This is something that I know is very simple but I’m getting very confused by it all and would love it if someone could just explain this to me quickly and simply. BEY = HPY(365/t) right? This is essentially an the way to calculate yields on discount securities on an annualized basis (i.e. no compounding) So a T-bill sold at 990 with face of 1000 and 28 days to maturity = 10/990*13 = 13.2% BEY right? Further on in my book I see that a BEY is '2x the semiannual discount rate that makes the PV of semiannual coupon payments = to market price followed by this formula: YTM annual-pay = (1+YTM semi-annual pay/2)^2 - 1 So let’s say the YTM on a semi annual pay is 5%, divided by 2 equal 2.5% + 1 = 1.025^2 -1 = 5.06% for the YTM on an annual pay bond. Firstly, why is the YTM/BEY greater for an annual pay bond? Surely it would be less given that there are less compounding periods. Also, why is there any compounding going on anyway, I though BEY were annualized yields… I’m so confused, hopefully this makes sense…
BEY for longer term coupon bonds means 2 x semiannual YTM. Example: 5Yr Semiannual 5% coupon note with FV 1000 and PV 940.89 Calculation: N=10, PMT=25, FV=1000, PV=-940.89 (- for calculator) Semiannual YTM = 3.20% Bey = 2x3.2=6.40% EAY - (1.032)^2-1=6.50% Hope that helps
Think about BEY in terms of simple interest. Bond with coupon of 4 YTM%, Semi. is quoted as a BEY of 8%. Even though the actual return the investor is 8.16% The formula you have above is the Money Market yield and it is 360 not 365 as is the case for most instruments which have maturities of less than a year. For an annual pay bond assuming it is trading at par YTM = Coupon. since there is no compunding WIth respect to your calc in the end. Te 5.06% is the YTM on the semi not the annual pay. You have halved the Coupon and rasied t to 2. Hope this helps
Thanks for your comments. C3Po, I agreed with you. However, I am looking at a page in my Schweser book that says: BEY = HPY(365/t) above that it also says MMY = HPY(360/t) I don’t get it - but that’s what it says, I’ll send you a picture of the page if you are comfortable enough sharing your email. With respect to the calculation at the end - I also agreed with you and that is why it doesn’t make sense to me but in the book it says, as clear as day, YTMannual-pay = (1+YTMsemi-annual/2)^2-1 So if you take my example again of YTM on semi annual pay bond being 5%, you get the YTM on the annual pay bond as 5.06%. Perhaps I am still missing something from your explanations and I apologize if I am but thanks for your patience. I can send you a copy of this information if that might help - my email robjames1984@hotmail.com Thanks in advance.
sorry to bump this, but can someone shed more light on it please…
In reference to BEY = HPY(365/t) - don’t rely on Schwesser to much, curriculum calls it money market rate, and in fact there are many ways of calculating it, in you want to know more look here for example: http://www.riskglossary.com/link/bond_equivalent_yield.htm Anyway this only refers to short term money market instruments. Now with bonds, you are clearly confusing 2 things. Le me quote you: "Further on in my book I see that a BEY is '2x the semiannual discount rate that makes the PV of semiannual coupon payments = to market price followed by this formula: YTM annual-pay = (1+YTM semi-annual pay/2)^2 - 1 And that is exactly it. Let’s start with semiannual bond which has 2.5 YTM (semiannually). YTM annual-pay =EAY= (1+2.5%)^2-1 = 5,0625% BEY = 2.5% * 2 = 5.0000 % Do you see the difference ? Edit: Sorry.finished too soon. So for semiannual bond YTM (same as EAY) in annual term will be more than BEY. For annual bond it will be the same as there is no calculation for semiannual YTM for such bond so BEY = annual YTM
there are two different “BEYs” in the CFA level 1 curriculum. if you get the question in quant/fixed income, it’s the semi annual discount rate x 2. ie as someone said earlier, if you see a BEY of 8%, the effective annual yield is actually (1 + (.08/2)^2), or 8.16%. if, however, it’s BEY in a corpfin question, then it’s HPY x (365/t). ie exactly the same as the money market yield except over 365 days, whereas money market is 360. hope that helps.
this helps a lot - I think I’ve nearly got it! haha So, YTM for an annual pay bond = EAY which is (1+BEY/2)^2-1, right? and of course 2 x semi-annual YTM = BEY, correct? Kiakaha, it seems that way. I’m glad you could clarify that for me - I found the way it was explained really confusing.
you got it…just make sure, if we get a BEY question, you refer back to what topic the question is in, and use the right formula 