Buy a 10-year bond at 5% YTM and hold for 7 years. Did you earn 5%? The answer depends on what happens to rates and how that interacts with one specific number: the bond's Macaulay duration.
To calculate and interpret a bond's total return, separate it into 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 YTM, and your realized yield equals the YTM at purchase. Any deviation from those conditions creates the gap between promised and realized return.
Reinvestment risk is the risk that future coupons earn less than the original YTM. Market price risk is the risk that the sale price differs from the constant-yield projection. These two risks move in opposite directions when rates change. Rising rates hurt prices but help reinvestment. Falling rates help prices but hurt reinvestment.
Common mistakes
- Forgetting to convert semiannual MacDur to years. Computing duration with semiannual periods returns periods, not years. Divide by 2. Trap: reporting "7.4" when the answer should be 3.7 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.
- Macaulay duration = weighted average time to cash flow receipt, weights are PV(CFt) / Price, and those weights sum to 1.
- Coupon bonds: MacDur < maturity; a zero-coupon bond: MacDur = maturity exactly.
- Higher coupon shortens duration, higher YTM shortens duration, longer maturity lengthens duration.
Exam shortcut
For the three sources, remember CRC: Coupon, Reinvestment, Capital gain/loss. For the horizon rule, "match horizon to duration to lock in YTM." For fast MacDur on coupon bonds, weight each cash-flow time by its PV fraction if N is small. For zeros, skip the math: MacDur equals maturity.
The full lesson (about 1,442 words, 10 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- interest rate risk and return
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