Decomposing FI returns and reinvestment income for reading 11

CFA Level III Fixed Income
#1

Really starting to feel the pressure. I don’t understand how and what’s going on with reinvestment income when find expected return for bonds. Book says that:

  1. Coupon income is the income that an investor receives from coupon payments relative to bond’s price and interest on reinvestment income.
  2. Assuming there is no reinvestment income, current yield = coupon/current bond price.

The question in text (BB4 has no reinvestment income) so do the other similar questions. What do we do if there is REINVESTMENT INCOME? How would it look then? Would it just be:
Current yield = (Coupon + reinvestment income)/Current bond price?

Thanks.

#2

Current yield is defined as:

Current\ yield = \frac{Annual\ coupon}{Current\ price}

Whether there is reinvestment or not doesn’t matter.

#3

If there was reinvestment income:

  1. would we have to accumulate all the coupons forward to maturity at the reinvestment rate.
  2. Subtract the total number of coupons from above.
  3. Add this to the current yield.

Is that thinking right? I’m assuming they wouldn’t ask that even as I wrote that. Thanks again.

#4

Reinvestment income doesn’t affect the current yield; it involves only the coupon payment and the market price of the bond.

#5

I get that it doesn’t affect current yield. But does it affect rolling yield? I know rollling yield is this (with no reinvestment income):

RY = CY + Roll return

What does roll yield become with reinvestment of income if that comes up?

RY = CY + Reinvestment income + Roll return.

Sorry for the annoying questions on this. I don’t see it coming up but just curious.