What Is Reinvestment Risk?
After each coupon arrives, what rate can it earn? That can change the final outcome of the same bond.
Try it and see the difference
The same 250 in coupons, but different final wealth?
Buy a five-year bond for 1,000, with 5% coupon and nominal YTM, paying semiannually. Hold to maturity and vary only coupon reinvestment.
- Maturity principal
- 1,000.00
- Five years of coupons · fixed
- 250.00
- Reinvestment income · changes with rate
- 30.08
Reinvesting every coupon at nominal 5% with semiannual compounding produces 5.0625% effective annually, matching the effective annual form of the original YTM.
1,000 + 250.00 + 30.08 = 1,280.08
Each semiannual coupon is 25; earlier coupons have more periods to grow. No interim sale, default, early call, taxes or fees are modeled.
Why does this happen?
The contract still pays the same coupons, but early coupons have years left to grow. A lower reinvestment rate reduces interest earned after receiving coupons, not the coupons themselves. Holding to maturity avoids interim sale-price changes, but not coupon reinvestment risk.
Separate two effects of changing rates
Market yield affects an interim sale price; the reinvestment rate affects coupon growth. This interaction holds to maturity with fixed principal repayment and changes only reinvestment. Bond total return also includes price gain or loss.
Show formal definition and formula
Reinvestment risk is the possibility that future coupons must earn a rate different from the original assumption, changing final wealth and realized compound return.
Principal plus the terminal value of each coupon
Convert accumulation into effective annual return
Convert nominal yield into effective annual yield
- W / P
- Maturity wealth / purchase price
- F / C
- Maturity principal / coupon per period
- r / y
- Nominal reinvestment rate / original nominal YTM, decimals
- m / N
- Coupon frequency / total periods
- t / T
- Period when a coupon arrives / holding years
Fixed scheduled payments, valued on a coupon date with decimal rates. Default, taxes, fees and calls not defined in the example are excluded.
A common misconception
YTM is an implied yield, not a promise that every coupon can be reinvested at that rate. Here a nominal 5% YTM compounded semiannually corresponds to 5.0625% effective annually; those annual conventions are different.