Hull chapter 6 / Discount rate

[Milan]

Hi all,

I have a question regarding discount rate and true yield (Hull, reading page 79).
I found on the internet, from various sources (for example http://people.stern.nyu.edu/wsilber/treasurybills.pdf and http://www.investopedia.com/exam-guide/series-7/debt-securities/compute-treasury-discount-yield.asp) that discount rate is
r = (Face - Cash price)/Cash price * 360/number of days, while Hull indicates: r = (100 - Cash price) * 360/n.
This is definitely not the same thing they are referring to, could someone shed some light on the difference?

Thanks.

 

[Matthew Graves]

From what I understand, Hull is giving you information on how the quoted price is calculated, rather than the actual yield. The quoted price is always given with reference to the face value rather than the cash price. The discount rate (yield) you refer to is the return you would receive if bought for the cash price, hence the Cash Price in the denominator.

The Hull formula is really:
p = 100 * (Face - Cash Price)/Face * 360/n

Whereas the yield in (%) is:
r = 100 * (Face - Cash Price)/Cash Price * 360/n

Bond and bill pricing usually uses 100 as the face value, hence Hull simplifies to p = (100 - Cash Price) * 360/n.

That's how I understand this. Happy to be corrected if I've made any errors!

 

[ShaktiRathore]

Hi
Yes agree with above Mathews discount rate is p above where discount is divided by FV while r, a variant of above discount rate, is the actual yield on the tbill where discount is divided by cash price. Discount rate does not give true yield earned therefore we divide discount by cash price instead of face value to give true yield.
Thanks