Treasuries

[wrongsaidfred]

Hi David,

Since I began studying for the FRM I have come across quite a few different yields for treasury bills.

Besides the relationship between the quoted price (which is just 100 times the discount rate) ad the cash price, what other types 0f yields or returns do we need to know?

For instance, Hull uses something called the true rate of interest which is (face - cash price)/cash price, but this is a strange one since it refers only to the holding period.

Then I have read about the holding period return, the bond equivalent yield, true yield, the effective annual yield and a couple of others. To make things worse is that some of these are defined differently from one source to the next.

I guess my question is: which of these terms do we need to be familiar with and is there some place where they I can see the relationships as they pertain to how the exam defines them?

Thanks in advance for any help you can provide.

Mike

 

[David Harper CFA FRM]

Hi Mike,

This is absolutely a true characterization, and I empathize, but I think you are aware I have this as a specific agenda item to GARP's attention; in fact, consistency of interest rates methodology has been my #1 item for the last two years (in fact, I am linking to the this thread, as part of my input w.r.t. an upcoming conference call that includes 2012 FRM agenda as i think, again, you've summarized the problem very well ... but that doesn't help you now ...)

Re: "is there some place where they I can see the relationships as they pertain to how the exam defines them?"
Not that I am aware, I think this is a great idea: I have a revised formula sheet issuing this Friday and I will try to include ....
... otherwise I do think I can improve this XLS to incorporate all terms: http://www.bionicturtle.com/how-to/spreadsheet//3.b.1-compound-frequency

Re: "which of these terms do we need to be familiar with?" It's hard for me to answer since, as you imply, the AIMs are assigned in such a way (unfortunately) to make them all fair game
(FWIW, my recommendation to GARP is that they develop a standard definitions term sheet; I will even provide the draft), but please note:

• Some of this is merely semantic due to different authors
• We definitely want to include the money market discount rate, which is strange in a way because it's not a real rate; e.g., T-bill quote of 92 --> 8% discount rate. Need to know, but at the same time, it's not an "accurate" rate in the sense that we would never use the 8% to compute actual returns, it's more like a feature of money market instruments
• "Holding period return" is also a little out-of-place for our purposes, and only b/c Tuckman uses it, to my knowledge; it's just a general term for the realized return and could be expressed annually (CAGR) or semi-annually/etc. I am going to suggest that, if we understand the others, "holding period return" is superfluous
• The rest all fit generally, i think, into our typology (Hull's really) of:
  • Continuous, including most importantly log returns; e.g., LN(S1/S0) is continuously compounded
  • Discrete; effective annual yield (EAY, EAR) is just the name for annual discrete; bond-equivalent yield is just the name for semi-annual discrete; CAGR is just the name for realized annual discrete
    
    The learning spreadsheet above (link here) generally gives practice to this discrete/continuous conversion

But, i do think, although not helpful for Nov 2011, you've given me an idea on how we can better summarize this for May/Nov 2012. Thanks, David

 

[wrongsaidfred]

Hmmm... That is unfortuante that they do not hav their act together on this.

I thought if the discount rate of of T-bill was 8% it was quoted at 8. Is this not correct? And then we get the cash price through Quoted=(360/n)(100-cash)

Also, I do not remember coming across the money market discount rate. I know that money market type instuments accrue interest on an actual/360 basis but I am not quite sure where else it came up. Is there anything else to know?

Finally, I have seen the bond equivalent yield (for a treasury) listed as BEY = [(FV - PP)/PP] * [365 or 366/M]. Is this accurate at all?

Thanks again for your help and your patience.

Mike

 

[David Harper CFA FRM]

Hi Mike

• Yes, correct but the 8% is a quote on a so-called "discount instrument:" as reflected in your formula, specifically the (100-Y), it's 8% of the face value (100) so it's not a "true return" (e.g., if you pay 92 to get back 100, it's not really 8%)
• The Treasury bill is a money market instrument, so it's priced as a discount instrument
• I don't specifically recognize your formula, i don't know the definition of PP (I am not asking you for it, i don't have time to go down a new rabbit hole today, based on a totally unassigned formula). For us, bond-equivalent = semi-annual discrete per Tuckman. The above formula is not found in any FRM reading that i am aware.

Thanks, David

 

[wrongsaidfred]

So the treasury discount rate and money market rate are the same thing. That makes sense.

And the PP is just the purchase price or cash price. I think they also call the bond equvalnet yield the investment yield

Thanks again,
Mike

 

[David Harper CFA FRM]

Re BEY (since i can't resist, ugg), see http://www.investopedia.com/terms/b/bey.asp#axzz1bexwu9rW
so it's just an annualized discrete rate; if days are 90, it's a "quarterly per annum rate"

David

 

[wrongsaidfred]

Thanks again.

Mike