On the Efficient Market Hypothesis

 In this post, we examine the historical developments of the efficient market hypothesis (EMH). We also discuss questions surrounding the EMH.

Historical Development

Random Walk

In mathematics, the random walk concept describes a path that consists of a succession of random steps. The process is completely memoryless, meaning each step the walker takes is independent of their previous steps.

Early Development

In 1900, a French mathematician, Louis Bachelier, published his doctoral thesis, “The Theory of Speculation”. It was a pioneering work in the development of financial mathematics. The work introduced a model in which the changes in stock prices could be viewed as a random walk. In other words, future price movements are unpredictable based on past trends.

What insights did Bachelier have in order to come up with a model of stock prices based on a random walk? In his time, financial markets were certainly nowhere as developed today in terms of size as well as sophisticated market participants, so the insights should be generic and independent of the characteristics of modern financial markets. 

Market Insights

Suppose an intelligent agent (humans or computers) discovers a predictable pattern in a financial market. In the simplest scenario, that predictable pattern could be a combination of market signals (past prices, news, events, economics data,...) that points to an upward (downward) movement in asset prices with a higher than chance probability. The intelligent agent who discovered the pattern should simply react by buying the asset in order to benefit from a raise in prices. However, in doing so, the intelligent agent is not including their own expectation of what their reaction will do to the asset price. By buying the asset, the agent causes the asset price to incrementally rise (Veisdal, 2021). 

In a 1935 paper, the economist Oskar Morgenstern drew a conclusion that economic prediction is essentially impossible. He posed the issue using the following plot from Sherlock Holmes’ characters.

Sherlock Holmes, pursued by his opponent, Moriarty, leaves London for Dover. The train stops at a station on the way, and he alights there rather than traveling on to Dover. He has seen Moriarty at the railway station, recognizes that he is very clever and expects that Moriarty will take a faster special train in order to catch him in Dover. Holmes' anticipation turns out to be correct. 

But what if Moriarty had been still more clever, had estimated Holmes' mental abilities better and had foreseen his actions accordingly? Then, obviously, he would have traveled to the intermediate station. Holmes, again, would have had to calculate that, and he himself would have decided to go on to Dover. Whereupon, Moriarty would again have "reacted" differently. 

Because of so much thinking they might not have been able to act at all or the intellectually weaker of the two would have surrendered to the other in the Victoria Station, since the whole fight would have become unnecessary.

In other words, the belief is that, any predictable pattern in a financial market will soon be acted on by intelligent agents, causing the pattern to vanish. That was indeed the key insight in Bachelier’s thesis (Veisdal, 2021):

If asset prices in the short term show an identifiable pattern, speculators will find this pattern and exploit it, thereby eliminating it.

Development of the EMH (1960s-1970s)

The modern form of the EMH was largely developed by Eugene Fama (2013 Nobel Laureate). His influential 1965 paper, “The Behavior of Stock Market Prices", posited that stock prices fully reflect all available information. In other words, stocks always trade at their fair value. In a subsequent work, the 1970 paper "Efficient Capital Markets: A Review of Theory and Empirical Work.”, he described three forms of the EMH (weak, semi-strong and strong).  

The Behavior of Stock Market Prices

In the 1965 paper, Fama started with the following question, which had been a source of continuing controversy in academic and business circles: “To what extent can the past history of a common stock’s price be used to make meaningful predictions concerning the future price of the stock?” (Fama 1965, 34). Technical analysts (“chart readers” as called in the paper) believe the answer is yes. In his paper, Fama presented the empirical data and stated that the data shows a strong support for the model that price changes following a random walk. In other words, price changes have no memory of the past, and the past cannot be used to predict the future in any meaningful way. As Fama put it, “this implies, of course, that chart reading, though perhaps an interesting pastime, is of no real value to the stock market investor” (Fama 1965, 34). Fama described the model of stock prices as random walk:

• Successive price changes are independent. That is, knowledge of the sequence of price changes leading up to time period t cannot help assessing the probability distribution for the price change during time period t (Fama 1965, 35). For the stock market, Fama mentioned a more practical criterion for independent price changes, from the trader’s point of view, that is the actual degree of dependence in the series of price changes is not sufficient to allow past historical data to be used to predict the future in a way which makes expected profits greater than they would be under a naive buy-and-hold model (Fama 1965, 35). 

In his work, Fama pointed out the assumption that stocks have “intrinsic values'' which depend on economic and political factors that affect individual companies, and that assumption is not inconsistent with the random walk hypothesis. He mentioned that even though successive bits of new information and noise/uncertainty generating process may not be independent, offsetting market forces will produce independence in price changes for individual common stocks (Fama 1965, 37). Fama stated an assumption that there are many sophisticated traders in the market, which can be classified in two forms: superior value-analysts and superior technical-analysts. He further explained how the actions of these superior analysts tend to cancel statistical dependency and cause price changes to be independent. He did raise the questions (1) how many superior analysts are necessary to ensure independence? (2) Who are the “superior” analysts? (3) What is a rational investment policy for an average investor if the stock market follows the random walk model? (Fama 1965, 40). Fama pointed out that for 1) it is impossible to give a firm answer but perhaps a single specialist in each security is sufficient, for 2) “superior” analysts should consistently outperform the market, and for 3) the average investor just needs to concern with portfolio analysis rather than security analysis because under the random walk model, actual prices at any point in time are good estimates of intrinsic values.

• Distribution of price changes

As Fama stated that successive price changes are independent, they should conform to some probability distribution. Fama mentioned the earlier work of Bachelier that proposed price changes following the normal distribution, and later empirical tests did not support this hypothesis (Fama 1965, 42). Empirical data showed that price changes often have “fat tails”, or leptokurtosis; in other words, frequent large jumps occur much more often than in a normal distribution. In contrast to earlier approaches that treated these large price changes as outliers and excluded them from statistical tests, Fama cited works by Mandelbrot who pointed out that there are classes of probability distributions that can generate fat tails. These are called stable Paretian distributions (Fama 1965, 43). The normal distribution is a special case of the stable Paretian distribution where the variance is finite. As Fama pointed out, stable Paretian distributions have a mathematical property that makes them the only possible limiting distributions for sums of independent and identically distributed random variables. That property can be used to explain why price changes follow these distributions: if price changes between consecutive transactions are independent, identically distributed, then daily, weekly, monthly price changes will follow stable Paretian distributions, since they are just the sum of these random variables (Fama 1965, 44). In the rest of his 1965 paper, Fama described his dataset which consists of daily prices for 30 stocks in the Dow-Jones from 1956 to 1962. Statistical tests were performed and Fama concluded that there is strong statistical evidence that price changes follow a random walk (Fama 1965, 98). 

Introduction of the EMH

The 3 modern forms of EMH: weak-form, semi-strong, and strong form were introduced in Fama’s 1970 paper: "Efficient Capital Markets: A Review of Theory and Empirical Work.”. 

At the start of his discussion on market efficiency, Fama mentioned the “fair game” models. A fair game is a game in which each player has an equal chance of winning and the expected value of the game is 0. Applied to the context of financial markets, a fair game model implies that the expected excess return on a security (beyond what is predicted by its risk level), given all available information, is 0. Stated in this way, the definition of “efficient market” is even more general than the “random walk” model that Fama discussed in his 1965 paper: the “fair game” model just says that the mean of the distribution of price change is independent of the available information, whereas the “random walk” model says that the entire distribution is independent of the available information (Fama 1970, 387). In other words, the “fair game” model says little about the details of the stochastic process that generates returns (Fama 1970, 387).

Fama pointed out a simplified version of the market in which the EMH should hold: (i) no transaction costs, (ii) all available information is free, (iii) all implications of current information and future forecast are agreed on. He then stated that even without these properties, as in real-world markets: transaction costs, costs of gathering information , disagreement among investors are not necessary sources of market inefficiency (Fama 1970, 388). 

Fama stated the three forms of EMH, in terms of the subset of available of information that is fully reflected in current market prices:

• Weak form: the information subset is just past price/volume histories.

• Semi-strong form: the information subset includes all publicly available information: announcements of stock splits, quarterly earnings… The semi-strong form also concerns the speed of price adjustment to newly available information.

• Strong form: the information subset includes all information, including private information (even insider information).

Challenges to the EMH (1980s-1990s)

Despite widespread acceptance, the EMH started to face significant challenges during this period. Behavioral economists, most notably, Robert Shiller, argued that prices can deviate far from fundamental values due to investors’ psychological factors. 

Robert Shiller’s 1981 paper titled “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?” uses a simple present value model of stock prices, which equates the price of a stock with the present value of expected future dividends. If markets are efficient, the stock prices should change only when there is new information that changes the expected future stream of dividends. Shiller presented empirical data and concluded that measures of historical stock price volatility appear to be far too high - 5 to 13 times too high - to be attributed to new information about future real dividends (Shiller 1981, 434).

Other Factors

The Joint Hypothesis Problem

One argument that is often used to refute claims that the EMH is false is the Joint Hypothesis Problem. The problem is discussed in Fama’s 1970 paper. The joint hypothesis problem says that testing for market efficiency is difficult or even impossible. Any attempts to test for market efficiency must involve asset pricing models, and so abnormal market returns may reflect market inefficiency, or inaccurate asset pricing models, or both. 

To put it in words from other researchers:

An efficient market will always “fully reflect” available information, but in order to determine how the market should “fully reflect” this information, we need to determine investors’ risk preferences. Therefore, any test of the EMH is a test of both market efficiency and investors’ risk preferences. For this reason, the EMH, by itself, is not a well-defined and empirically refutable hypothesis.
Sewell (2006)

"The notion of market efficiency is not a well-posed and empirically refutable hypothesis. To make it operational, one must specify additional structure, e.g., investors’ preferences, information structure, etc. But then a test of market efficiency becomes a test of several auxiliary hypotheses as well, and a rejection of such a joint hypothesis tells us little about which aspect of the joint hypothesis is inconsistent with the data."

Lo (2000) in Cootner (1964), page x

Market Bubbles and Crashes

The existence of market bubbles and crashes is often used to challenge the EMH: during bubbles and crashes, prices often rise far above or below fundamental values, suggesting overreactions and subsequent reactions to information.

Proponents of EMH would argue that “bubbles” and “crashes” are poorly defined terms. If bubbles are meant to imply that asset prices have become detached from their fundamental values, this raises the question of how fundamental values are measured. From EMH viewpoint, market prices reflect all available information and are the best estimate of fundamental values at any given time.

Grossman-Stiglitz paradox

If EMH is true, a simple paradox is posed: the EMH requires sophisticated traders in order to make a market efficient. But if the market is efficient, why would sophisticated traders bother to enter the market?

The paradox is discussed in the 1980 paper, "On the Impossibility of Informationally Efficient Markets" by economists Sanford J. Grossman and Joseph E. Stiglitz. One resolution to this paradox is that markets can’t be perfectly efficient, but can only be “efficient enough”. Markets are kept efficient by the efforts of sophisticated traders who are trying to profit from information, but these traders can’t earn unlimited profits, because their trading activities ensure that the information gets reflected in prices quickly.

Adaptive market hypothesis

The adaptive market hypothesis (AMH) is a financial theory proposed by economist Andrew Lo in 2004. The AMH borrows concepts from evolutionary biology. The main idea is trading behavior is driven by heuristics which are not always optimal but are usually effective. Traders adapt their trading strategies over time as they gain experience and learn from mistakes. Competition between traders should drive adaptation and learning. AMH suggests that the level of market efficiency can vary over time and is influenced by environmental factors such as the number of market participants, the availability of information, market volatility, and the level of competition among participants. Markets might be closer to efficient during stable periods, but less efficient during times of high uncertainty and volatility.

Looking from another angle, the AMH reconciles opposite claims from the EMH proponents and behavioral finance. In the AMH world, market participants are mostly rational and can quickly become irrational during periods of heightened market volatility. He postulates that investor behaviors—such as loss aversion, overconfidence, and overreaction—are consistent with evolutionary models of human behavior (Rasure, n.d.).

Emerging Markets

There are many reasons to believe that market efficiency is greater in large and developed markets than in emerging markets. One study attempts to rank efficiency for emerging markets, and found some evidence that the emerging markets are less efficient than the US and Japan (Cajueiro and Tabak, n.d.).

Cryptocurrency Market

A 2019 survey looked at the prior research testing the efficiency of the cryptocurrency market and concluded that weak-form EMH did not hold well in the cryptocurrency market (Kyriazis, n.d.). That means sophisticated traders can likely identify predictable price patterns and profit from them. The survey also found that the cryptocurrency market tends to become more efficient as it becomes larger and more sophisticated traders enter the market.

Conclusion

The EMH continues to be a foundational theory in finance. It is not typically viewed as being universally true or false in all of its 3 forms. Instead, it can be considered as a useful benchmark or starting point. Views on the EMH vary among academics and practitioners. Among investment practitioners, proponents of passive investment strategies largely agree with EMH. Other active hedge funds are built on the premise of exploiting inefficiencies in markets. With advancements in technology and AI, sophisticated algorithms likely will bring markets closer to efficiency. 

References

Cajueiro, Daniel O., and Benjamin M. Tabak. n.d. “Ranking efficiency for emerging markets.”

Fama, Eugene F. 1965. “The behavior of stock-market prices.” Journal of Business 38 (1): 34-105. http://www.e-m-h.org/Fama65.pdf.

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

Kyriazis, Nikolaos A. n.d. “A Survey on Efficiency and Profitable Trading Opportunities in Cryptocurrency Markets.” MDPI. Accessed July 26, 2023. https://www.mdpi.com/1911-8074/12/2/67.

Rasure, Erika. n.d. “Adaptive Market Hypothesis (AMH): Overview, Examples, Criticisms.” Investopedia. Accessed July 26, 2023. https://www.investopedia.com/terms/a/adaptive-market-hypothesis.asp.

Shiller, Robert J. 1981. “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?”

VEISDAL, JØRGEN. 2021. “Louis Bachelier's Theory of Speculation (1900).” Privatdozent. https://www.privatdozent.co/p/louis-bacheliers-theory-of-speculation.