Why does YTM assume coupon reinvestment at the same rate, and when does this assumption fail?

Yield to maturity (YTM) is the internal rate of return on a bond's cash flows, and it implicitly assumes that every coupon received is reinvested at the YTM rate for the remaining life of the bond. This is a critical — and often unrealistic — assumption.

Why the Assumption Exists:

YTM solves for the single discount rate that equates the bond's price to the present value of all future cash flows. Mathematically, for the actual realized return to equal the YTM, the investor must:

1. Hold the bond to maturity
2. Reinvest every coupon at exactly the YTM rate
3. Face no default

Example — Dunfield Corp 7% Bond (fictional):

Scenario 1: Reinvestment at 7% (YTM holds)

• FV of coupons = $70 x [(1.07^10 - 1)/0.07] = $70 x 13.8164 = $967.15
• Total wealth = $967.15 + $1,000 = $1,967.15
• Realized return = (1,967.15/1,000)^(1/10) - 1 = 7.00%

Scenario 2: Rates drop to 4% after purchase

• FV of coupons = $70 x [(1.04^10 - 1)/0.04] = $70 x 12.006 = $840.42
• Total wealth = $840.42 + $1,000 = $1,840.42
• Realized return = (1,840.42/1,000)^(1/10) - 1 = 6.29%

Scenario 3: Rates rise to 10%

• FV of coupons = $70 x [(1.10^10 - 1)/0.10] = $70 x 15.9374 = $1,115.62
• Total wealth = $1,115.62 + $1,000 = $2,115.62
• Realized return = (2,115.62/1,000)^(1/10) - 1 = 7.78%

Key Takeaways:

• When rates fall, reinvestment income drops, and realized return is below YTM
• When rates rise, reinvestment income increases, and realized return is above YTM
• Reinvestment risk is greater for longer maturity bonds and higher coupon bonds (more cash flows to reinvest)
• Zero-coupon bonds have zero reinvestment risk because there are no coupons to reinvest

Exam Tip: The CFA exam loves testing the relationship between reinvestment risk and bond characteristics. Remember: longer maturity and higher coupons mean more reinvestment risk.

Practice reinvestment analysis in our CFA Level I question bank.