Seeking alpha is flawed. Ex-ante alpha must be 0.

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acegolfer
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Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by acegolfer »

Some investors (perhaps non BHs) calculate ex-post alpha using asset pricing models such as CAPM, 3-factor, 4-factor, etc. What's the objective?

1. If the model is correct, then ex-ante alpha for any security is 0. There's no alpha to seek.
2. If the model is wrong, then one is using a wrong model to estimate alpha. Flawed alpha.
3. Or, is it strictly for evaluating past investment performance and not for seeking alpha?

Can you explain why one measures alpha?
Purelife304
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by Purelife304 »

Just when I thought I was beginning to understand investing, I see this post...and have no idea what it means.

I'll go back to my corner with my head down now. :oops:
dkturner
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by dkturner »

acegolfer wrote:Some investors (perhaps non BHs) calculate ex-post alpha using asset pricing models such as CAPM, 3-factor, 4-factor, etc. What's the objective?

1. If the model is correct, then ex-ante alpha for any security is 0. There's no alpha to seek.
2. If the model is wrong, then one is using a wrong model to estimate alpha. Flawed alpha.
3. Or, is it strictly for evaluating past investment performance and not for seeking alpha?

Can you explain why one measures alpha?
I like this. I can never generate positive alpha unless my investments deviate from my chosen model. If I do manage to generate positive alpha It is only because I chose the wrong model not because my investments performed well.

I guess one measures alpha because one is asked to measure it. This is a play on Lord Keynes quip that "economists don't make predictions because they can, they make predictions because they are asked".
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knpstr
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by knpstr »

acegolfer wrote: Can you explain why one measures alpha?
Job security.
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k66
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by k66 »

acegolfer wrote: 1. If the model is correct, then ex-ante alpha for any security is 0. There's no alpha to seek.
Can you explain why one measures alpha?
Is the model absolutely correct, or merely "good"? I might suggest that it is probably the latter, especially if we subscribe to the notion that securities (price) behaviour is a constantly in a non-linear state. Thus, there is some alpha, but it would be hard to detect routinely--but for some people that is enough to keep on believing!
LOSER of the Boglehead Contest 2015 | lang may yer lum reek
dkturner
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by dkturner »

knpstr wrote:
acegolfer wrote: Can you explain why one measures alpha?
Job security.
+1

If alpha isn't positive the model needs to be "tweaked" :wink:
staythecourse
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by staythecourse »

Not sure how to answer the question, but more simply a question of alpha in the ex post world should be: 1. Was it luck or skill? and 2. How repeatable is alpha anyway?

All the data I have seen has shown if anything there is RTM when it comes to alpha so if one shows positive alpha from date x to date y in retrospect then it is a BETTER option probability wise to avoid that fund as it is likely to be a loser (negative alpha) from date y to date z prospectively. So, of one is sitting now in 2015 and see funds that have +alpha the last 5 years (2010-2014) it is a BETTER chance of success avoiding those funds then putting money into those funds if one is looking for +alpha for the next 5 years (2015-2019)

Good luck.
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Rob Bertram
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by Rob Bertram »

I'm not sure what your reasoning is behind the results, but we might need to go back and define some of the terms.
"Alpha" means risk-adjusted returns above the line connecting the risk-free asset (cash) and the benchmark (usually the market portfolio).
"Ex-ante" (predicting the future) means forecast future results
"Ex-post" means using past data to evaluate results

1. If you're saying alpha = 0 for all efficient portfolios, then you're directly saying that the efficient frontier is a straight line.
2. Predicting the future is hard. We can try using PE/10 or bond yields, but it's not perfect. There is a wide margin of error in the model as well as in the predicted alpha.
3. I think you might be confusing ex-ante with ex-post.

In most discussions around alpha, the assumed benchmark is the total stock market or S&P 500 unless otherwise stated. The investing world has more than just domestic equities. There are international stocks, bonds, commodities, etc. If your benchmark is the total market of all assets cap weighted, then there's a strong argument that it is the efficient portfolio.

If the benchmark is the total US domestic stock market but the investing world is global stocks and bonds, there's a strong case for discussing risk-adjusted returns (alpha) of a balanced portfolio.
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midareff
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by midareff »

knpstr wrote:
acegolfer wrote: Can you explain why one measures alpha?
Job security.

My first chuckle of the day... THANK YOU!
richard
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by richard »

acegolfer wrote:Some investors (perhaps non BHs) calculate ex-post alpha using asset pricing models such as CAPM, 3-factor, 4-factor, etc. What's the objective?

1. If the model is correct, then ex-ante alpha for any security is 0. There's no alpha to seek.
2. If the model is wrong, then one is using a wrong model to estimate alpha. Flawed alpha.
3. Or, is it strictly for evaluating past investment performance and not for seeking alpha?

Can you explain why one measures alpha?
When you run a CAPM, 3-factor, etc. model, you're running it on historic data. The model allows you to determine exposure to the relevant factor or factors over the relevant time period and to determine if there was any alpha under the model. The models themselves say nothing about the future.

For example, you might determine that a portfolio did very well, but only because of high exposure to this and that factor. Or you might determine that the performance of the portfolio could not be fully explained by the model, suggesting there might have been alpha.
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by nisiprius »

The last time we took up the subject of "smart beta" I made a fool of myself by quoting from an investing textbook and saying that's what the word "beta" means and there can't be any such thing as "smart beta," beta is beta.

I was a dumb literal-minded engineering-world guy who thinks he can tell the difference between a nit and an apostilb, and I got my head handed to me.

It turns out there's no accepted authority as to the meaning of β in financial sciencialistics. If there isn't one for β then there probably isn't one for α.

It's just like the old days when some of us foolishly thought "watt" meant RMS(volts x amperes) like the EE textbooks say, and scratched our heads over hi-fi gear rated in "peak watts" and "music watts" and even "peak music watts."

I should have realized this from a paper mentioned in the forum whose summary reads like a joke:
The Equity Premium in 150 Textbooks
...recommendations regarding the equity premium range from 3% to 10%, and that 51 books use different equity premia in various pages.... Some confusion arises from not distinguishing among the four concepts that the phrase equity premium designates...
It's Humpty Dumpty in the world of finance:
'But "glory" doesn't mean "a nice knock-down argument",' Alice objected.

'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.'

'The question is,' said Alice, 'whether you can make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be master — that's all.'
We must defer to the Financial Sciencialistics masters.
Last edited by nisiprius on Fri Feb 13, 2015 11:29 am, edited 4 times in total.
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swaption
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by swaption »

Rob Bertram wrote:I'm not sure what your reasoning is behind the results, but we might need to go back and define some of the terms.
"Alpha" means risk-adjusted returns above the line connecting the risk-free asset (cash) and the benchmark (usually the market portfolio).
"Ex-ante" (predicting the future) means forecast future results
"Ex-post" means using past data to evaluate results

1. If you're saying alpha = 0 for all efficient portfolios, then you're directly saying that the efficient frontier is a straight line.
2. Predicting the future is hard. We can try using PE/10 or bond yields, but it's not perfect. There is a wide margin of error in the model as well as in the predicted alpha.
3. I think you might be confusing ex-ante with ex-post.

In most discussions around alpha, the assumed benchmark is the total stock market or S&P 500 unless otherwise stated. The investing world has more than just domestic equities. There are international stocks, bonds, commodities, etc. If your benchmark is the total market of all assets cap weighted, then there's a strong argument that it is the efficient portfolio.

If the benchmark is the total US domestic stock market but the investing world is global stocks and bonds, there's a strong case for discussing risk-adjusted returns (alpha) of a balanced portfolio.
Yes this, mostly. In my mind alpha is only really relevant ex-post in terms of any determination of results. One seeks alpha so that some ex-post view of their results can conclude that alpha was found. Implicit in the search for alpha is a belief that markets are not necessarily efficient. The determination of ex-post alpha can be done thorugh what is called attribution analysis, where the sources of return are 'attributed' to various factors (asset allocation, exposure to risk factors, etc.) with anything left being manager skill or alpha.
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acegolfer
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by acegolfer »

knpstr wrote: Job security.
lol.
k66 wrote: Is the model absolutely correct, or merely "good"? I might suggest that it is probably the latter, especially if we subscribe to the notion that securities (price) behaviour is a constantly in a non-linear state. Thus, there is some alpha, but it would be hard to detect routinely--but for some people that is enough to keep on believing!
All asset pricing models are linear. Ask Merton about intertemporal-CAPM, or Ross about APT. For a correct model, alpha has to be zero. Otherwise, the model is not correct.
staythecourse wrote:All the data I have seen has shown if anything there is RTM when it comes to alpha so if one shows positive alpha from date x to date y in retrospect then it is a BETTER option probability wise to avoid that fund as it is likely to be a loser (negative alpha) from date y to date z prospectively. So, of one is sitting now in 2015 and see funds that have +alpha the last 5 years (2010-2014) it is a BETTER chance of success avoiding those funds then putting money into those funds if one is looking for +alpha for the next 5 years (2015-2019)
Mean reverting alpha? A good one.
Rob Bertram wrote:1. If you're saying alpha = 0 for all efficient portfolios, then you're directly saying that the efficient frontier is a straight line.
2. Predicting the future is hard. We can try using PE/10 or bond yields, but it's not perfect. There is a wide margin of error in the model as well as in the predicted alpha.
3. I think you might be confusing ex-ante with ex-post.
1. No. Can anyone explain how alpha = 0 means straight line EF?
2. I agree. The objective of this thread is to explain that picking + alpha stocks is useless.
3. I fully understand the difference between ex-post and ex-ante. I think you misread OP. Even with a correct model, ex-post estimated alpha can be 0. Look up wiki Jensen's alpha. It's ex-post alpha. But with a correct model, ex-ante true alpha must be 0.
richard wrote: When you run a CAPM, 3-factor, etc. model, you're running it on historic data. The model allows you to determine exposure to the relevant factor or factors over the relevant time period and to determine if there was any alpha under the model. The models themselves say nothing about the future.
I agree. Hence seeking alpha to pick stocks is useless.
swaption wrote: Yes this, mostly. In my mind alpha is only really relevant ex-post in terms of any determination of results. One seeks alpha so that some ex-post view of their results can conclude that alpha was found. Implicit in the search for alpha is a belief that markets are not necessarily efficient. The determination of ex-post alpha can be done thorugh what is called attribution analysis, where the sources of return are 'attributed' to various factors (asset allocation, exposure to risk factors, etc.) with anything left being manager skill or alpha.
I agree that ex-post alpha is meaningful because it can measure the past performance. But I'm trying to say that managers are using a wrong model (such as CAPM) to estimate alpha and fool clients with a positive but flawed alpha.
Rob Bertram
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by Rob Bertram »

acegolfer wrote:
Rob Bertram wrote:"Alpha" means risk-adjusted returns above the line connecting the risk-free asset (cash) and the benchmark (usually the market portfolio).
1. If you're saying alpha = 0 for all efficient portfolios, then you're directly saying that the efficient frontier is a straight line.
1. No. Can anyone explain how alpha = 0 means straight line EF?
Draw the capital asset line between the risk free asset and your benchmark asset. By definition, anything on this line has alpha = 0. Pick any efficient portfolio. If it has alpha = 0, then it must be on this line.
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acegolfer
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by acegolfer »

Rob Bertram wrote: Draw the capital asset line between the risk free asset and your benchmark asset. By definition, anything on this line has alpha = 0. Pick any efficient portfolio. If it has alpha = 0, then it must be on this line.
TY for responding. Let me clear up some confusions.
1. In asset pricing model, alpha = 0 for not only efficient portfolios but for any securities.
2. There are 2 straight lines: CML (sigma vs Er for efficient portfolios) and SML (mkt beta vs Er for any securities). When you say efficient ptf must be on the straight line, I think you are talking about CML.
3. Not all efficient portfolios are on the straight line CML. http://en.wikipedia.org/wiki/Efficient_frontier. Only 1 of them (aka tangency portfolio) is on the straight line CML. If you don't like the single risk factor model, then look at Fig 2 of http://faculty.chicagobooth.edu/john.co ... 3Q99_4.pdf Not all efficient portfolios (blue) are on the efficient cone (black).
4. (minor) It's called capital allocation line not capital asset line. http://en.wikipedia.org/wiki/Capital_allocation_line
Rob Bertram
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by Rob Bertram »

acegolfer wrote:2. There are 2 straight lines: CML (sigma vs Er for efficient portfolios) and SML (mkt beta vs Er for any securities). When you say efficient ptf must be on the straight line, I think you are talking about CML.
There can be many CALs. It's just a line from the risk-free asset through any particular portfolio. The optimal one is indeed called the CML. When talking about alpha, we have a benchmark in mind. If that benchmark is the optimal portfolio, then we can call its CAL the CML. (Sharpe proved that in an efficient market the market portfolio is the optimal one. Though, there's disagreement on whether the markets are actually efficient. But I think it's fair to still say the market portfolio is the optimal portfolio.)
acegolfer wrote:3. Not all efficient portfolios are on the straight line CML. http://en.wikipedia.org/wiki/Efficient_frontier. Only 1 of them (aka tangency portfolio) is on the straight line CML. If you don't like the single risk factor model, then look at Fig 2 of http://faculty.chicagobooth.edu/john.co ... 3Q99_4.pdf Not all efficient portfolios (blue) are on the efficient cone (black).
It is indeed true that not all efficient portfolios are on the efficient cone / Markowitz bullet. What's also true is that they are not all on the CML which means that they have some alpha that is not zero which violates your premise.

It doesn't have to be complicated. Single-risk factor vs multi-risk factor adds an extra layer of confusion. Draw your CAL on the mean/variance chart. Plot the point of any portfolio. Draw a vertical line between that point and the CAL. That is your alpha. It's the difference in return for the same risk of your benchmark.
Image

As an observation, the efficient frontier charts that you posted were all for a single asset class -- stocks. In general we accept that the total stock market is the benchmark to beat. When you expand your investing world to stocks and bonds, what is the market portfolio? Let's say market cap is about $55 trillion stocks and $83 trillion in bonds. (I haven't checked in a while, the numbers have probably changed slightly.) That's about 40% stock, 60% bond. Is your benchmark for alpha still 100% stocks or is it 40/60?

Oddly, many stick with 100% stocks as the benchmark when bonds are available. This means that it's not the market portfolio in a stock/bond world, and by extension it's not the optimal one. There will be portfolios with positive alpha in this case because the benchmark is not optimal.

I agree with you that the optimal choice would be to buy the market portfolio. If the return isn't where you need it, lever to your risk tolerance. "Leverage" is a scary word, so people instead trade alpha for peace of mind and get a riskier non-leveraged portfolio.
acegolfer wrote:4. (minor) It's called capital allocation line not capital asset line. http://en.wikipedia.org/wiki/Capital_allocation_line
Thank you for the correction! I think I had "asset" on the brain. :oops:
nisiprius wrote:It turns out there's no accepted authority as to the meaning of β in financial sciencialistics. If there isn't one for β then there probably isn't one for α.
Nisiprius has a good point. I'm using the following definition of alpha (Investopedia): "A measure of performance on a risk-adjusted basis. Alpha takes the volatility (price risk) of a mutual fund and compares its risk-adjusted performance to a benchmark index. The excess return of the fund relative to the return of the benchmark index is a fund's alpha."

In factor models, the model tries to "explain" the alpha as a function of the factor weighting. There's a concept of an alpha coefficient that is the "unexplained" alpha. If the model is perfect, the alpha coefficient is 0. This doesn't mean that the portfolio has zero alpha, it means that the model completely explains why the alpha is not zero. Is this what you mean -- that the unexplained alpha must be 0?
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by knpstr »

I prefer the second definition:
"2. The abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like the capital asset pricing model (CAPM)."

So once you realize these models don't really predict anything, you realize alpha doesn't mean anything.
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acegolfer
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by acegolfer »

Rob,

I didn't know investopedia had different definitions of alpha. Throughout this thread, I was using the definition that knp prefers:

2. The abnormal rate of return on a security or portfolio in excess of what would be predicted by an equilibrium model like the capital asset pricing model (CAPM)

I hope this settles our differences.
tarahill
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by tarahill »

Hi Rob,

Your graph points out that the high-risk (but efficient) portfolio at the bottom end of the red arrow has a negative Alpha. I say this because the Tangency Portfolio (assumed to be the Total Market Portfolio) has an Alpha of zero and a Beta of one (by definition) and that any levering/de-levering of that portfolio along the CAL will not change that. Would you agree, then, that ALL efficient portfolios should also have negative Alphas (except for the Tangency Portfolio whose Alpha is exactly zero) as they all fall below the CAL?

This negative Alpha effect is paradoxically strongest for efficient portfolios that are less risky than the Tangency Portfolio, as the gap between the efficient frontier and the CAL widens there. I say paradoxically because there is so much talk now about the 'Low Volatility Anomaly" that suggests that low-Beta portfolios significantly out-perform. Would you agree that this anomaly, if true, is completely at odds with the basic premise of MPT?

Thanks in advance for your thoughts...

Rob Bertram wrote:
acegolfer wrote:2. There are 2 straight lines: CML (sigma vs Er for efficient portfolios) and SML (mkt beta vs Er for any securities). When you say efficient ptf must be on the straight line, I think you are talking about CML.
There can be many CALs. It's just a line from the risk-free asset through any particular portfolio. The optimal one is indeed called the CML. When talking about alpha, we have a benchmark in mind. If that benchmark is the optimal portfolio, then we can call its CAL the CML. (Sharpe proved that in an efficient market the market portfolio is the optimal one. Though, there's disagreement on whether the markets are actually efficient. But I think it's fair to still say the market portfolio is the optimal portfolio.)
acegolfer wrote:3. Not all efficient portfolios are on the straight line CML. http://en.wikipedia.org/wiki/Efficient_frontier. Only 1 of them (aka tangency portfolio) is on the straight line CML. If you don't like the single risk factor model, then look at Fig 2 of http://faculty.chicagobooth.edu/john.co ... 3Q99_4.pdf Not all efficient portfolios (blue) are on the efficient cone (black).
It is indeed true that not all efficient portfolios are on the efficient cone / Markowitz bullet. What's also true is that they are not all on the CML which means that they have some alpha that is not zero which violates your premise.

It doesn't have to be complicated. Single-risk factor vs multi-risk factor adds an extra layer of confusion. Draw your CAL on the mean/variance chart. Plot the point of any portfolio. Draw a vertical line between that point and the CAL. That is your alpha. It's the difference in return for the same risk of your benchmark.
Image

As an observation, the efficient frontier charts that you posted were all for a single asset class -- stocks. In general we accept that the total stock market is the benchmark to beat. When you expand your investing world to stocks and bonds, what is the market portfolio? Let's say market cap is about $55 trillion stocks and $83 trillion in bonds. (I haven't checked in a while, the numbers have probably changed slightly.) That's about 40% stock, 60% bond. Is your benchmark for alpha still 100% stocks or is it 40/60?

Oddly, many stick with 100% stocks as the benchmark when bonds are available. This means that it's not the market portfolio in a stock/bond world, and by extension it's not the optimal one. There will be portfolios with positive alpha in this case because the benchmark is not optimal.

I agree with you that the optimal choice would be to buy the market portfolio. If the return isn't where you need it, lever to your risk tolerance. "Leverage" is a scary word, so people instead trade alpha for peace of mind and get a riskier non-leveraged portfolio.
acegolfer wrote:4. (minor) It's called capital allocation line not capital asset line. http://en.wikipedia.org/wiki/Capital_allocation_line
Thank you for the correction! I think I had "asset" on the brain. :oops:
nisiprius wrote:It turns out there's no accepted authority as to the meaning of β in financial sciencialistics. If there isn't one for β then there probably isn't one for α.
Nisiprius has a good point. I'm using the following definition of alpha (Investopedia): "A measure of performance on a risk-adjusted basis. Alpha takes the volatility (price risk) of a mutual fund and compares its risk-adjusted performance to a benchmark index. The excess return of the fund relative to the return of the benchmark index is a fund's alpha."

In factor models, the model tries to "explain" the alpha as a function of the factor weighting. There's a concept of an alpha coefficient that is the "unexplained" alpha. If the model is perfect, the alpha coefficient is 0. This doesn't mean that the portfolio has zero alpha, it means that the model completely explains why the alpha is not zero. Is this what you mean -- that the unexplained alpha must be 0?
691175002
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Re: Seeking alpha is flawed. Ex-ante alpha must be 0.

Post by 691175002 »

Models are constructed with different intent depending on whether you are trying to explain or evaluate performance.

In an explanatory model, alpha (or simply the residual) is a failure to fully predict prices.

When attempting to evaluate a manager, risk factors represent an opportunity cost. Risk factors used in these models are chosen to be measurable, reproducible, investible.


As a quick example, CAPM has clearly failed as a predictor of asset prices but can still be used for performance evaluation. Imagine an investor must select between investing all his money in the S&P500 and an active manager. Alpha is the incremental risk-adjusted return of selecting the active fund.

Similarly, an institutional investor who can select between several low-cost tilted ETFs can use a 3 or 4 factor model to determine what portion of the active managers returns are better achieved passively.


We measure alpha because there aren't really any alternatives. At some point people need to compare investment performance on a risk adjusted basis. Sharpe ratio and similar measures don't differentiate between systematic and nonsystematic risk.

The objective of this thread is to explain that picking + alpha stocks is useless.
I'm not following the train of thought here. Using a pricing model requires that you purchase stocks with the highest expected return. In CAPM this would involve buying stocks that are high risk. This is not a desirable strategy if your believe that your factors are proxies for efficiently priced risk.

You cannot pick positive alpha stocks because pricing models do not predict alpha. Purchasing stocks that have historically had high alpha is analogous to a momentum strategy and may or may not produce excess returns.

I just realized I might have missed the question entirely. Ex-ante alpha is never measured or published. As I mentioned earlier, the use of a pricing model involves picking stocks with high E(r). The error term/alpha has nothing to do with ex-ante stock selection.
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