The Efficient Market Hypothesis, Random Walk Theory, Capital Asset Pricing Model

The Efficient Market Hypothesis, Random Walk Theory, Capital Asset Pricing Model

An issue that is the subject of intense debate among academics and financial professionals is the Efficient Market Hypothesis (EMH). The Efficient Market Hypothesis states that at any given time, security prices fully reflect all available information. The implications of the efficient market hypothesis are truly profound. Most individuals that buy and sell securities (stocks in particular), do so under the assumption that the securities they are buying are worth more than the price that they are paying, while securities that they are selling are worth less than the selling price. But if markets are efficient and current prices fully reflect all information, then buying and selling securities in an attempt to outperform the market will effectively be a game of chance rather than skill.

The Efficient Market Hypothesis evolved in the 1960s from the Ph.D. dissertation of Eugene Fama who persuasively made the argument that in an active market that includes many well-informed and intelligent investors, securities will be appropriately priced and reflect all available information. If a market is efficient, no information or analysis can be expected to result in out performance of an appropriate benchmark. 1

“An ‘efficient’ market is defined as a market where there are large numbers of rational, profit-maximizers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants. In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future. In other words, in an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value.”

Eugene F. Fama, “Random Walks in Stock Market Prices

The random walk theory asserts that price movements will not follow any patterns or trends and that past price movements cannot be used to predict future price movements. Much of the theory on these subjects can be traced to French mathematician Louis Bachelier whose Ph.D. dissertation titled “The Theory of Speculation” (1900) included some remarkably insights and commentary. Bachelier came to the conclusion that “The mathematical expectation of the speculator is zero” and he described this condition as a “fair game.” Unfortunately, his insights were so far ahead of the times that they went largely unnoticed for over 50 years until his paper was rediscovered and eventually translated into English and published in 1964

There are three forms of the efficient market hypothesis

The “Weak” form asserts that all past market prices and data are fully reflected in securities prices. In other words, technical analysis is of no use.

The “Semistrong” form asserts that all publicly available information is fully reflected in securities prices. In other words, fundamental analysis is of no use.

The “Strong” form asserts that all information is fully reflected in securities prices. In other words, even insider information is of no use.

Securities markets are flooded with thousands of intelligent, well-paid, and well-educated investors seeking under and over-valued securities to buy and sell. The more participants and the faster the dissemination of information, the more efficient a market should be.

The debate about efficient markets has resulted in hundreds and thousands of empirical studies attempting to determine whether specific markets are in fact “efficient” and if so to what degree. Many novice investors are surprised to learn that a tremendous amount of evidence supports the efficient market hypothesis. Early tests of the EMH focused on technical analysis and it is chartists whose very existence seems most challenged by the EMH. And in fact, the vast majority of studies of technical theories have found the strategies to be completely useless in predicting securities prices. However, researchers have documented some technical anomalies that may offer some hope for technicians, although transactions costs may reduce or eliminate any advantage.

Researchers have also uncovered numerous other stock market anomalies that seem to contradict the efficient market hypothesis. The search for anomalies is effectively the search for systems or patterns that can be used to outperform passive and/or buy-and-hold strategies. Theoretically though, once an anomaly is discovered, investors attempting to profit by exploiting the inefficiency should result its disappearance. In fact, numerous anomalies that have been documented via back-testing have subsequently disappeared or proven to be impossible to exploit because of transactions costs.

The paradox of efficient markets is that if every investor believed a market was efficient, then the market would not be efficient because no one would analyze securities. In effect, efficient markets depend on market participants who believe the market is inefficient and trade securities in an attempt to outperform the market.

In reality, markets are neither perfectly efficient nor completely inefficient. All markets are efficient to a certain extent, some more so than others. Rather than being an issue of black or white, market efficiency is more a matter of shades of gray. In markets with substantial impairments of efficiency, more knowledgeable investors can strive to outperform less knowledgeable ones. Government bond markets for instance, are considered to be extremely efficient. Most researchers consider large capitalization stocks to also be very efficient, while small capitalization stocks and international stocks are considered by some to be less efficient. Real estate and venture capital, which don’t have fluid and continuous markets, are considered to be less efficient because different participants may have varying amounts and quality of information.

The efficient market debate plays an important role in the decision between active and passive investing. Active managers argue that less efficient markets provide the opportunity for outperformance by skillful managers. However, its important to realize that a majority of active managers in a given market will underperform the appropriate benchmark in the long run whether markets are or are not efficient. This is because active management is a zero-sum game in which the only way a participant can profit is for another less fortunate active participant to lose. However, when costs are added, even marginally successful active managers may underperform. (See “The Arithmetic of Active Management” from Nobel laureate William Sharpe for more on this subject.)

“I believe a third view of market efficiency, which holds that the securities market will not always be either quick or accurate in processing new information. On the other hand, it is not easy to transform the resulting opportunities to trade profitably against the market consensus into superior portfolio performance. Unless the active investor understands what really goes on in the trading game, he can easily convert even superior research information into the kind of performance that will drive his clients to the poorhouse . . . why aren’t more active investors consistently successful? The answer lies in the cost of trading.”

Jack Treynor, “What Does It Take to Win the Trading Game?” Financial Analysts Journal, January/February 1981

If markets are efficient, the serious question for investment professionals is what role can they play (and be compensated for). Those that accept the EMH generally reason that the primary role of a portfolio manager consists of analyzing and investing appropriately based on an investor’s tax considerations and risk profile. Optimal portfolios will vary according to factors such as age, tax bracket, risk aversion, and employment. The role of the portfolio manager in an efficient market is to tailor a portfolio to those needs, rather than to beat the market.

While proponents of the EMH don’t believe its possible to beat the market, some believe that stocks can be divided into categories based on risk factors (and corresponding higher or lower expected returns). For instance, some believe that small stocks are riskier and therefore are expected to have higher returns. Similarly some believe “value” stocks are riskier than “growth” stocks and therefore have higher expected returns.2 See also Still on a random walk by Burton Malkiel in Bloomberg Personal Finance (July/August 98).

Faced with the inference that they cannot add value, many active managers argue that the markets are not efficient (otherwise their jobs can be viewed as nothing more than speculation). Similarly, the investment media is generally considered to be ambivalent toward the efficient market hypothesis because they make money supplying information to investors who believe that the information has value (beyond the time when it initially becomes public). If the information is rapidly reflected in prices, there is no reason for investors to seek (or purchase) information about securities and markets.

While many argue that outperformance by one or more participants in a market signifies an inefficient market, it’s important to recognize that successful active managers should be evaluated in the context of all participants. Its difficult in many cases to determine whether outperformance can be attributed to skill as opposed to luck. For instance, with hundreds or even thousands of active managers, its common and in fact expected (based on probability) that one or more will experience sustained and significant outperformance. However, the challenge is to identify an outperformer before the fact, rather than in hindsight. (See Coin-Flipping & Graham-and-Doddsville and A Stock Market Scam for more on these topics.)

Additionally, in many cases, strong performers in one period frequently turn around and underperform in subsequent periods. A substantial number of studies have found little or no correlation between strong performers from one period to the next. The lack of consistent performance persistence among active managers is further evidence in support of the EMH. (See Do Past Winners Repeat? and Cherry-Picking).

“Market efficiency is a description of how prices in competitive markets respond to new information. The arrival of new information to a competitive market can be likened to the arrival of a lamb chop to a school of flesh-eating piranha, where investors are – plausibly enough – the piranha. The instant the lamb chop hits the water, there is turmoil as the fish devour the meat. Very soon the meat is gone, leaving only the worthless bone behind, and the water returns to normal. Similarly, when new information reaches a competitive market there is much turmoil as investors buy and sell securities in response to the news, causing prices to change. Once prices adjust, all that is left of the information is the worthless bone. No amount of gnawing on the bone will yield any more meat, and no further study of old information will yield any more valuable intelligence.”

Robert C. Higgins, Analysis for Financial Management (3rd edition 1992)

1.Appropriate benchmarks refer to comparable securities of similar characteristics. In other words, its important to compare apples to apples and oranges to oranges. For instance, small stock fund performance is best compared to an index of small stocks and growth stock fund performance is best compared to a growth stock index. See also The Vanguard Groups’s TIC-TAC-TOE: Style Analysis and Mutual Fund Performance by John C. Bogle.

2. Value stocks are generally defined as stocks with a high ratio of book value/market while growth stocks have low book value to market ratios.

Capital Asset Pricing Model

CAPM decomposes a portfolio’s risk into systematic and specific risk. Systematic risk is the risk of holding the market portfolio. As the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique to an individual asset. It represents the component of an asset’s return which is uncorrelated with general market moves.

According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification, the investor’s net exposure is just the systematic risk of the market portfolio.

Systematic risk can be measured using beta . According to CAPM, the expected return of a stock equals the risk-free rate plus the portfolio’s beta multiplied by the expected excess return of the market portfolio. Specifically, let Zs and Zm be random variables for the simple returns of the stock and the market over some specified period. Let zf be the known risk-free rate, also expressed as a simple return, and let B be the stock’s beta. Then

image1.png [1]

where E denotes an expectation .

Stated another way, the stock’s excess expected return over the risk-free rate equals its beta times the market’s expected excess return over the risk free rate.

For example, suppose a stock has a beta of 0.8. The market has an expected annual return of 0.12 (that is 12%) and the risk-free rate is .02 (2%). Then the stock has an expected one-year return of

E(Zs) = .02 +.8[.12 – .02] = 0.10 [2]

Because [ 1 ] is linear, it generalizes to portfolios. Let Zp be a portfolio’s simple return, and let image2now denote the portfolio’s beta. We obtain

image3.png [3]

Formula [ 1 ] is the essential conclusion of CAPM. It states that a stock’s (or portfolio’s) excess expected return depends on its beta. Stated another way, excess return depends upon systematic risk and not on total risk.

We call CAPM a “capital asset pricing model” because, given a beta and an expected return for an asset, investors will bid its current price up or down, adjusting that expected return so that it satisfies formula [ 1 ].

CAPM concludes that only the risk which cannot be diversified away by holding a well-diversified portfolio (e.g. the market portfolio) will affect the market price of the asset. This risk is called systematic risk, while risk that can be diversified away is called diversifiable risk (or “nonsystematic risk”).

Unfortunately, the CAPM is more difficult to implement in practice than the alternative binomial option pricing model or the Black-Scholes formula because to price an asset it requires measurement of the asset’s expected return and its beta. But, on the other hand, it also attempts to answer a more difficult question: The binomial option pricing model or the Black-Scholes formula asks what is the value of a derivative relative to the concurrent value of its underlying asset. The CAPM asks what is the value of an asset (or derivative) relative to the return of the market portfolio. Because of this, the option models are often referred to as “relative” valuation models, while the CAPM is considered an “absolute” valuation model. Accordingly, the CAPM predicts the equilibrium price of an asset. This works because the model assumes that all investors agree on the beta and expected return of any asset. In practice, this assumption is unreasonable, so the CAPM is largely of theoretical value. It is the most famous example of an equilibrium pricing model . William Sharpe won the Nobel Prize in Economics principally for his role in the development of the CAPM.

Footnote on Rational behavior

In economics, rational behavior in economics means that individuals maximize some objective function (e.g., their utility function) under the constraints they face. The concept of rational behavior has – in addition to making the analysis of individual behavior a good deal more tractable than a less structured assumption would permit – two interpretations. First, it allows to derive optimal economic behavior in a normative sense. Second, models of rational behavior can be used to explain and predict actual (i.e., observed) economic behavior.

Theory of subjective (expected) utility: The theory of subjective (expected) utility (Savage, 1954) is the central element of the neoclassical theory of rational economic behavior. As such, it is the most important example of a theory of rational behavior. Its basic assumptions are that choices are made:

· among a given, fixed set of alternatives;

· with (subjectively) known probability distributions of outcomes for each alternative; and

· in such a way as to maximize the expected value of a given utility function.

While these assumptions are convenient for many purposes, they may not fit empirically many situations of economic choice. This is the subject of the theory of bounded rationality and the research interest of behavioral economics.

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