Macaulay Duration and Investment Horizon: When Price Risk Offsets Reinvestment Risk

Macaulay duration is easiest to remember when you stop treating it as a mystical bond statistic. It is a present-value-weighted average time to receive the bond's promised cash flows. That timing interpretation is what connects Macaulay duration to the investment-horizon rule: at about the Macaulay duration, price risk and reinvestment risk can offset each other for a small parallel yield change.

For CFA questions, the fastest path is to classify the question before calculating:

• Is it asking when the cash flows arrive?
• Is it asking how price changes when yield changes?
• Is it asking what happens to realized return over a holding horizon?

Those are related, but they are not the same question.

Macaulay duration is weighted timing

Macaulay duration weights each payment date by the present value of the cash flow received on that date.

For an option-free fixed-rate bond:

Macaulay duration = sum of (time to cash flow x PV of cash flow / full bond price)

A zero-coupon bond has Macaulay duration equal to its maturity because the investor receives the entire promised cash flow at the end. A coupon bond usually has Macaulay duration shorter than maturity because some value arrives earlier through coupons.

Worked example: timing weights

Harbor Glassworks issues a 3-year annual-pay bond with a face value of 1,000, a 6% coupon, and a yield of 5%.

The promised cash flows are:

• Year 1: 60
• Year 2: 60
• Year 3: 1,060

Because the final principal repayment is large, most of the present value still sits near year 3. But the two earlier coupons pull the weighted average time below 3 years. If the coupon were higher, more value would arrive earlier and Macaulay duration would fall. If the bond were zero-coupon, all value would arrive at maturity and Macaulay duration would equal 3 years.

Modified duration answers a different question

Modified duration translates timing into approximate price sensitivity. It estimates the percentage price change for a change in yield.

The relationship is:

Modified duration = Macaulay duration / (1 + periodic yield)

The exam trap is to see "duration" and jump to one interpretation. If the prompt asks why coupon income and sale price offset around a target date, think Macaulay duration and horizon. If the prompt asks for the price effect of a 50 basis point yield increase, think modified duration.

The investment-horizon rule

When yields change after a bond is purchased, two forces push realized return in opposite directions:

• Price risk: if yields rise, the bond's price falls; if yields fall, the bond's price rises.
• Reinvestment risk: if yields rise, future coupons can be reinvested at higher rates; if yields fall, future coupons are reinvested at lower rates.

The holding period determines which force matters more.

The phrase "can offset" matters. This is an approximation, not a promise that every bond earns the original yield under every rate path. The classic intuition assumes an option-free bond, parallel yield shifts, no default, no taxes or transaction costs, and a horizon close to the Macaulay duration.

When the horizon is shorter than duration

Suppose Northgate Transit Authority buys a 7-year coupon bond with a Macaulay duration of 5.6 years but expects to sell it after 2 years.

If market yields rise shortly after purchase:

• the bond's price falls,
• there are only a few coupon reinvestment periods before sale,
• the higher reinvestment income has limited time to offset the capital loss.

For a short horizon, price risk tends to dominate. Yield increases are usually harmful, and yield decreases are usually helpful.

When the horizon is longer than duration

Now suppose Northgate Transit Authority plans to hold the same bond for 9 years through reinvestment of coupons.

If yields rise early:

• the bond's current market price falls,
• but the investor may hold long enough for coupons to compound at higher rates,
• the reinvestment benefit can dominate the initial price decline.

For a long horizon, reinvestment risk can dominate. Yield decreases can become harmful because coupons are reinvested at lower rates for many periods.

When the horizon is close to Macaulay duration

If the planned holding horizon is close to Macaulay duration, the price and reinvestment effects are more likely to offset for small parallel yield changes. This is the intuition behind basic bond immunization: choose a bond or portfolio duration that aligns with the target horizon, then monitor and rebalance because duration changes as time passes and rates move.

Worked example: three horizons

Assume Seafield Utilities holds a coupon bond with Macaulay duration of 4.8 years.

The correct CFA answer often depends less on memorizing a phrase and more on identifying the horizon.

Coupon structure changes the starting point

Higher coupons generally shorten Macaulay duration because more value is received earlier. Lower coupons generally lengthen Macaulay duration because more value is pushed toward maturity.

That is why two bonds with the same maturity can have different duration:

• A high-coupon premium bond often has shorter Macaulay duration.
• A low-coupon discount bond often has longer Macaulay duration.
• A zero-coupon bond has Macaulay duration equal to maturity.

Exam framing

Trap 1: saying duration is just years

Macaulay duration is quoted in years because it is a weighted average time measure. Modified duration may also be quoted in duration units, but its use is price sensitivity.

Trap 2: saying rising rates are always bad

Rising rates hurt bond price immediately, but they improve the reinvestment rate on interim coupons. Whether realized return rises or falls depends on the holding horizon.

Trap 3: ignoring coupon timing

Maturity alone is not enough. Coupon rate, yield, and cash-flow timing determine the present-value weights.

Trap 4: treating immunization as permanent

Even if horizon and duration match today, duration changes over time. A portfolio may need rebalancing to keep the hedge aligned.

Quick decision rule

Use this order on CFA questions:

1. Identify whether the prompt asks about timing, price sensitivity, or realized return.
2. If it asks about timing, use Macaulay duration.
3. If it asks about price sensitivity, use modified or effective duration depending on the bond.
4. If it asks about holding-period return, compare the investment horizon with Macaulay duration.
5. If the horizon is short, expect price risk to dominate; if long, expect reinvestment risk to matter more.

That sequence turns duration from a memorized label into a risk map.