HPY from Elan

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fullset

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Q. An investor purchases a T-bill for $950 and there are 180 days left to maturity. What is HPY and EAY>
 
Yo homie!
HPY=(1000/950)^(180/360)-1
= 2.60%
Don’t know how to claculate EAY though, may be HAY=EAY for zero coupon bonds.
 
Thanks, so the HPY is 2.6, but HPR would be 5.2?
For some reason, I never thought of multiplying (180/360) because I thought that you don’t have to annualize since you can hold for whatever amount of time you want to.
For T-bill, HPY should be (ending - beginning price)/beginning price or D/P0 right?
 
As far as I know HPY and HPR means the same. May be you meant EAR.
The generalize formula to calculate return for any asset is (end/beg)-1
I think 5.2% is the annualized return hence EAR and 2.60% is the periodic return for holding period of 180 days.
 
fullset wrote:
Q. An investor purchases a T-bill for $950 and there are 180 days left to maturity. What is HPY and EAY>
Click to expand...
I’m pretty sure HPY (as you said) is (1000/950)-1= 5.26% you earned $50 on $950 in 180 days, so 5.26% is the return in less than a year.
EAY/EAR= is [(1000/950)^(365/180)] -1 = 10.96% –> If you could replicate your investment (365/180) times in a year, so your investment is over the course of a year, you would earn 10.96%
The holding period is less than a year here, so it only makes sense that the annualized yield is greater than the HPY.
 
Pompey wrote:
As far as I know HPY and HPR means the same. May be you meant EAR.
The generalize formula to calculate return for any asset is (end/beg)-1
I think 5.2% is the annualized return hence EAR and 2.60% is the periodic return for holding period of 180 days.
Click to expand...
EAR/EAY = equivalent annual rate/equivalent annual yield… same deal
5.2% is the HPR/HPY not the annualized return. I would revist the logic in your approach.
 
S2000magician wrote:
tickersu wrote:EAR/EAY = equivalent effective annual rate/equivalent effective annual yield… same deal
Click to expand...
Fixed that for you.
Click to expand...
No need to fix it. Effective and equivalent are interchangeable here. Effective is probably consistent with the CFAI texts. It is the equivalent rate when annual compounding occurs as opposed to the non-annual compounding. For example, a quarterly compounded rate can be restated as an equivalent (effective) rate for annual compounding. Most basic is the adjustment of an APR with compounding more frequently than once a year. This rate can be restated as an equivalent or effective rate for annual compounding. Same idea. I will say one is more common than the other, though.
 
Thank you guys for all your responses.
Unfortunately, this is still confusing me. Now I remembered/crammed these formulas when I took my L1, and I probably wouldn’t get an answer wrong on the test. But I’m still not grasping the intuition.
I’ll re-type the question as it is in Elan notes (available for free on their old website) topic 5-12, page 38, Example 16:
An investor purchases a T-bill for $950 when the money market yield on it is 5.2% and there are 180 days left to maturity. Compute HPY and EAY for the T-bill.
Now, I know I will get HPY of 2.6% since HPY = rMM X (180/360) = 2.6%
But isn’t HPY (ending price - beginning price + cash flow of dividends or interest)/beginning price or (1000 - 950)/950 = 5.26%
What is the difference between the two HPYs that we calculate? Are there two different terms, one for each? Or are they interchangeable? But if they are, there shouldn’t be two different answers, right?
I can calculate the EAY as well, but how do you know which one you use i.e 2.6 or 5.26?
Thank you guys for your help. I hope it helps someone else out along with me.
 
tickersu wrote:
fullset wrote:
Q. An investor purchases a T-bill for $950 and there are 180 days left to maturity. What is HPY and EAY>
Click to expand...
I’m pretty sure HPY (as you said) is (1000/950)-1= 5.26% you earned $50 on $950 in 180 days, so 5.26% is the return in less than a year.
EAY/EAR= is [(1000/950)^(365/180)] -1 = 10.96% –> If you could replicate your investment (365/180) times in a year, so your investment is over the course of a year, you would earn 10.96%
The holding period is less than a year here, so it only makes sense that the annualized yield is greater than the HPY.
Click to expand...
I agree. Since we are calculating anualized return we should get the power of ^(360/180) instead of ^(180/360) which converts the annualized rate in to periodic.
I think zero coupon bonds uses 360 days per year convention. So the numerator should be 360 instead of 365.
Thanks!
 
fullset wrote:
Thank you guys for all your responses.
Unfortunately, this is still confusing me. Now I remembered/crammed these formulas when I took my L1, and I probably wouldn’t get an answer wrong on the test. But I’m still not grasping the intuition.
I’ll re-type the question as it is in Elan notes (available for free on their old website) topic 5-12, page 38, Example 16:
An investor purchases a T-bill for $950 when the money market yield on it is 5.2% and there are 180 days left to maturity. Compute HPY and EAY for the T-bill.
Now, I know I will get HPY of 2.6% since HPY = rMM X (180/360) = 2.6%
But isn’t HPY (ending price - beginning price + cash flow of dividends or interest)/beginning price or (1000 - 950)/950 = 5.26%
What is the difference between the two HPYs that we calculate? Are there two different terms, one for each? Or are they interchangeable? But if they are, there shouldn’t be two different answers, right?
I can calculate the EAY as well, but how do you know which one you use i.e 2.6 or 5.26?
Thank you guys for your help. I hope it helps someone else out along with me.
Click to expand...
Read the tickersu’s comment I think he got it right.
So, HPR is the 5.26% and EAR is (1+0.0526)^(360/180)-1 = 10.79%
This is from Fixed Income right? Just watch the schweser video relating to this topic. As I remember at the end of the video dr. doug van eaton gave us a nice summary of all the yield measures.
 
This is from Elan L1 notes on quant. reading 6 on discounted cash flow applications.
In their notes, their answer to this question is 2.6% for HPY and 5.34% for EAY.
I understand tickersu’s comment and that is the way I thought too. When I saw that the answer that I got wasn’t right, I was like wtf?
The thing is that if you do take HPR to be 5.26%, and you convert it to rMM, you won’t get the value that is stated in the question.
 
Pompey wrote:
Read the tickersu’s comment I think he got it right.
So, HPR is the 5.26% and EAR is (1+0.0526)^(360/180)-1 = 10.79%
This is from Fixed Income right? Just watch the schweser video relating to this topic. As I remember at the end of the video dr. doug van eaton gave us a nice summary of all the yield measures.
Click to expand...
You’re right that the T-bill is on 360 days, but EAR/EAY uses 365 days, so it’s (365/180) for the power. See Magician’s article, as he covers this directly.
 
To be clear:
  • Bank Discount Yield (BDY) is an annualized measure using a 360-day year
  • Holding Period Yield (HPY) or Holding Period Return (HPR) is an unannualized measure
  • Effective Annual Yield (EAY) or Effective Annual Return (EAR) is an annualized measure using a 365-day year
  • Money Market Yield (MMY) is an annualized measure using a 360-day year
  • Bond Equivalent Yield (BEY) is an annualized measure using a 365-day year
 
Thank you again for your responses.
But, what is your answer for the problem. For convenience, I’ll paste it again:
Q. An investor purchases a T-bill for $950 and there are 180 days left to maturity. What is HPY and EAY?
 
S2000magician wrote:
The HPY is:
$50 / $950 = 5.2632%
The EAY is:
1.052632^(365/180) – 1
= 10.9613%
Click to expand...
Thanks. I got the same answer. If the question also says that rMM is 5.2%, shouldn’t the HPY remain the same i.e 5.2632% ?
When we calculate rMM = HPY * (days/360), HPY ends up being 2.6%. How is this different than HPY of 5.2632% that you calculated? Are we calculating different things?
 
If it says that rMM is 5.2% (for a 180-day investment), then HPY = 2.6%: rMM is an annualized measure, while HPY is not. For this problem,
rMM = 10.5263% (= 5.2632% × (360/180)).
 
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