Jenson's alpha and and IR
- Thread starter hsuwang
- Start date
Hi Jack,
Yes = IR = residual return/residual risk = alpha/tracking error.
But, no Grinold's active return does *not* equal alpha. (I wish i had a slide in foundations for that, I will insert for review. The problem, IMO, is that it is nearly impossible to grasp Grinold with only chapters 7 & 17. I realize it is more time, but you can see why I recommend Grinold 1 to 6, they introduce some difficult, but foundational ideas. Including
"alpha" = residual return but "active return" = return above benchmark; e.g, in CAPM terms:
if ERP = 6% and portfolio beta = 1.5 and benchmark is S&P 1500 index (beta=1), say manager excess (net of RF rate) returns = 10%
(Jensen's) alpha = 10% - (6%)(1.5) = 1% alpha/residual
active return = 10% - (6%; i.e., benchmark) = 4%
This last difference sets up the more difficult Grinold 17; e.g. this manager gets credit for "skill" not only for the alpha of 1% but for (part of) the timing choice to expose smartly to the beta (a.k.a. alternative beta)
David
Yes = IR = residual return/residual risk = alpha/tracking error.
But, no Grinold's active return does *not* equal alpha. (I wish i had a slide in foundations for that, I will insert for review. The problem, IMO, is that it is nearly impossible to grasp Grinold with only chapters 7 & 17. I realize it is more time, but you can see why I recommend Grinold 1 to 6, they introduce some difficult, but foundational ideas. Including
"alpha" = residual return but "active return" = return above benchmark; e.g, in CAPM terms:
if ERP = 6% and portfolio beta = 1.5 and benchmark is S&P 1500 index (beta=1), say manager excess (net of RF rate) returns = 10%
(Jensen's) alpha = 10% - (6%)(1.5) = 1% alpha/residual
active return = 10% - (6%; i.e., benchmark) = 4%
This last difference sets up the more difficult Grinold 17; e.g. this manager gets credit for "skill" not only for the alpha of 1% but for (part of) the timing choice to expose smartly to the beta (a.k.a. alternative beta)
David
Hello David,
In the example that you provided above, if alpha and active returns are different (and I see how they are different), then how do I make sense of the formula: IR= E(Rp)-E(Rb) / stdev(Rp-Rb), since alpha deals with the excess returns between the portfolio and the CAPM's forecasted benchmark return, while active returns simply deals with the difference between the portfolio return - benchmark return (without adjusting for beta at all). In the formula, it seems to me that active returns fits the numerator E(Rp)-E(Rb) better than alpha.
and also you mentioned in the video that E(Rp)-E(Rb) is what Grenold calls it "active return", and it really does look more like active return to me than alpha.
I'm sorry for being imprecise on words,I hope I'm getting my question through.
Thanks!
In the example that you provided above, if alpha and active returns are different (and I see how they are different), then how do I make sense of the formula: IR= E(Rp)-E(Rb) / stdev(Rp-Rb), since alpha deals with the excess returns between the portfolio and the CAPM's forecasted benchmark return, while active returns simply deals with the difference between the portfolio return - benchmark return (without adjusting for beta at all). In the formula, it seems to me that active returns fits the numerator E(Rp)-E(Rb) better than alpha.
and also you mentioned in the video that E(Rp)-E(Rb) is what Grenold calls it "active return", and it really does look more like active return to me than alpha.
I'm sorry for being imprecise on words,I hope I'm getting my question through.
Thanks!
Hello David,
sorry to append. I was looking over the Grinold.04.01 example you posted on WIKI, and I spent a long time trying to figure out the answers, but all the different terms really seem overwhelming and confusing. I would like to know if it is possible that you can somehow create a diagram to graphically illustrate how they relate to each other. I will try my best to get the Grenold text and read the chapters that you suggested, but in the mean time, it would be great to have the basic ideas down just so I don't feel insecure moving on into other sections of the FRM exam. Thanks!
[Time premium, Risk premium, Exceptional benchmark return, Alpha, Consensus expected return, Expected excess return, Exceptional expected return]
sorry to append. I was looking over the Grinold.04.01 example you posted on WIKI, and I spent a long time trying to figure out the answers, but all the different terms really seem overwhelming and confusing. I would like to know if it is possible that you can somehow create a diagram to graphically illustrate how they relate to each other. I will try my best to get the Grenold text and read the chapters that you suggested, but in the mean time, it would be great to have the basic ideas down just so I don't feel insecure moving on into other sections of the FRM exam. Thanks!
[Time premium, Risk premium, Exceptional benchmark return, Alpha, Consensus expected return, Expected excess return, Exceptional expected return]
Hi Jack,
Re: diagram: yes, I will add to our production list, I can't promise timing, but I agree that would be helpful!
A few things:
* You are ahead of the game. The Grinold is *very* difficult - you are grappling more (IMO) with Chap 17 (Level II). As hard as anything in the exam, maybe. It took me many many hours to follow Grinold.
* Amenc, in notation that you will *not* find in Grinold for precisely the confusion you cite, does subsequently call E(Rp)-E(Rb) the "residual" and equal to Jensen's alpha. I think your observation is very keen; Grinold would not write that. The E(Rb) is confusing, as Amenc cleary refers not to a market benchark (i.e., not S&P 1500 or market portolio) but the portolio's benchmark (beta * market portfolio). Put another way, I'd ignore the first version under 4.2.7 in favor of his second version, b/c it's the one that maintains consistency (and sanity)
Re: diagram: yes, I will add to our production list, I can't promise timing, but I agree that would be helpful!
A few things:
* You are ahead of the game. The Grinold is *very* difficult - you are grappling more (IMO) with Chap 17 (Level II). As hard as anything in the exam, maybe. It took me many many hours to follow Grinold.
* Amenc, in notation that you will *not* find in Grinold for precisely the confusion you cite, does subsequently call E(Rp)-E(Rb) the "residual" and equal to Jensen's alpha. I think your observation is very keen; Grinold would not write that. The E(Rb) is confusing, as Amenc cleary refers not to a market benchark (i.e., not S&P 1500 or market portolio) but the portolio's benchmark (beta * market portfolio). Put another way, I'd ignore the first version under 4.2.7 in favor of his second version, b/c it's the one that maintains consistency (and sanity)
Hello David,
Sorry but I'm back to this thread topic once again.. so are you basically saying that Information Ratio is indeed alpha/TE, and the formula notation here: IR = E(Rp) - E(Rb) / stdev(Rp - Rb) , we are treating E(Rb) here as a portfolio benchmark (Beta*excess market)?
I felt a bit frustrated because I'm not sure what happens on exam day if we happen to be given, say,
benchmark return
portfolio return
beta
risk-free rate
market return
TE
then what should we use to calculate IR?
Is it going to be: (portfolio return - Beta*market return) / TE
or: (portfolio return - benchmark) / TE?
Thanks!
Sorry but I'm back to this thread topic once again.. so are you basically saying that Information Ratio is indeed alpha/TE, and the formula notation here: IR = E(Rp) - E(Rb) / stdev(Rp - Rb) , we are treating E(Rb) here as a portfolio benchmark (Beta*excess market)?
I felt a bit frustrated because I'm not sure what happens on exam day if we happen to be given, say,
benchmark return
portfolio return
beta
risk-free rate
market return
TE
then what should we use to calculate IR?
Is it going to be: (portfolio return - Beta*market return) / TE
or: (portfolio return - benchmark) / TE?
Thanks!
Hi Jack,
Candidly, it frustrates me, too: in my view, when we have *apparently* conflicting definitions (e.g., alpha, SaR, LVaR), it is GARP's responsibility to standardize on a definition for practical purposes of the exam. I have repeatedly requested they "arbitrate" a single definition of alpha (and the several other terms with real or perceived conflicts)
...in the meantime...
My advice is that we rely on the most precise definition. For alpha, that is given by Grinold; i.e., residual return that (if ex post) would be unexplained by common factor exposure and therefore cannot include the beta term. Alpha = portfolio return - beta * benchmark return
but, okay, secondarily, please note about this expression: (portfolio return - benchmark) / TE?
...Amenc's is not necessarily wrong, right? It depends on the definition of benchmark & TE
the most important rule is ratio consistency, so the ultimately best (i suppose) is:
IR = Return over benchmark / Standard deviation of (Return over benchmark), or
i.e., proper benchmark = beta * benchmark, but if that is not given, we can certainly settle for just benchmark!
IR = alpha / Standard Deviation (alpha)
...viewed with the "ratio consistency" rule, if the question were to lamely define alpha as return - market return (i.e., without beta), you can still use in the denominator: Standard Deviation (return - market return)...because while not technically correct IR, it's still a valid ratio
Hope that helps...David
Candidly, it frustrates me, too: in my view, when we have *apparently* conflicting definitions (e.g., alpha, SaR, LVaR), it is GARP's responsibility to standardize on a definition for practical purposes of the exam. I have repeatedly requested they "arbitrate" a single definition of alpha (and the several other terms with real or perceived conflicts)
...in the meantime...
My advice is that we rely on the most precise definition. For alpha, that is given by Grinold; i.e., residual return that (if ex post) would be unexplained by common factor exposure and therefore cannot include the beta term. Alpha = portfolio return - beta * benchmark return
but, okay, secondarily, please note about this expression: (portfolio return - benchmark) / TE?
...Amenc's is not necessarily wrong, right? It depends on the definition of benchmark & TE
the most important rule is ratio consistency, so the ultimately best (i suppose) is:
IR = Return over benchmark / Standard deviation of (Return over benchmark), or
i.e., proper benchmark = beta * benchmark, but if that is not given, we can certainly settle for just benchmark!
IR = alpha / Standard Deviation (alpha)
...viewed with the "ratio consistency" rule, if the question were to lamely define alpha as return - market return (i.e., without beta), you can still use in the denominator: Standard Deviation (return - market return)...because while not technically correct IR, it's still a valid ratio
Hope that helps...David
Hello David,
As we were just discussing about this term and notation difference, I bumped into a sample test question that really address just what I was worried about -
A portfolio has an average return over the last year of 13.2%. Its benchmark has an average return of 12.3%. The portfolio's standard deviation is 15.3%, its beta is 1.15, its tracking error is 6.5%. lastly the risk free rate is 4.5%. Calculate IR.
The answer simply use Rp-Rb as the numerator (13.2-12.3) divide by TE. The fact that the question gives us the risk-free rate really confuses me on whether benchmark = market. I realized that the benchmark being addressed here is equivalent to beta(market)+Rf, but that was only after I checked with the answer options and found that none will do if I treat it as a market return (ie. Rp-Rf - Beta(Rm-Rf)).
Thanks.
As we were just discussing about this term and notation difference, I bumped into a sample test question that really address just what I was worried about -
A portfolio has an average return over the last year of 13.2%. Its benchmark has an average return of 12.3%. The portfolio's standard deviation is 15.3%, its beta is 1.15, its tracking error is 6.5%. lastly the risk free rate is 4.5%. Calculate IR.
The answer simply use Rp-Rb as the numerator (13.2-12.3) divide by TE. The fact that the question gives us the risk-free rate really confuses me on whether benchmark = market. I realized that the benchmark being addressed here is equivalent to beta(market)+Rf, but that was only after I checked with the answer options and found that none will do if I treat it as a market return (ie. Rp-Rf - Beta(Rm-Rf)).
Thanks.
Hi Jack,
Can i trouble you for the source, so I can explicitly point GARP to the example?
(they've got to flush this out or fix them, IMO)
in this case, as we discussed, in my view, if we follow the assigned Grinold, the alpha (numerator in IR) is 13.2% - 1.15 beta *(12.3 - 4.5%) - 4.5% = -0.27% alpha
...your approach is the best you can do. Note the answer is an acceptable ratio *if* the tracking error is defined as StdDev (portfolio - benchmark) rather than a "proper" StdDev (alpha)
...so the problem here is (i) either ratio can be used but (ii) the question needs to be more specific about which one (especially to introduce beta and then, apparently, to not use the beta when the beta should be used, is wrong)
David
Can i trouble you for the source, so I can explicitly point GARP to the example?
(they've got to flush this out or fix them, IMO)
in this case, as we discussed, in my view, if we follow the assigned Grinold, the alpha (numerator in IR) is 13.2% - 1.15 beta *(12.3 - 4.5%) - 4.5% = -0.27% alpha
...your approach is the best you can do. Note the answer is an acceptable ratio *if* the tracking error is defined as StdDev (portfolio - benchmark) rather than a "proper" StdDev (alpha)
...so the problem here is (i) either ratio can be used but (ii) the question needs to be more specific about which one (especially to introduce beta and then, apparently, to not use the beta when the beta should be used, is wrong)
David
oh okay, right, actually i included this in my error list to GARP last year (i.e., as part of the request to define "alpha" in accordance with the assignment). Thanks, David
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