Yield-Based Bond Duration Measures and Properties

A portfolio manager holds $50 million face value of 10-year Treasuries and needs to know exactly how many dollars are at risk if yields jump 25 basis points before tomorrow's FOMC announcement. Modified duration, money duration, and PVBP convert one bond math concept into three answers the trading desk actually uses.

Modified duration measures the percentage change in a bond's full price for a 1 percentage point (100 basis point) change in yield-to-maturity. It is yield-based, meaning the inputs are the bond's own cash flows and YTM, not a benchmark curve.

$$\text{ModDur}=\frac{\text{MacDur}}{1+r}$$

The interpretation: a ModDur of 7.2 means a 1% rise in yield reduces price by about 7.2%. The relationship is linear in yield change (first-order approximation):

$$\%\Delta P{V}^{\text{Full}}\approx -\text{ModDur}\times \Delta \text{Yield}$$

When MacDur is not given, use the approximate modified duration formula. Reprice the bond after a small yield bump up and down:

$$\text{ApproxModDur}=\frac{P{V}_{-}-P{V}_{+}}{2\times \Delta \text{Yield}\times P{V}_0}$$

Common mistakes

• Reversing the numerator in ApproxModDur. Using $P{V}_{+}-P{V}_{-}$ produces a negative duration. Trap value: $-13.73$ on Example 2.
• Forgetting to divide MacDur by (1 + r). Reporting MacDur as ModDur understates the correction. For a 5-year bond at 5% YTM with MacDur 4.62, reporting "4.62" instead of 4.40 is the classic error.
• Mixing percent and decimal in the duration formula. Plugging $\Delta \text{Yield}=100$ (for 1%) instead of 0.01 inflates the loss estimate 100-fold. Always use decimal yield changes.

Bottom line

• Modified duration = Macaulay duration / (1 + periodic yield). It estimates the percentage price change for a 1% yield change.
• Money duration = modified duration × full price. It converts the percentage into dollars at risk.
• PVBP = money duration × 0.0001. It is the dollar price change for a one basis point yield move.
• Longer maturity, lower coupon, and lower yield all raise interest rate risk.

Exam shortcut

For unit conversion: ModDur is percent, MoneyDur is dollars per 100% yield change, PVBP is dollars per 0.01% yield change. Multiply by 0.0001 to step from MoneyDur to PVBP. For properties, memorize "Long, Low, Low": Long maturity, Low coupon, Low yield all maximize interest rate risk.

The full lesson (about 1,859 words, 12 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• yield-based duration measures

Browse all free CFA Level I lessons or jump into free CFA Level I practice questions.