Buy a 4-year, 6% annual-coupon bond at par and watch its yield jump to 8% the day after you buy. Sell after 1 year and you earn 0.85%. Hold for 3.67 years and you earn 6.00%. The number that separates those outcomes is the bond's Macaulay duration.
Every dollar you earn from a fixed-rate bond comes from one of three sources:
- Coupon and principal payments received from the issuer
- Reinvestment income earned by reinvesting coupons at prevailing rates
- Capital gain or loss if the bond is sold before maturity at a price different from its constant-yield trajectory
KEY: Hold to maturity AND reinvest every coupon at the original yield to maturity (YTM), and your realized yield equals the YTM at purchase. Realized return drifts from that YTM when reinvestment rates or the sale price change. An early sale still earns the original YTM if coupons earn that rate and you sell at the carrying value (Example 3a).
Reinvestment income is interest on interest. You calculate it as the future value of the coupons at the rate you actually reinvest them, minus the coupons themselves.
Common mistakes
- Forgetting to convert semiannual MacDur to years. Computing duration with semiannual periods returns periods, not years. Divide by 2. Trap: reporting 5.640 for the Example 4 bond when the answer is 2.820 years.
- Confusing Macaulay with modified duration. Macaulay = weighted average time. Modified = MacDur / (1 + r). Modified is the price-sensitivity number. The exam tests the conceptual gap.
- Listing only two sources of return. Many candidates name coupon and reinvestment but skip the third: capital gain or loss on sale before maturity. Hold to maturity and the third source disappears.
Bottom line
- Three return sources: coupon payments, reinvestment of those coupons, and capital gain/loss if sold before maturity. Holding to maturity removes the third.
- Horizon yield = (coupons + reinvestment income + sale price) / purchase price, raised to 1/H, minus 1.
- Capital gain or loss = sale price minus carrying value (the price at the original YTM), never minus the purchase price.
- Macaulay duration = weighted average time to cash flow receipt, weights are PV(CFt) / Price, and those weights sum to 1.
Exam shortcut
For the three sources, remember CRC: Coupon, Reinvestment, Capital gain/loss. When a question asks for realized return, build the total future value first, then take the 1/H root on the time-value-of-money (TVM) keys (N = H, PV = −price, PMT = 0, FV = total). Measure any gain or loss against the carrying value at the original YTM.
The full lesson (about 3,624 words, 24 min read) adds 10 worked examples, all 8 common mistakes, a self-check, free in the app.
Learning objectives
- interest rate risk and return
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