The Generalised Efficient Market Hypothesis

Another approach to market efficiency

Originally published in the March 2009 issue

In this article another approach to market efficiency, the Generalised Efficient Market Hypothesis (GEMH), is discussed. It is based on the assumption that market participants do not aim to optimise their utility as expressed in monetary terms but rather act in a more complex world where goals are manifold and constraints abound. In this world, the market is efficient but may be outperformed by a profit seeking participant.

The Efficient Market Hypothesis (EMH) was first coined by Louis Bachelier (1900) and later developed by Paul Samuelson (1965) and Eugene Fama (1965, 1970). It has not only been widely discussed in the academic literature, but it migrated into finance textbooks and has had vast and profound implications for the practice of investment management.

In its pure form the EMH states that market prices reflect all available information and, as the market participants seek to maximize their utility as expressed in monetary terms, and the information arrives randomly and is accounted for by the market without any delay, it is impossible to outperform the market without having any informational advantage.

The hypothesis was challenged in many papers, often based on empirical results that are difficult to explain if the EMH holds. Refer to Nicholson (1968) or Basu (1977) as examples of such work.

The EMH was also criticised by apologists of behavioral finance, a theory that gained popularity in the 1990s and was explained in Shefrin (2002), among others. The main premise in their arguments is that the market participants are not rational, a condition required by the EMH.

Andrew Lo (2004) attempted to incorporate behavioural and evolutionary considerations into the concept but also only considered the economic benefits as the ultimate goal of the market participants. From experience, we know that this assumption does not hold in real life. The motives for trading financial assets and derivatives are much more diverse than just earning profits.

It has thus become commonplace to mention index trackers who buy or sell stocks, bonds or commodities simply because they follow the index, central banks that trade currencies to dampen volatility, exporters and importers who are forced to enter currency conversion trades without having any view on the future direction of the exchange rates. This list is extensive. Add to it active traders (hedge funds, for example) who have to manage the active risk of their portfolios and are often forced to close their positions despite their strong view that the asset they sell is bound to increase in price, rebalancing activities of all sorts, as well as crowd behaviour and agency issues that make market participants feel better when they are doing the same thing as their next door neighbour (and rightfully so – remember headlines like “In 20XX the XXX pension fund’s investments returned X% compared to the country average of Y%”?)

What does all this have to do with the use of “all available information” for the sole purpose of making profits? Or is this all irrational? I believe it is rational, but this rationality is a great deal more complex than just maximizing profits.

Market participants do not act in a fully relaxed environment. They have all sorts of limitations that do not offer them the possibility of processing information immediately or instantaneously expressing their views in the market. Time is needed to formulate a view and express it properly. Investment guidelines may also limit their ability to act. Margin requirements and borrowing limitations are parts of any real life non-long-only strategy.

On the top of that, all these preferences and limitations change over time.

The Generalised Efficient Market Hypothesis
This leads us to what I call the Generalised Efficient Market Hypothesis. In his own way, and changing over time, each investor optimises his own multivariate vector function F where the component functions are economic benefit, risk aversion, and personal comfort, including behavioural biases. The ever changing (and, in many cases, quite fuzzy) parameters are time, market prices, information available to the investor, personal wealth and its recent change, mood, investment horizon, fee structure, and transaction costs.

The independent variables on which F is optimized are this investor’s market positions at each point in time, given such constraints as available assets, investment guidelines, current ability to optimise (including time required to process information and access the market), and borrowing ability. This also varies depending on a number of variables, time being one of them.

The lists above are by no means complete. As we can see, they consist of concepts that are very difficult to formalise. In real life, simplifications are used, and judgment is applied. The ability to optimise F is limited and varies between different investors.

According to the GEMH, each market participant at any given time owns a portfolio optimised as described above. From the GEMH, it immediately follows that the fair value G(t) of a security is equal to its market price M(t) at all times.

The GEMH and the EMH
The GEMH-optimal portfolio is generally different from the EMH-optimal portfolio, because a different target function is used. From the GEMH perspective, the economic fair value (the EMH fair value) V(t) is nonessential because it only reflects a part, though an important part, of the story. From the EMH perspective, the market price M(t) is always equal to, admittedly unobservable, V(t).

Those who believe that the markets are inefficient in the EMH sense and seek to find an economic fair value for each security, can explain the deviations of M(t) from V(t) by the existence of these very inefficiencies.

Within the GEMH framework, these deviations should be considered as deviations of V(t) from G(t), or, equivalently, from M(t). They are a part of the generally efficient process and, in many cases, can be successfully modeled and exploited. This is possible because the price changes do not only depend on changes in the economic fair value (and thus do not only depend on the information flow), but also on a number of other factors many of which are quite predictable.

Those who believe that the markets are inefficient in the EMH sense but do not seek to find an economic fair value for each security, often explain the deviations of M(t) from V(t) by noise (for example, Arnott et al. (2007)).

If the GEMH is accepted, this noise must be considered as noise of V(t) around G(t). It has both transient and non-transient elements. The former cause mean reversion, the latter cause drift. For some applications it is reasonable to assume that the math expectancy of this noise is zero. As M(t)=G(t), this would imply that V(t) mean reverts to G(t), but as discussed above, it is difficult to assert with certainty that this is necessarily true.

In this article we introduced the Generalised Efficient Market Hypothesis, according to which the market always trades at a fair price, and this fair price appears as an equilibrium of the market participants’ interactions based on their complex and poorly formalised optimisation processes. From the GEMH, it follows that it is possible to outperform the market. The relationship between the GEMH and EMH fair values seems to be complex and not readily available for simple assumptions.

Arnott, Robert, Jun Liu, Jason Hsu, Harry Markowitz “Can Noise Create The Size And Value Effect?” (working paper), December 2007.

Bachelier, Louis “Théorie de la Spéculation”, Annales Scientifiques de l’Ecole Normale Superieure, I I I, vol. 17, 1900.

Basu, Sanjoy “Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratios: A test of the Efficient Markets Hypothesis.” Journal of Finance 1977, vol. 32.

Fama, Eugene “The Behavior of Stock Market Prices”. Journal of Business, 1965, vol. 38, 1.

Fama, Eugene “Efficient Capital Markets: A Review of Theory and Empirical Work”. Journal of Finance, 1970, vol. 25, 2.

Lo, Andrew W. “The adaptive Market Hypothesis: Market Efficiency From an Evolutionary Perspective,” Journal of Portfolio Management, 2004.

Nicholson, Francis “Price-Earnings Ratios in Relation to Investment Results.” Financial Analysts Journal. January/February 1968.

Samuelson, Paul “Proof That Properly Anticipated Prices Fluctuate Randomly”. Industrial Management Review, 1965, 6.

Shefrin, Hersh “Beyond Greed and Fear: Understanding behavioral finance and the psychology of investing.” Oxford University Press, 2002.