Bond horizons, reinvestment and Macaulay duration

Learning goals

• Explain return components using mechanisms and limitations.
• Explain horizon trade-off using mechanisms and limitations.
• Explain cash-flow timing using mechanisms and limitations.

Draft · approximately 35 minutes, excluding further revision.

Return components

Bond holding return combines coupons, reinvestment income and sale or redemption proceeds relative to purchase cost; YTM alone does not describe every investment horizon.

Rising yields reduce sale price but can improve coupon reinvestment rates; the two effects can offset over an appropriate horizon.

Horizon trade-off

Macaulay duration is the present-value-weighted average payment time; weights sum to one when discounted cash flows equal price.

Matching a horizon to Macaulay duration can reduce sensitivity to a small immediate parallel yield change under restrictive reinvestment and cash-flow assumptions.

Cash-flow timing

A zero-coupon bond’s Macaulay duration equals maturity when its sole payment is at maturity; coupon bonds normally have earlier weighted payment times.

Credit events, nonparallel curve changes and changing cash flows can break simple horizon immunization; review exposures as time passes.

Reinvest the first coupon and sell at the horizon

Buy a two-year annual5% coupon bond at100 when yield5%. After an immediate permanent parallel move to6%, a one-year investor receives coupon5 and sells the remaining one-year claim for105/1.06=99.0566. One-year wealth104.0566 gives4.0566% return. This investor is exposed mainly to the sale-price effect.

A two-year holder instead reinvests the first5 at6%, ending with105+5×1.06=110.3; annualized return=(110.3/100)^0.5−1=5.0238%. With this cash-flow pattern, Macaulay duration initially is(1×5/1.05+2×105/1.05²)/100=1.95238 years. Duration-horizon matching locally balances effects; it is not exact protection against large or nonparallel moves.

Formula and assumptions

DMac=Σ[t×PV(CFt)]/price

Original applied case: Bond horizons, reinvestment and Macaulay duration

1. A bond has present-value payments 5 at year one and 95 at year two; total price 100.
2. Macaulay duration=(1×5+2×95)/100=1.95 years.
3. The time-weighted value differs from the two-year final maturity because some value arrives earlier.

Errors to catch

• Do not assume: Coupon reinvestment never affects bond holding return.
• Do not assume: Rising rates improve both sale price and reinvestment.
• Do not assume: Macaulay duration is an unweighted average of dates.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov