How to Arrive at Bond Equivalent Yield?

[achokshi]

I came across this question and the answer converted everything to BEY’s. First off, why convert everything to BEY’s, and secondly how did they arrive at that answer? I’m also a little shaky on what the convention has to do with it (discount vs. add-on). Can anyone help me out? Thanks!
Which of the following 90-day money market instruments most likely offers the investor the highest rate of return?
Money Market Instrument
Quoted Rate
Quotation Basis
Day Convention
Instrument A
5.78%
360
Discount rate
Instrument B
5.80%
365
Discount rate
Instrument C
5.96%
365
Add-on rate
Instrument C
Instrument A
Instrument B



Incorrect.
Instrument C provides a bond equivalent yield of 5.96%, compared with 5.946% for Instrument A and 5.883% for Instrument B.

 

[SHoot85]

You convert, I believe, b/c rates in the Money Market are quoted as add-on, and discount rates, whereas semi-annual bond yields and such are quoted differently, so you need to adjust the money market rates to the same basis as the other rates.
1. AOR 365 is the Bond Equivalent Yield (they are one in the same). So you naturally wouldn’t even need to convert that rate (Instrument C).
2. To convert the Discount rates, you need to first convert those rates to the right number of days. 5.78% becomes 1.445% (multiply by 90/360 to get 90 day rate). Now is when I convert to add-on; the difference is add-on uses PRICE in denominator, discount uses FACE value in denominator. So I would take 1.445% and subtract that figure from 100. You get 98.555. Now the Add-on rate is that same discount (100-98.555 = 1.445) but we divide 1.445/98.555 (instead of using 100). This equals 1.466% (as opposed to 1.445%). We’re not done though, we obviously need to convert this to 365 days; therefore 1.445% x 365/90 = 5.946 %
Do the same with Instrument B.
Hope this helps; I’m sorry if the way I do it is much longer/less efficient than others’ way; that’s what’s easiest for me.

 

[madgirl1991]

Why are you converting B and A through 90 days? Whynot just go from the discount rate to the HPR, then EAY then BEY?

 

[SHoot85]

SHoot85 wrote:
Hope this helps; I’m sorry if the way I do it is much longer/less efficient than others’ way; that’s what’s easiest for me.

…

 

[madgirl1991]

Sorry just reread the question and saw that all the instruments are 90 days

 

[SHoot85]

madgirl1991 wrote:
Sorry just reread the question and saw that all the instruments are 90 days

It’s too late; I had a good cry this morning in self-pity of my stupidity