Bond Duration in CFA Level I: The Measure Depends on the Rate Shock

Duration is one word with several related meanings. That is what makes it feel slippery. Macaulay duration answers a timing question: when, on a present-value-weighted basis, does the investor receive the bond's promised cash flows? Modified duration answers a sensitivity question: how much should the bond's price change for a small change in its own yield? Effective, key rate, spread, and empirical duration refine the sensitivity question when the yield curve or cash flows behave differently.

The fastest way to choose the right measure is to ask: what is changing?

Macaulay Duration: The Timing Anchor

Macaulay duration is the present-value-weighted average time to receive the bond's promised cash flows. For a zero-coupon bond, all cash flow arrives at maturity, so Macaulay duration equals maturity. For a coupon bond, some cash is received before maturity, so Macaulay duration is less than maturity.

Worked Timing Example

Silverline Transit Authority has a three-year annual-pay bond with:

• Face value: $1,000
• Coupon rate: 6%
• Yield to maturity: 5%
• Annual coupons

Present values:

Macaulay duration = 2,912.93 / 1,027.21 = 2.84 years

The bond matures in three years, but its present-value-weighted cash-flow timing is 2.84 years because coupons arrive earlier.

Modified Duration: The Price Sensitivity Approximation

Modified duration turns Macaulay duration into a first-order price sensitivity measure. For a small change in the bond's own yield:

Approximate % price change = -Modified duration x Change in yield

If Silverline's modified duration is 2.70 and its yield rises by 40 basis points, the approximate price change is:

-2.70 x 0.0040 = -0.0108 = -1.08%

This is why candidates get confused by units. Modified duration may be quoted as a duration number, often in years, but it is used as a sensitivity multiplier. The yield change must be entered in decimal form.

Money Duration and PVBP: Scaling the Risk

Modified duration estimates a percentage price change. Money duration scales that sensitivity by the market value of the position.

If a portfolio holds $4,000,000 of bonds with modified duration of 5.25:

Money duration = 5.25 x $4,000,000 = $21,000,000
PVBP = $21,000,000 x 0.0001 = $2,100

PVBP estimates the dollar change for a one-basis-point yield move. This is useful for risk budgeting and hedging because portfolio managers often care about dollars, not only percentages.

Effective Duration: When Cash Flows Can Change

Modified duration assumes the bond's cash flows do not change when yield changes. That assumption is weak for bonds with embedded options.

A callable bond may be called when rates fall, shortening expected cash flows and limiting upside price appreciation. A putable bond may extend or shorten differently depending on the option holder's behavior. Effective duration uses model prices under up-rate and down-rate scenarios, so it is more appropriate when expected cash flows can change.

Key Rate Duration: When the Curve Does Not Move in Parallel

Modified and effective duration often summarize sensitivity to a broad yield or benchmark curve change. Key rate duration asks a more targeted question: how sensitive is the bond to a change at a specific maturity point on the benchmark curve?

For example, a bond may have:

If the 10-year point rises while the 2-year and 5-year points are stable, the 10-year key rate duration is the relevant risk measure. This matters when yield curves steepen, flatten, or twist.

Spread Duration and Empirical Duration

Spread duration measures sensitivity to a change in a bond's spread over a benchmark. It is especially useful for credit-risky bonds when the analyst wants to separate benchmark rate risk from credit spread risk.

Empirical duration uses historical data to estimate how a bond's price has actually responded to rate changes. This can capture market behavior that a purely analytical measure may miss, especially when benchmark yields and credit spreads move together during stress.

Exam Framing

For CFA Level I, duration questions usually become straightforward when you match the measure to the shock:

• Weighted-average receipt timing: Macaulay duration.
• Small change in the bond's own yield, fixed cash flows: modified duration.
• Dollar exposure to yield changes: money duration or PVBP.
• Embedded options or rate-sensitive cash flows: effective duration.
• Non-parallel benchmark curve shift: key rate duration.
• Credit spread change: spread duration.
• Historical observed price-rate relationship: empirical duration.

The common trap is using one measure everywhere. Modified duration is powerful, but it is not the right tool when the question changes cash flows, isolates one part of the curve, or asks about spread risk rather than the bond's own yield.