<p>The efficient market hypothesis does <strong>not</strong> imply that there are no patterns!</p>

<p>As Eugene Fama pointed out decades ago, any test of market efficiency is a joint test of market efficiency and an asset pricing model. The EMH on its own is not a testable theory.</p>

<p>If I understand your statement properly, you're claiming that forecasting variance would violate market efficiency? For that to be true, you would need to assume an asset pricing model where variance is not forecastable. That's a strange claim. It would imply that risk free government bonds must have the same volatility as small biotech firms (otherwise, I can forecast volatility based upon whether a security is a stock or a bond).</p>

<p>It well known that volatility is forecastable, both in the cross section and in the time series. For example, there is the widely used <a href="https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity" rel="nofollow noreferrer">GARCH</a> model and all kinds of other <a href="https://en.wikipedia.org/wiki/Stochastic_volatility" rel="nofollow noreferrer">stochastic volatility</a> models. Forecasting volatility is interesting, but it in no way constitutes a per se violation of market efficiency.</p>

<p><a href="https://quant.stackexchange.com/questions/35008/does-the-existence-of-anomalies-disprove-the-efficient-markets-hypotheses/35020#35020">This answer of mine</a> goes into greater depth on what the efficient market hypothesis actually says and how to test it.</p>

<h3>References</h3>

<p>Fama, Eugene F., 1991, "Efficient Capital Markets: II," <em>Journal of Finance</em></p>

CC BY-SA 3.0
2017-07-29T12:28:54.243Z
I cannot see how I assumed that assets should have the same variance. Nevertheless, the minimum variance of my portfolios should have no pattern. Thus, the distribution fitting of a stock should have been an irrelevant variable, since it does not reflect any information given. Also, patterns indeed may occur, but having a pattern with something irrelevant is either irrational or an outlier.
Commissar Vasili Karlovic
CC BY-SA 3.0
2017-07-29T20:43:10.480Z
@CommissarVasiliKarlovic Please formulate a precise, mathematical statement about stock returns that: (1) you believe *should* be true and (2) you show is violated (based upon the work you have done).
Matthew Gunn
CC BY-SA 3.0
2017-07-30T11:10:01.583Z
I will upload a graph as soon as I have some time to spare.
Commissar Vasili Karlovic
CC BY-SA 3.0
2017-08-03T05:53:30.657Z
It amazes me that people openly discus without contest that Fama's theory cannot be tested yet still treat it as a meaningful theory. What use is there for untedtable theory in science?? What can we possibly learn?
123
CC BY-SA 3.0
2017-08-07T20:16:27.487Z
@123 If you put zero constraints on asset pricing models, that's basically right. **But** rationality puts some constraints on the space of sensible asset pricing models. Eg. we know that stocks tend to decline dramatically after an earnings miss. One conclusion is that markets aren't strong-form efficient, that public markets aren't incorporating the earnings miss into the price until it's publicly announced. It would be hard to create a rational, sensible asset pricing model where markets *know* a firm is going to miss earnings but the price doesn't decline until after the earnings call.
Matthew Gunn
CC BY-SA 3.0
2017-08-10T12:06:39.377Z
I hope the irony is not lost on anyone here reading the thoughts of PhD student in Chicago defending Fama's theory. You say above that Fama himself claimed that any test of the EMH is also a test of an asset pricing model. If this is true then his theory is untestable by his own admission. Limiting the space of sensible asset pricing models is independent of whether or not the EMH is testable.
123
CC BY-SA 3.0
2017-08-10T12:13:11.527Z
@123 Perhaps Fama's 1991 article "[Efficient Capital Markets: II](http://faculty.chicagobooth.edu/jeffrey.russell/teaching/Finecon/readings/fama.pdf)" might be of interest.
Matthew Gunn
CC BY-SA 3.0
2017-08-10T12:16:21.347Z
It is not. I am already familiar. I personally find the EMH useless and a byproduct of an era that preceded our ability to produce reliable evidence of bubble formation and sunspot equilibria. My opinion is that how Fama addresses these market phenomena in the context of the EMH is handwavy (at best) and he only gets away with it because he is Eugene Fama.
123
CC BY-SA 3.0
2017-08-10T13:49:08.050Z
@123 By that standard, perhaps modeling agents as rational utility maximizers is useless and a byproduct of an era that preceded our ability to produce reliable evidence of psychological bias (eg. framing effects, choice overload and violation of weak axiom of revealed preference, etc...)?
Matthew Gunn
CC BY-SA 3.0
2017-08-10T14:58:21.293Z
Yes - those models are largely useless because they fail to provide even a reasonable approximation of reality. Then again, I am of the opinion that macroeconomics is mired in dogmatism and that macroeconomists in general have fallen down a completely useless DSGE rabbit hole.
123
CC BY-SA 3.0
2017-08-10T15:32:14.003Z
@123 Box famously said that all models are wrong, but some are useful. Maximizing utility is an assumption at the foundaton of numerous useful economic models. The efficient market hypothesis (EMH) is similarly at the base of numerous useful asset pricing models.
Matthew Gunn
CC BY-SA 3.0
2017-08-10T15:33:52.800Z
@123 The real test of a model though is whether it's is useful. Fama speaks of whether it helps you understand the data. And I recall a comment of physicist Sidney Drell that to him, a theory wasn't a theory unless it made falsifiable predictions. A theory must say something! There are many useful economic theories which use utility or EMH to make testable predictions. On the other hand, I share some of your skepticism. There's far too much in economics that's less like testable science and more like storytelling with math. There are vacuous frameworks which can be tweaked to match anything.
Matthew Gunn
CC BY-SA 3.0
2017-07-28T02:23:43.730Z
2018-03-14T00:32:46.773Z
2018-03-14T00:32:46.773Z
Matthew Gunn
<p>By itself, no it does not, at least how I am understanding your post.  While I am an opponent of the Efficient Market Hypothesis, what you would need to show is that there is a "free lunch," with your methodology.  You would also have to show it persists out-of-sample and does so for decades.  You would need to measure commissions as well.  A $\$3$ gain that costs $\$5$ to get isn't a gain.</p>

<p>The second way to show it would be if your distribution implied a strong informational asymmetry by its structure.</p>

CC BY-SA 3.0
2017-07-25T02:30:07.083Z
2017-07-25T02:30:07.083Z
Dave Harris
<p>The latest Freakonomics podcast topic <a href="http://freakonomics.com/podcast/stupidest-money/" rel="nofollow noreferrer">Stupidest money</a> may shed some light. </p>

<p>I just quote part of the conversation from John Bogle:</p>

<blockquote>
  <p>The markets are highly efficient — although, importantly, not
  perfectly efficient. Sometimes they’re very efficient and sometimes
  they’re not. It’s hard for we poor souls on Earth to know which is
  which</p>
</blockquote>

<p>It is a gamble of randomness.</p>

<p>(update)
Extreme cases like Comcast and Enron show so call "public offering" are not immunized to information opacity and wrong doing. In addition, fake news, manipulation using various rumor mills or even human error may skew "market efficiency".</p>

<p>In addition, so call "market analytical tools" are anything but hindsight self-fulfillment prophecy. Currently, there is little proof that so call market-analytical tools are able to produce reliable results when compare to solid information collected (e.g. whether the business is managed by competence hand ) </p>

CC BY-SA 3.0
2017-07-29T18:42:58.120Z
I just upvoted your answer for your cool quote! But let's get serious. Philosophically speaking, this may answer to my dilemma-question. If there was a quantitative methodology to evaluate market efficiency and the probability of stock market not to be efficient is 0.009%, then modeling would have correctly evaluated it as perfectly efficient, although there may still be methodologies to expose that inefficiency. Burned.
Commissar Vasili Karlovic
CC BY-SA 3.0
2017-07-31T07:12:57.543Z
@CommissarVasiliKarlovic   The randomness occur every now and then, mostly due to irrational human behavior. Behavior economic are mean to study rationality of the irrational behavior.
mootmoot
CC BY-SA 4.0
2017-07-28T13:00:46.907Z
2019-04-22T00:28:26.117Z
2019-04-22T00:28:26.117Z
mootmoot
<p>The long story short, I have developed an index based on a certain distribution. Then I aligned NYSE stocks according to this index i.e. the stocks with the best fit are first and the worst are last. The index is irrelevant with economic theory.</p>

<p>Afterwards, I created a group of portfolios with equal number of stocks and equal observations and then I calculated the minimum variance per portfolio.</p>

<p>The result suggests that the portfolios with better fit have lower variances than the ones with "bad" fit. Does this prove market inefficiency assuming that it didn't occur just by chance?</p>

<p>Edit: According to efficient market hypothesis, asset prices reflect all information given and "patterns" should not occur. However, according to the results, patterns occur and they are independent to the information given.</p>

CC BY-SA 3.0
2017-07-24T13:35:08.823Z
*"According to efficient market hypothesis, asset prices reflect all information given and "patterns" should not occur."* - that's not quite true. It's more accurate to say that any patterns that do occur, don't enable you to make returns that are higher than those commensurate with the risks taken. And I'm going to guess that that's the case here, because if you could make those returns, you wouldn't be telling us anything about it ...
410 gone
CC BY-SA 3.0
2017-07-28T01:58:44.300Z
Are you asking if forecastable volatility violates the efficient market hypothesis? Does it violate the efficient market hypothesis if stock returns have higher volatility than government bonds? Perhaps examine [the definition of the efficient market hypothesis here](https://quant.stackexchange.com/questions/35008/does-the-existence-of-anomalies-disprove-the-efficient-markets-hypotheses/35020#35020).
Matthew Gunn
CC BY-SA 3.0
2017-07-29T20:39:26.200Z
What do you specifically mean by, "I calculated the minimum variance per portfolio." What does, "I developed an index based on a certain distribution." It's quite ambiguous what you're doing.
Matthew Gunn
CC BY-SA 3.0
2017-07-31T11:41:42.313Z
I think laboratory evidence of sunspots in and the creation of bubbles in asset markets both do more to cast doubt on the EMH than does what you've written about here.
123
<stock-market><efficient-markets><portfolio-theory>
Does my research prove market inefficiency?
Commissar Vasili Karlovic
# Does my research prove market inefficiency?

(Asked by: username_0 on 2017-07-24)

The long story short, I have developed an index based on a certain distribution. Then I aligned NYSE stocks according to this index i.e. the stocks with the best fit are first and the worst are last. The index is irrelevant with economic theory.

Afterwards, I created a group of portfolios with equal number of stocks and equal observations and then I calculated the minimum variance per portfolio.

The result suggests that the portfolios with better fit have lower variances than the ones with "bad" fit. Does this prove market inefficiency assuming that it didn't occur just by chance?

Edit: According to efficient market hypothesis, asset prices reflect all information given and "patterns" should not occur. However, according to the results, patterns occur and they are independent to the information given.

**Tags:** stock-market, efficient-markets, portfolio-theory
> **Comments:**
> **username_1**: *"According to efficient market hypothesis, asset prices reflect all information given and "patterns" should not occur."* - that's not quite true. It's more accurate to say that any patterns that do occur, don't enable you to make returns that are higher than those commensurate with the risks taken. And I'm going to guess that that's the case here, because if you could make those returns, you wouldn't be telling us anything about it ...  
> **username_2**: Are you asking if forecastable volatility violates the efficient market hypothesis? Does it violate the efficient market hypothesis if stock returns have higher volatility than government bonds? Perhaps examine [the definition of the efficient market hypothesis here](https://quant.stackexchange.com/questions/35008/does-the-existence-of-anomalies-disprove-the-efficient-markets-hypotheses/35020#35020).  
> **username_2**: What do you specifically mean by, "I calculated the minimum variance per portfolio." What does, "I developed an index based on a certain distribution." It's quite ambiguous what you're doing.  
> **username_3**: I think laboratory evidence of sunspots in and the creation of bubbles in asset markets both do more to cast doubt on the EMH than does what you've written about here.  

---

## 3 answers

### Answer by username_2 on 2017-07-28. Score: 8

The efficient market hypothesis does **not** imply that there are no patterns!

As Eugene Fama pointed out decades ago, any test of market efficiency is a joint test of market efficiency and an asset pricing model. The EMH on its own is not a testable theory.

If I understand your statement properly, you're claiming that forecasting variance would violate market efficiency? For that to be true, you would need to assume an asset pricing model where variance is not forecastable. That's a strange claim. It would imply that risk free government bonds must have the same volatility as small biotech firms (otherwise, I can forecast volatility based upon whether a security is a stock or a bond).

It well known that volatility is forecastable, both in the cross section and in the time series. For example, there is the widely used [GARCH](https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity) model and all kinds of other [stochastic volatility](https://en.wikipedia.org/wiki/Stochastic_volatility) models. Forecasting volatility is interesting, but it in no way constitutes a per se violation of market efficiency.

[This answer of mine](https://quant.stackexchange.com/questions/35008/does-the-existence-of-anomalies-disprove-the-efficient-markets-hypotheses/35020#35020) goes into greater depth on what the efficient market hypothesis actually says and how to test it.

### References

Fama, Eugene F., 1991, "Efficient Capital Markets: II," *Journal of Finance*

> **Comments:**
> **username_0**: I cannot see how I assumed that assets should have the same variance. Nevertheless, the minimum variance of my portfolios should have no pattern. Thus, the distribution fitting of a stock should have been an irrelevant variable, since it does not reflect any information given. Also, patterns indeed may occur, but having a pattern with something irrelevant is either irrational or an outlier.  
> **username_2**: @CommissarVasiliKarlovic Please formulate a precise, mathematical statement about stock returns that: (1) you believe *should* be true and (2) you show is violated (based upon the work you have done).  
> **username_0**: I will upload a graph as soon as I have some time to spare.  
> **username_3**: It amazes me that people openly discus without contest that Fama's theory cannot be tested yet still treat it as a meaningful theory. What use is there for untedtable theory in science?? What can we possibly learn?  
> **username_2**: @123 If you put zero constraints on asset pricing models, that's basically right. **But** rationality puts some constraints on the space of sensible asset pricing models. Eg. we know that stocks tend to decline dramatically after an earnings miss. One conclusion is that markets aren't strong-form efficient, that public markets aren't incorporating the earnings miss into the price until it's publicly announced. It would be hard to create a rational, sensible asset pricing model where markets *know* a firm is going to miss earnings but the price doesn't decline until after the earnings call.  
> **username_3**: I hope the irony is not lost on anyone here reading the thoughts of PhD student in Chicago defending Fama's theory. You say above that Fama himself claimed that any test of the EMH is also a test of an asset pricing model. If this is true then his theory is untestable by his own admission. Limiting the space of sensible asset pricing models is independent of whether or not the EMH is testable.  
> **username_2**: @123 Perhaps Fama's 1991 article "[Efficient Capital Markets: II](http://faculty.chicagobooth.edu/jeffrey.russell/teaching/Finecon/readings/fama.pdf)" might be of interest.  
> **username_3**: It is not. I am already familiar. I personally find the EMH useless and a byproduct of an era that preceded our ability to produce reliable evidence of bubble formation and sunspot equilibria. My opinion is that how Fama addresses these market phenomena in the context of the EMH is handwavy (at best) and he only gets away with it because he is Eugene Fama.  
> **username_2**: @123 By that standard, perhaps modeling agents as rational utility maximizers is useless and a byproduct of an era that preceded our ability to produce reliable evidence of psychological bias (eg. framing effects, choice overload and violation of weak axiom of revealed preference, etc...)?  
> **username_3**: Yes - those models are largely useless because they fail to provide even a reasonable approximation of reality. Then again, I am of the opinion that macroeconomics is mired in dogmatism and that macroeconomists in general have fallen down a completely useless DSGE rabbit hole.  
> **username_2**: @123 Box famously said that all models are wrong, but some are useful. Maximizing utility is an assumption at the foundaton of numerous useful economic models. The efficient market hypothesis (EMH) is similarly at the base of numerous useful asset pricing models.  
> **username_2**: @123 The real test of a model though is whether it's is useful. Fama speaks of whether it helps you understand the data. And I recall a comment of physicist Sidney Drell that to him, a theory wasn't a theory unless it made falsifiable predictions. A theory must say something! There are many useful economic theories which use utility or EMH to make testable predictions. On the other hand, I share some of your skepticism. There's far too much in economics that's less like testable science and more like storytelling with math. There are vacuous frameworks which can be tweaked to match anything.  

---

### Answer by username_4 on 2017-07-25. Score: 1

By itself, no it does not, at least how I am understanding your post. While I am an opponent of the Efficient Market Hypothesis, what you would need to show is that there is a "free lunch," with your methodology. You would also have to show it persists out-of-sample and does so for decades. You would need to measure commissions as well. A $\$3$ gain that costs $\$5$ to get isn't a gain.

The second way to show it would be if your distribution implied a strong informational asymmetry by its structure.


---

### Answer by username_5 on 2017-07-28. Score: 1

The latest Freakonomics podcast topic [Stupidest money](http://freakonomics.com/podcast/stupidest-money/) may shed some light.

I just quote part of the conversation from John Bogle:

> The markets are highly efficient — although, importantly, not
> perfectly efficient. Sometimes they’re very efficient and sometimes
> they’re not. It’s hard for we poor souls on Earth to know which is
> which

It is a gamble of randomness.

(update)
Extreme cases like Comcast and Enron show so call "public offering" are not immunized to information opacity and wrong doing. In addition, fake news, manipulation using various rumor mills or even human error may skew "market efficiency".

In addition, so call "market analytical tools" are anything but hindsight self-fulfillment prophecy. Currently, there is little proof that so call market-analytical tools are able to produce reliable results when compare to solid information collected (e.g. whether the business is managed by competence hand )

> **Comments:**
> **username_0**: I just upvoted your answer for your cool quote! But let's get serious. Philosophically speaking, this may answer to my dilemma-question. If there was a quantitative methodology to evaluate market efficiency and the probability of stock market not to be efficient is 0.009%, then modeling would have correctly evaluated it as perfectly efficient, although there may still be methodologies to expose that inefficiency. Burned.  
> **username_5**: @CommissarVasiliKarlovic   The randomness occur every now and then, mostly due to irrational human behavior. Behavior economic are mean to study rationality of the irrational behavior.  

---

