Reinvestment coupon income question

Question #110 Schweser Exam 1 - Afternoon Session A 3-year, 6% coupon, semi-annual-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: A. 5.46% B. 5.57% C. 5.68% This questions is killing me, and Schweser gives a lame explanation. Can some please help me out with this. Thank You -Simon

YTM assumes that coupons are reinvested at YTM. This investor earns 4.5% on the coupon income which is less than YTM. So realized yield has to be less than 5.5. By the process of elimination it should be A.

is there a way to calculate the realized yield and not do it just by elimination??

What is the actual calculation to get to the answer?

Current market price of bond is $1,013 (N=6, I/Y=5.5/2=2.75, PMT=$30, FV=$1000, CPT PV) If coupons are reinvested at 4.5%, FV of coupons at end of three years is $191. (N=6, I/Y=4.5/2=2.25, PMT=$30, PV=0, CPT FV) YTM for investment in this bond is 5.46% (PV=$1,013, N=6, PMT=0, FV=$1,191 (191+1000), CPT I/Y = 2.73 X2 = 5.46%)

Thank You

The coupon rate (or the PMT value) above did not change until maturity (it was always $30).

The par value (or Face Value or FV) of the bond also stays the same.

Coupons get re-invested at the YTM by default.

What could be the reasons for re-investment rate on the coupon(coupon yield?) to be less than the YTM?

Is this because of interest rate risk alone (change in the PV of the bond due to change in YTM)? Or can we say the investor took a coupon payment out and chose not to re-invest it…

Thank you,