Efficient Market Hypothesis vs Modern Portfolio Theory

The Markowitz Efficient Frontier

Note: Unlike my previous articles this is "supposedly" a bit more technical, although no mathematics will be employed in its process. The response to those who claim that the EMH and MPT are not contradictory in the long-run can be found here.

What is the current state of the economics profession? From what we can witness any person who is not an economist would think that the state is bad (although there have been many within the profession which share this opinion, for example Paul Krugman not to mention many bloggers). Lately, I have had some time available to have a look at what appears to be the most influential theories of the 20th century (regarding stock markets that is):  the Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH). The former was introduced in the early 1950's by Harry Markowitz and the latter was introduced by Paul Samuelson and Eugene Fama in the early 1960's. Of the three people mentioned above two (Markowitz and Samuelson) received a Nobel price later on.*

I will waste no time in discussing whether the assumptions used by both theories are valid or not. This debate has been raging for nearly 40 years and I do not think that anything can be said to settle it. Besides, the limitations of the assumptions used were first presented by the persons who introduced it (for example one may have a look at Markowitz's or Samuelson's articles). Other than the assumptions and their implications as to the validity of the models, no article has ever stated what I think is the most important aspect of the debate:

If the MPT holds then EMH cannot hold and vice versa.

What do I mean by that? Having a a look at the EMH forms as presented by Fama we get the following:

1. Weak-form efficiency

Future prices cannot be predicted by analyzing past prices or past returns.

2. Semi-strong-form efficiency

In addition to the point (1), share prices adjust to publicly available new information very quickly and in an unbiased fashion, such that no excess returns can be earned by trading on that information.

3. Strong-form efficiency

In addition to point (2), share prices reflect all information, public and private, and no one can earn excess returns. 

Given that the Strong-form efficiency is considered impossible in the real world we are only left with the first two alternatives. These two take for granted what Samuelson proved: properly anticipated prices fluctuate randomly, i.e. that future price movements are determined entirely by information not contained in the price series. In simple words, prices must follow a random walk.

The random-walk hypothesis is the pillar of the EMH. Without it nothing holds. If one could prove that prices do not fluctuate randomly then everything would collapse. Yet, as it has yet to be proven we may take for granted that prices do indeed follow a random walk. Even proponents of the EMH who have stated that markets may not always be perfectly efficient, such as Burton Malkiel, continue to believe that this holds.

Let us now have a look at the MPT as presented by Markowiz:

The underlying assumption is that higher expected returns also mean higher risk assumed by the investor. While many may argue that this does not hold, this sort of discussion is beyond the scope of this article. In any case, the MPT uses the expected returns of an asset, either by employing past returns or by using investors' "beliefs" for the future (which are rational and match the true distribution of returns) to form a portfolio of assets which maximizes expected return over a given risk amount. 

Economists have been raging over the years if the models' assumptions are correct, what could happen if the assumptions are altered or whether the world functions this way. Now here I just assume that both models are correct. 

Then ponder on the following:

If the EMH holds (even at its weakest form) then past prices are not a good forecast of future prices since future prices are to follow a random walk. In addition, any forecast of the future prices, given that they follow a random walk, would be erroneous as it would not be a good proxy for neither risk nor expected return. Thus, we would not be able to use MPT for investing purposes as it would not yield proper results.

Conversely, if MPT holds it would mean that either past prices can predict future returns or that investors beliefs are the real distributions of returns the random walk hypothesis does not hold. 

Which of the two theories is correct? I would not know. Yet, what I would know is that if one of them holds, as described in its original form, then the other cannot. The worst part for their proponents is that the answer cannot lie in-between this as any deviation would mean that the random-walk hypothesis is discarded. If it holds and investors cannot forecast anything then why should they bother putting their money in the market? It appears that we can either forecast or not. It all boils down to whether stocks follow a random walk. If they do then the the EMH holds and the MPT is discarded. If they do not the opposite is true.

Simple enough isn't it?

*Update: Since the writing of this article, Eugene Fama has won the Nobel Prize in Economics for 2013. There has been a lot of talk about whether it was a good call or whether it was right to award Robert Shiller alongside with him. Dan Davies has an excellent article on why this was done, which reminded me of the conclusions in Paul Samuelson's paper which started the whole EMH literature (titled "Properly anticipated prices fluctuate randomly"):

“I have not here discussed where the basic probability distributions are supposed to come from. In whose minds are they ex ante? Is there any ex post validation of them? Are they supposed to belong to the market as a whole? And what does that mean? Are they supposed to belong to the “representative individual”, and who is he? Are they some defensible or necessitous compromise of divergent expectation patterns? Do price quotations somehow produce a Pareto-optimal configuration of ex ante subjective probabilities? This paper has not attempted to pronounce on these interesting questions.”

It appears that Paul Samuelson had a much greater understanding of what he was doing than most economists have about his work since.