YTM is yield achieved irrespective of reinvestment of coupons.
Consider a $1000 bond with 10% YTM that pays 10% coupons for 3 years.
Case 1: With reinvestment of coupons
| 1st year coupon | 2nd year coupon | Coupon reinvested at 10% | 3rd year value of old coupons |
|---|---|---|---|
| $100 | - | 100 * 1.12 | = $121 |
| - | $100 | 100 * 1.11 | = $110 |
Total return = $121 + $110 + $1100 = $1331
(where $1100 is the final coupon + par value).
FV = PV (1 + r)n
Since FV = $1331, PV = $1000, n = 3:
Annualized return, r = (1331/1000)1/3 - 1 = 0.1 = 10% = YTM
Case 2: No reinvestment of coupons
| 1st year coupon | 2nd year coupon | 3rd year value of old coupons |
|---|---|---|
| $100 | - | = $100 |
| - | $100 | = $100 |
Total return = $100 + $100 + $1100 = $1300
(where $1100 is the final coupon + par value).
But now we cannot use the compound interest formula as the coupons were not reinvested, so we use simple interest:
FV = PV (1 + r * n)
Since FV = $1300, PV = $1000, n = 3:
r = ((1300/1000) - 1) / 3 = 0.1 = 10% = YTM
Thus, the bond will always return the YTM, irrespective of reinvestment of coupons.
I think there are just different perspectives to look at it.
The investor is definitely at loss if coupon payments are not reinvested, but the YTM is always delivered by the bond as promised during initial investment.
References:
http://www.economics-finance.org/jefe/econ/ForbesHatemPaulpaper.pdf
http://www.economics-finance.org/jefe/econ/CebulaYangpaper.pdf
