# BEY versus Effective Annual Yield

This is what happens when you study too much… But I’m obsessed with getting the right answer to this. In my Schweser class notes, the point was made pretty strongly that we should be able to calculate the equivalent yield to a lender / borrower engaging in a loan hedged with puts / calls in either bond equivalent yield or effective annual yield. I don’t think I saw BEY anywhere in the curriculum. But I’m going to worry about it anyway. My problem is that the one example I have from Schweser for this calculation doesn’t appear correct to me. Anyone want to try this one on for size?? _________ In 60 days a bank plans to lend \$1 million for 180 days. The lending rate is LIBOR+100 bps and current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of \$1 million and a strike rate of 4.3%. The put premium is \$3,000. Calculate the annual rate of the loan if at expiration LIBOR = 4%. (Show both EAR and BEY…)

Value of premiums in 60 days . 3027 Amount Lent 1003027 Profit 1mil*.05*(180/360)=25000 Option payoff 0.3%*1mil*180/360=1500 EAR 26500/1003027=2.64% BEY 2.622%

Is this assumed to be a loan that pays semiannually?

EAR= 4.803% BEY= 4.68% ?

I forgot to annualize so it would be ear 5.43 and Bey 5.32 … maybe

I get 5.43 for EAR and 5.357 for BEY, but i’m not sure at all on bey. haven’t done that in a long time… same calculations as florin on the EAR. bond equivalent yield just multiplied by 365/180.

premium value (at time=60): 3000 * (1+(4.5% + 1%)*(60/360)) = 3027.5 principal + interest (at time=270): 1000000*(1+(4%+1%)*180/360) = 1,025,000 option payoff (at time=270, see footnote): 1000000*(4.3%-4%)*(180/360) = 1500 return = (1,025,000 + 1500) / (1,000,000 + 3027.5) = 1.023402 EAR = [1.023402 ^ (365/180)] - 1 = 4.802413% BEY = [((1 + EAR)^0.5) - 1] * 2 = 4.7461% * I follow schweser and cfa assumption that the option payoff is received at the same day as the loan due, so that they can be add up with the loan and interest repayment without future value adjustment.

That looks right to me. I was getting the BEY by taking half of the year EaR and milt by two which is wrong.

I see where I screwed up

yeah. think you guys are right. I’m not sure what happened to my calculations.

cfasf1 I think you just took the profit/amt loaned - just like me- which is incorrect because you have to take all amt received/amt loaned the 26500 is not all interest, 3027 of it is return of investment… so if you substract the put premium from profit you will have the same ans like these guys.

yeah, i needed to have the 1mm in the numerator, didn’t i? details, details. thanks, florinpop.

Have you guys noticed that (25,000 + 1,500)/1,003,027 =0.02642 while (1,000,000+25,000+1,500)/(1,000,000+3,027)]-1= 0.0234 Am I going nuts? I think in the first equation you are implicitly assuming your principal was 1,003,027 instead of 1,000,000. Thoughts? Edit: you guys beat me to it.

yeah. that’s where florin’s calculation and mine went wrong. trying to wrap my head around it.

>I think in the first equation you are implicitly assuming your principal was 1,003,027 >instead of 1,000,000. I guess the first method is wrong. Back to basic, return is: what you get / what you invest

For example (St-So)/So= Rtn or St/So -1 = Rtn Since you said that the numerator was 26,500 you are saying that you got a 26,500 on 1,003027 and not 26,500 on 1,000,000…I think. It is like backwards from the way we normally do it.

mwvt9, you are exactly right !!

Thanks for helping me figure this out, guys. Now where the heck is plyon?

Just having fun watching you guys post! I think hksteven is correct all around and on his first try – so I won’t recap too much there, except to focus on the EAR versus BEY. The Schweser answer for EAR is 4.80%. We can all agree on that one so far. However, they give 4.68% for BEY and they calculated it the same way you did, MW. I think that’s wrong and the correct BEY should be the 4.746% figure (computed the way HKsteven did). Anyone here AGREE with Schweser or do we all think they calc’d the BEY incorrectly?

the profit is (26500-3027)/1003027=2.34% the 3027 is basically return of capital not profit