An Atlas Corporation bond is quoted with a YTM of 4% on a semiannual bond basis. What yields should be used to compare it with a quarterly pay bond and an annual pay bond?
I know that the semiannual bond basis = 2 times the semiannual discount rate. So we have a semiannual discount rate of 2%.
Afterwards, I am completely confused on the difference between effective yields, effective annual yields, YTM (is EAY and YTM the same thing??), and the rest of the jargon and calculation used in this problem.
Semiannual bond basis (i.e. 2 x semiannual discount rate) = YTM measure
Can stake a semiannual bondās YTM measure (Semiannual bond basis), divide by 2 to get the semiannual discount rate and then find the effective quarterly rate
Multiply effective quarterly rate to get the YTM (or BEY) rate for a quarter pay bonds.
As I wrote above, typically YTM is quoted as a BEY, not an EAY. I imagine that there must be some bonds somewhere for which the YTM is quoted as an EAY, but I havenāt seen them.
This is incorrect. BEY is twice the semiannual effective yield, so it is a nominal rate, not an effective rate. EAY is the semiannual effective yield compounded for two periods, so it is, as its name suggests, an effective rate.
Yes: BEY is twice the semiannual effective discount rate, and is the most common convention for quoting YTM.
I donāt know what you mean by āstakeā in this context.
If a bondās YTM is quoted as a BEY, then you are correct: you divide by 2 to get the semiannual (effective) discount rate, and, if you will, uncompound that for two periods to get the effective quarterly rate.
If you multiply the effective quarterly rate by 4 to get an annual rate, it will be a nominal rate (compounded 4 times per year). It will not be a BEY (which is a nominal annual rate that is compounded twice per year), nor will it be an EAY (which is an effective rate, not a nominal rate). You could describe it as a YTM, but I donāt know whether anyone would adopt that convention for presenting a YTM on a quarterly pay bond.
As I mentioned above, without knowing how the quarterly pay bondās YTM is presented (nominal rate compounded 4 times per year, nominal rate compounded twice per year (BEY), or effective rate being the three most likely candidate methods), you cannot say for certain exactly what a quarterly pay bondās YTM means.
In one of the Corporate Finance readings they define something they call BEY.
It isnāt BEY.
For that reading, you need to know that definition, but otherwise, forget it. In the real world, BEY means only one thing: 2 times the effective semiannual yield.
The (annual, effective) discount rate that you use to discount the cash flows on an annual pay bond is an EAY.
However, that may not be how the bondās YTM is quoted.
If you use an 8% effective annual rate to discount the cash flows on an annual pay bond to get todayās price, then that bondās EAY is 8%. And if they quote its YTM as an EAY (which is uncommon, but possible), then its YTM would be quoted as 8%. However, if they quote its YTM as a BEY (which is much more common), then you have to convert that 8% annual effective rate into a semiannual effective yield and double it:
Respectively, semiannual effective rates and quarterly effective rates.
Yes, they is.
All of the 8% numbers are nominal yields, or annual percentage yields (APYs).
For the annual pay bond, 8% is also the EAY; note that Schweser says that the effective yield is 8%.
For the semiannual pay bond, 8.16% is the EAY, and 8% is the BEY.
For the quarterly pay bond, 8.24% is the EAY, but they didnāt calculate a BEY. To do that, you need the effective semiannual yield, which you get by compounding the effective quarterly yield for 2 quarters:
Thanks! Going to recap it all for my sake so as to understand it (think I understand all the questions I have on this thread!!):
BEY = Semiannual bond basis = effective semiannual yield x 2.
EAY = (1 + effective quarterly yield)^4 - 1ā¦This is to get the EAY for a quarterly paying bond. Since the # of compounding periods are greater than an annual paying bond, the EAY consequently is higher as well.
EAY = (1+effective semiannual yield) ^2 - 1ā¦This EAY is for semiannual paying bonds.
Effective semiannual yield = (1 + effective quarterly yield)^2 - 1ā¦We can then multiply this figure by 2 to get the BEY (a.k.a. semiannual bond basis)
Effective semiannual yield = (1 + EAY)^0.5 - 1ā¦We can then multiply this figure by 2 to get the BEY.
