Bond duration versus maturity
Maturity identifies a repayment date; duration measures sensitivity to a specified yield change. Coupon timing and embedded options explain why the two measures diverge.
Bond maturity is the contractual date on which a bond’s final principal payment is due. Duration is a measure of cash-flow timing or price sensitivity, depending on the convention used. A maturity date does not by itself state how much the bond’s price will change when yields move.
Cash-flow timing changes rate sensitivity
A zero-coupon bond returns its contractual cash at maturity. A coupon bond pays interest before maturity, and an amortizing bond returns some principal earlier. These payment schedules place different amounts of value at different dates.
Holding credit and other relevant features constant, earlier cash flows reduce the dependence of present value on discounting over the full remaining term. Two bonds maturing on the same day can therefore have different durations.
The word “duration” needs its convention. Macaulay duration describes the present-value-weighted timing of cash flows. Modified duration expresses the approximate percentage price response to a small yield change when cash flows are held fixed. Effective duration estimates sensitivity using a model that can allow cash flows to change as rates move.
Modified duration gives a local approximation
Take a bond worth $1,000 with modified duration of 5. A yield increase of 0.5 percentage points gives an approximate price change of minus 5 multiplied by 0.005, or minus 2.5%. The estimated price decline is $25.
The calculation uses the yield change in decimal form. A 0.5-percentage-point increase is 0.005, not 0.5.
This is a local sensitivity calculation, not a predicted return. It holds other influences fixed and omits curvature in the price-yield relationship. Convexity describes that curvature; larger yield changes make a duration-only estimate less adequate.
Embedded options change the cash flows
A callable bond gives the issuer a contractual right to repay before final maturity under specified terms. When falling rates make refinancing attractive, expected repayment can move earlier. The investor’s projected cash flows change along with the discount rate.
Mortgage-backed securities have a related timing problem because borrower prepayments change principal return. A fixed-cash-flow sensitivity can miss that change. Effective duration depends on the model and assumptions used to project the option-sensitive payments.
Duration is not a complete risk measure
A lower duration establishes less sensitivity to the specified rate change under the calculation’s assumptions. It does not establish lower default risk, better liquidity, or a more favorable purchase price.
A bond’s price can also move because its credit spread changes. Its realized return includes coupon income, reinvestment, purchase and sale prices, and any default loss. Duration isolates one part of that result; maturity identifies a contractual endpoint.
Questions
- Can two ten-year bonds have different durations?
- Yes. Coupon amounts, payment timing, yields, amortization, and embedded options can produce different rate sensitivities despite the same final maturity.
- Does duration predict a bond’s return?
- No. Duration approximates sensitivity to a specified yield change. Realized return also depends on income, reinvestment, credit, and the eventual sale or repayment.
- Why use effective duration for a callable bond?
- Effective duration can account for projected cash flows changing when rates change. A callable bond’s expected repayment date depends partly on the issuer’s exercise of its option.