation becomes less accurate as the yield move grows. For moves beyond 50 bps, adding the convexity correction significantly improves the estimate. For very large moves, full repricing using the bond's cash flows and the new yield is more reliable.