realized yield on a note

CFA Level I Fixed Income
#1

Hi,

I am trying to solve the following question, but I can’t come up with the right answer:

A 3-year, 6% coupon, semiannual-pay note has a yield to maturity of 5.5%. If an investor holds this note to maturity and earns a 4.5% return on reinvested coupon income, his realized yield on the note is closest to:

First, I calculate the FV of the coupon payments with an interest rate of 4.5%.

30*(1.045)^2.5 + 30*(1.045)^2 + … + 30 = 190.32

In t=3 years the investor will have a FV of 1000+190.32=1190.32. He buys the bond at t=0 for:

N=6, I/Y=2.75, PMT=30, FV=1000 -> PV=-1013.66

His yield will be (1190.32/1013.66)^(1/3)-1~5.5%.

Shouldn’t his yield be lower than 5.5% since he can only reinvest his coupon payments at a rate lower than the YTM of the bond?

The correct answer according to Schweser is closest to 4.6%, but I don’t know how to arrive at that result.

I appreciate your help.

#2

A couple of points:

  1. You’re calculating the reinvestment return on the coupons as if the 4.5% is an annual _ effective _ rate; make sure that it isn’t intended to be a BEY. (The difference is small, but as long as you’re learning this stuff, you should make sure you’re doing it correctly.)
  2. I get the PV of the bond as -$1,124.58. You should recheck your calculation. It appears that you may simply have discounted the ending value of $1,190.32 back to today at 5.5%.