Add on vs. discount rate

[difanchen]

Hi All,
What is the different between add-on and discount in calculation?
Example:
The following are 90-day money market instruments:
Instrument A=Quote: 5.78%, 360 days, discount rate
Instrument B=Quote: 5.96%, 365 days, add-on rate
Which has the highest rate of return?
Thank you so much in advance if you can help me understand this.

 

[Ernest Seow]

Hello,
Is the answer- Instrument B?
What we are required to do basically is to convert either one of them to be of the same quotation as the other i.e. Convert Instrument A from Bank Discount Yield (“BDY”) to Add-On Rate (“AOR”) or vice-versa for Instrument B. In my working below, I will convert BDY of A to AOR.
The formula for BDY is = [ (P1-Po)/ P1 ] * (360/t) where P1 is the par value of the instrument, Po is the current value of the instrument and t is the duration of the instrument
We are given that BDY is 5.78% and we know P1 (we can assign a arbitary value of 100 or 1,000 ) and we need to solve for Po.
Equating the above equation to 5.78% we obtain a value of 98.555 for Po.
Next we will determine the AOR for Instrument A. We know that Instrument B is quoted as AOR on a 365 days basis. This basically means:
AOR= [ (P1-Po)/ Po ] * (365/t)
*Note that now the denominator is Po instead of P1*
AOR can be quoted on either a 360 days or 365 days basis.
If you now plug the values into the AOR formula you will get: 5.9462% ( < 5.96%)
Hope it helps!
Cheers,
Ernest