Financial Mathematics Text

Tuesday, October 28, 2014

The Efficient Markets Hypothesis is Meaningless

I'm going to begin a critique of the Efficient Markets Hypothesis (EMH). This is not the first nor will it be the last that have been presented. Most of these critiques accept the basic paradigm an attempt to empirically prove that one can "beat the market".

For the practitioner, this can be quite appealing as it allows one to find some strategy that would allow one to earn "excess returns".

My approach, which I've been toying with in my mind for the last year or so, is going to be a bit different. My contention is that the entire paradigm is questionable and perhaps "meaningless"1. At the very least, proponents of EMH have a a lot more work to do as there is a lot of ideological baggage and not much in the way of a legitimate scientific hypothesis.

Part of this will be an extension to what is referred to as The Joint Hypothesis Problem. In order to prove that markets are efficient (or inefficient), we would first have to have a model for the relationship between risk and return. If the data doesn't support the theory then either markets are inefficient or we have the wrong risk/return model.

To the practitioner, this approach is going to be more "academic". But my thesis rests on critiquing the relationship between risk and reward. So I'm going to look at "risk" in a variety of different contexts.

Having an understanding of risk (or, in my opinion, risks) is important. So I think there may be interest for that reason alone.

I will try to tag all of these posts under the "risk" label: Risk.

Thesis Outline

So I'm going to give a crude outline of what I think my thesis will amount to. The problem is I haven't worked out all of the details so I may modify this outline.

1) There is more than one type of risk.

This seems to be acknowledged by many proponents of EMH so it's not so much a critique but it is a prelude to my second point.

But it needs to be said because standard CAPM2 (you know, with beta and all that nonsense) is still taught in spite of the fact that empirical evidence doesn't support it.

One might object that Newtonian mechanics is still taught in physics courses in spite of the fact that it's been supplanted by quantum mechanics and relativity.

But Newtonian mechanics is still a decent approximation under certain conditions. Standard CAPM is not.

2) The Problem of Ordering Risk

Given that there is more than one type of risk, that creates the problem of how to order risk. For if I have one variable and I have quantified it via some subset of the real numbers, I can simply use the ordering of the real numbers to order my risks (e.g. if Asset A has a risk of 3 and Asset B has a risk of 5 then Asset B is riskier than Asset A since 5>3.)

But if there are multiple risks then we have to have some means of ordering those risks. For example, suppose that there are two types of risk which I'll aptly name Risk 1 and Risk 2. Consider the following two assets:

Asset A Asset B
Risk 1 3 5
Risk 2 7 2

Asset B is riskier than Asset A according to Risk 1 but not Risk 2. So which one is riskier?

This problem may not be insurmountable but the EMH proponents, to my knowledge, have not addressed this.

3) The Normativity of Risk Preference

As I've discussed before (see Some Thoughts on the Risk/Return Tradeoff and EMH), people have different risk preferences. So when an EMH proponent advocates a relationship between risk and return, she is insisting that there is a correct set of preferences.

This is not problematic in of itself but it is a problem for many economists. Many economists insist on a hard distinction between positive statements (statements of "fact") and normative statements (statements of "value")3. And they (wrongly) believe themselves to be entirely within the domain of positive statements when if fact that much of their work is actually quite normative.

For a critique of the Fact /Value Dichotomy, see Hilary Putnam's The Collapse of the Fact/Value Dichotomy and Other Essays. Philosopher and mathematician Putnam draws on the "nobel" winning economist Amartya Sen to critique a long-held, questionable tradition in philosophy.

4) The Grossman-Stiglitz Paradox

The idea here is that all of these market participants are spending time, money and resources collecting information to get them an edge in the market. This makes markets efficient so that no information can give you an advantage. So the time, money and resources spent acquiring market beating information is an inefficiency in the market. In other words:

If markets are efficient, then they are inefficient.

I suspect there's a way around this conclusion but it will end up looking fairly goofy as it requires some mispricings but that mispricing requires additional costs in information collection and analyst. The extra return then just are compensation for the time spent. This will have an economies of scale element to it as managers with a larger asset base will be able to spend more money on information research.

5) Does the risk of an asset differ depending upon what portfolio it's in?

Risk, in the academic literature, is sometimes defined in the context of a "diversified" portfolio (aka "the market"). So one question that can be asked here is whether or not an asset will have different risk attributes depending on which portfolio it is added to.

To give an example, buying put options in isolation is an extremely risky move which on average will give you negative returns (unless you can identify mispriced securities, perhaps).  But if put options gave positive expected returns then you could buy the put option and buy the stock and subsequently lower risk and returns.

This speculation on my part may go nowhere but I think it's interesting nonetheless.

6) Perfect Knowledge Assumption

This isn't implicit to EMH per se but many studies implicitly assume it (although the authors appear entirely unaware. The basic method of the study is to look at asset class returns, look at various factors (which are correlated with the returns) and draw conclusions about which asset classes and factors are "riskier" than others.

While all such studies assume EMH (often explicitly), it is also required that they assume that market participants have perfect knowledge in order to draw the conclusions that they draw.  This is a serious methological defect that ought be remedied.

1 For those familiar with the logical positivists and (early) Wittgenstein, this will sound much like that. I'm not an advocate of such views but there seems to be some adherence to this amongst economists (particularly the neoclassical variety.)
2 CAPM stands for "Capital Asset Pricing Model". Any model which attempts to "price" "capital assets" would be a "Capital Asset Pricing Model". Typically, however, CAPM refers to a particular theory which relates the returns of one asset compared to another asset (typically the market) by linear regression. The slope of the regression, referred to as beta, represents risk.
3 I distinctly remember using an introductory economics textbook that pointed out this distinction and made a fuss about it claiming that economists only focus on "positive" questions and not "normative" one. If EMH depends on asserting a fundamentally normative relationship then economists ought to abandon it entirely. They won't.

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