How does coupon reinvestment risk affect a bond's realized total return?
I'm studying CFA Level I Fixed Income and I keep reading that reinvestment risk is a major concern for bond investors. I understand that coupons are paid periodically, but I'm struggling to see exactly how reinvesting them at different rates changes my actual return. Can someone walk me through a concrete numerical example?
Coupon reinvestment risk is the risk that the cash flows you receive from a bond (coupons) will be reinvested at a rate different from the yield to maturity (YTM) that was assumed when you purchased the bond. This matters because YTM implicitly assumes every coupon is reinvested at that same rate for the remaining life of the bond.
Why It Matters
When you buy a bond at a given YTM, you're essentially locking in a promised return — but that promise depends on an assumption: that all intermediate coupons earn the same yield when reinvested. If rates fall after purchase, your coupons get reinvested at a lower rate, and your realized return falls below the original YTM.
Worked Example: Halcyon Corp 6% Semi-Annual Bond
Consider a 3-year, 6% semi-annual coupon bond purchased at par ($1,000). YTM = 6% (3% per semi-annual period). You receive 6 coupon payments of $30 each.
Scenario A — Reinvest at 6% (3% semi-annual):
| Coupon # | Payment | Periods Remaining | Future Value at Maturity |
|---|---|---|---|
| 1 | $30 | 5 | $30 x (1.03)^5 = $34.78 |
| 2 | $30 | 4 | $30 x (1.03)^4 = $33.76 |
| 3 | $30 | 3 | $30 x (1.03)^3 = $32.78 |
| 4 | $30 | 2 | $30 x (1.03)^2 = $31.83 |
| 5 | $30 | 1 | $30 x (1.03)^1 = $30.90 |
| 6 | $30 | 0 | $30.00 |
| Total | $194.05 |
Total return = $194.05 (coupons + reinvestment) + $1,000 (principal) = $1,194.05
Scenario B — Rates drop to 2% (1% semi-annual):
| Coupon # | Payment | Periods Remaining | Future Value at Maturity |
|---|---|---|---|
| 1 | $30 | 5 | $30 x (1.01)^5 = $31.53 |
| 2 | $30 | 4 | $30 x (1.01)^4 = $31.22 |
| 3 | $30 | 3 | $30 x (1.01)^3 = $30.91 |
| 4 | $30 | 2 | $30 x (1.01)^2 = $30.60 |
| 5 | $30 | 1 | $30 x (1.01)^1 = $30.30 |
| 6 | $30 | 0 | $30.00 |
| Total | $184.56 |
Total return = $184.56 + $1,000 = $1,184.56
The difference is $9.49 in lost reinvestment income. The realized annualized return in Scenario B is approximately 5.47% vs the original 6% YTM — a meaningful shortfall over just 3 years. Over longer horizons, this gap widens dramatically.
Key Takeaway: Reinvestment risk is largest for bonds with high coupons, long maturities, and when rates fall. Zero-coupon bonds have zero reinvestment risk because there are no intermediate cash flows to reinvest.
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