While reading up on the effective yield for bonds I noticed that it relies on the fact that the investor reinvests their coupon earnings in order to take advantage of compound interest. However, does the effective yield calculation assume that the investor is reinvesting at the same rate as the bond coupon?
However, does the effective yield calculation assume that the investor is reinvesting at the same rate as the bond coupon?
No - it assumes that the investor is reinvesting coupons at the risk-equivalent yield (not coupon rate) at the time the coupon is received.
Say you buy a 3-year annual-coupon bond with a coupon of 5% but a yield of 10%. In one year you receive a coupon payment. At that time, your bond is trading at a yield of 12%. The model assumes that you can invest the coupon for the remaining two years in something that offers a 12% yield.
So the model has to incorporate future expectations of interest rates in order to predict risk-equivalent yields.