realized compounded yield

This question is from Schweser A bond has a par value of $1,000, a time to maturity of 20 years, a coupon rate of 10 percent with interest paid annually, a current price of $850, and a yield to maturity (YTM) of 12 percent. If the interest payments are reinvested at 10 percent, the realized compounded yield on this bond is: A) 10.00%. B) 12.0%. C) 12.4%. D) 10.9%. I know the solution must be trivial, but my brain is kind of fried, can someone please help? Thanks!! I’m not sure why the answer is D

First, you have your interest payments (coupons) reinvested at 10%. This is an annuity PMT 100, for N 20 periods, invested at 10%, that currently costs you PV 0. Calculate the future value, this wouild give you $5,727.5. Than, at maturity of the bond you get the $1000. Your total Future value FV is $1,000+$5,727.5 = $6,727.5. Make this your FV, that is obtained by paying a single sum PV $850 now, after N 20 periods, as if you would receive PMT of $0 each year. CPT I/Y. That gives you 10.8975%. That’s D.

Thanks!!

if YTM is 12% and re-investment rate is 10%, then total realized yield will always be between 10% and 12% ----> hence D

Bonus question: what is the realized compounded yield on this bond if coupons are reinvested at 12%?

12% am i close dreary : ?

There you go. So YTM is a misleading measure! You get that rate only *if* you reinvest the coupons at that rate. This is almost always never the case.