Effective yield Vs Yield to maturity

CFA Level I Fixed Income
#1

I am trying to infer the relation between effective yield versus yield to maturity. To my understanding effective yield is the yield on the bond that is obtained when the coupons are reinvested. And yield to maturity is the rate that is obtained when the bonds are held until maturity.

I am looking at the data for some bonds and for some the effective yield < YTM and for some effective yield is > YTM. Can someone help me understand why this is the case and what does it mean when effective yield is greater or lesser than YTM? Thanks.

#2

Effective (annual) yield (EAY) is a measure of the coupon yield: if the annual coupon rate is r, then the effective yield is:

(1 + r/2)^2 – 1.

EAY doesn’t depend on the market price; it is calculated as if the bond were selling at par (and the coupons are reinvested at the coupon rate).

The YTM is the discount rate that equates the cash flows to the current market price; it is a bond equivalent yield, not an effective annual yield.

To compare them, you have to convert the EAY to a BEY, or convert the YTM to an EAY. Once done, if the (converted) effective annual yield is greater than the YTM, the bond is selling at a premium; if the (converted) effective annual yield is less than the YTM, the bond is selling at a discount.

#3

S2000magician,

It seems to me, for semi-annual pay bonds,

EAY = [1+ (BEY/2)^2] - 1 , where BEY = (YTM on semi-annual pay basis) x 2 and YTM is the dicount discount rate that equates the cash flows to the current market price.

That is, it is not the coupon rate (the r in your statements) that plays the role. Do you think so ?

#4

You’re correct. My brain wasn’t working fully this afternoon; I thought both neurons were firing, but apparently only one was.

When I wrote EAY I was thinking about APR (annual percentage rate).

Yes, EAY depends on the market price; APR is based only on the coupon rate.

(Don’t I feel like an idiot?)

#5

S2000magician,

My brain does not work well either, more often than you. Thank you so much for your contributions on this forum.

#6

My pleasure.

#7

You can also do this on your calculator with the iconv function.

#8

Can you share how to do this?

#9

So do 2nd ICONV to enter into the function. Specify your BEY on the NOM. Click enter. Specify your number of coupons per year on C/Y. So a semi annual question would have C/Y = 2. Then to compute EAY, go to the EFF and press Compute (CPT).

You can also start from the EAY and work out the BEY by hitting in the EFF first, putting in your # coupons, and then pressing CPT on NOM to get the BEY.

Ash

#10

Thanks Ash