8.2 Positive-Coupon Bond: An Examination of the Reinvestment Rate Assumption
By assuming a reinvestment rate (initially the YTM) for the bond’s interim cash flows, the FV (or “terminal value”) of a bond can be calculated. This would be equivalent to converting a coupon bond to a Zero-coupon bond, the FV of whose coupons and Face Value, in sum, would equal the maturity value of an equivalent Zero. The rate at which the terminal value of all the bond’s cash flows would be equal to its PV (i.e., cost) would be the bond’s discount rate, or YTM. We shall call this rate, the “Realized Compound Yield,” or RCY.
[latex]Price = \frac{(CPN\times FVAF @ REIN rate) + Par}{(1+RCY/p)^{np}}[/latex]
- Where REIN = the reinvestment rate.
- Note that you must add the bond’s Par Value to the numerator as it is the bond’s last cash flow – received at the horizon.
- Therefore:
[latex](1+RCY/p)^{np}=\frac{(CPN\times FVAF @ REIN rate)+Par}{Price}[/latex]
Practice:
Find the RCY for the following:
| CPN = .08 | N = 10 yrs. | Semi-Ann. |
| YTM = .08 | Price = Par | REIN = .08 |
Questions
- What is the likelihood that the investor will reinvest his coupon cash flow at the YTM?
- What is the relationship between the Y-T-M and RCY?
- What ex-ante assumptions have we posited (so far)?
Note:
FVAF is the “future value annuity factor” or multiplier.
