Efficiency in capital markets can be categorized into three types: 1) allocative efficiency; 2) transactional efficiency; and 3) informational efficiency. Allocative or Pareto efficiency is used in assessing the welfare effects of equilibrium-market resource allocations. Transactional efficiency is concerned with the costs and risks of exchange of economic resources (i.e., goods and services) and financial resources and assets in the marketplace. Informational efficiency deals with the relationship between market prices and information. Efficient markets hypothesis (EMH) pertains to the third type of efficiency. Markets are informationally efficient to the extent that prices reflect information. Fama (1970, 1976) uses the terms efficient capital markets while Beaver (1981) refers to it as market efficiency. More recently, Jensen and Smith (1985) prefer efficient market theory. Finally, Merton (1985) has introduced the rational market hypothesis to refer to the relationship between market prices and information. Most of the literature on EMH is concerned with empirical tests of the hypothesis of informational efficiency. These empirical papers have often preceded the formal development of any adequate theoretical statement of information efficiency. The main purpose of this essay is to explore the relevant theory and evidence regarding informationally efficient capital markets.

In Section Two, the normative concept of perfect capital markets is introduced as a benchmark against which the behavior of prices in actual economies can be compared. Section Three discusses the use of stochastic notion of random walk to characterize the behavior of security prices. The operationalized concept of informationally efficient market is given in Section Four by Fama (1970, 1976) through the fair game model and the martingale property to provide a theoretical foundation for empirical work. Fama also extends his EMH to include a strong-form market efficiency and the impacts of private information which are discussed in Section Five. Section Six summarizes the body of empirical studies, which attempts to test how informationally efficient the actual capital markets are against four criteria: 1) security prices' responsiveness to new information; 2) security expected returns' responsiveness to time-varying interest rates and market risk premia; 3) trading strategies' performance against the benchmark returns; and 4) professional investors' performance against the benchmark returns. Finally, my concluding remarks are provided in Section Seven.

 

The Perfect Capital Markets Back to Top

Dyckman and Morse (1986) provide a typical definition to efficient markets: "A securities market is generally defined as informationally efficient if 1) the prices of the securities traded in the market act as though they fully reflect all currently available information and 2) these prices react instantaneously, and in an unbiased fashion to new information."

The difficulty arises with such a definition with regard to the precise meaning of the terms "fully reflect", "available information", and "unbiased fashion." An approach towards solving this difficulty is to relate the actual market price behavior to the way that prices would behave under the ideal conditions. It is a normative approach to model security price behavior through the establishment of necessary conditions for the existence of the perfect capital markets.

The Perfect Capital Markets Assumptions

1. Perfect competition: All economic agents behave as if they have no market power over prices.
2. Frictionless markets: There are no transaction costs or restrictions on trade. In addition, all assets are perfectly divisible.
3. Homogeneous beliefs: All economic agents have homogeneous prior belief and receive the same information function.
4. Individual rationality: All economic agents are rational expectations utility maximizers.

The Perfect Capital Markets Model

f_m(P_t+1|F_tm) = f(P_t+1|F_t)

where:

F_tm = information set actually used by the market at time t

F_t = all relevant information set available at time t

f_m(.) = true joint probability of the price vector P_t+1 implied by F_t

f(.) = joint probability of the price vector P_t+1 as assessed by the market

The Perfect Capital Markets Implications

1. There are a large number of utility-maximizing economic agents who participate in the markets independently of each other.
2. All economic agents quickly adjust prices to reflect new information sets upon their arrivals.
3. New information set arrives at the markets at random and independently of any other information sets.

The market is said to be informationally efficient if market prices are identical to those prices that would rule in perfect capital markets in which the information under consideration is received by all individuals. By using the above perfect capital markets' conditions, the analysis of the behavior of prices is relatively straightforward. In particular, by combining these conditions with the models of expected returns formation (e.g., CAPM and APT), it is possible to generate testable implications relating to the stochastic behavior of security prices in relation to new information.

The Random Walk Hypothesis Back to Top

Several statisticians had noted that security prices tend to fluctuate randomly in the manner that security returns exhibit a very low degree of serial correlation. If prices reflect all currently available information and change to their new equilibrium values immediately and only on the receipt of new information, then price changes will be uncorrelated. Bachelier (1900) uses statistical methods to analyze gambling and later applied them to analyze returns on stocks, bonds, futures, and options. He also recognizes that the Weiner process is the Brownian motion. Cootner (1964) edits a volume called The Random Character of Stock Market Prices which has become the basis of the later EMH. Osborne (1959, 1964) in his paper Brownian Motion in the Stock Market formalizes that stock price follows a random walk when he develops its assumptions using the Brownian motion which is equivalent to the movement of a particle in a fluid.

The Random Walk Assumptions

1. Stochasticity: Price moves minimally and independently, and is identically distributed.
2. Finite Variance: Volume and variance are finite and not important.
3. Price-Value Correlation: Price is related to its fundamental value.
4. Unconditional Expectations: Expected return is a time-invariant probability weighted average.
5. General Equilibrium: Price equilibrium is obtained when traders mutually agree to trade.
6. Informational Efficiency: Traders trade at equilibrium price based on available information.
7. Normality: Distribution of price changes is normal with stable mean and finite variance.

The Random Walk Model

 f(r_j,t+1|F_t) = f(r_j,t+1)

where:

F_t = information set containing historical price series available at time t

r_j,t+1 = return on security j at time t+1

 

The Random Walk Implications

1. The information set of price series is important but the sequence on or the pattern of that information is not important for determining the security returns.
2. The price series and patterns will be detected and eliminated by all traders until it becomes impossible to predict the future course of the series by analyzing its past behavior.
3. The current security prices already reflect all past price series and are themselves the fully revealing market information set or sufficient statistic which can be observed by all traders, both informed and uninformed.

The weak-form EMH suggests that all relevant information contained in the past price series has already been reflected in the current price. Technical analysts believe that price movements follow some sort of repetitive and predictable pattern. The weak form EMH considers this analysis a waste of time; if there were such patterns, they would have been detected long ago, and current prices would reflect these patterns already.

Many empirical studies have shown that even though past price series exhibit some cyclical patterns, they occur by chance and are not predictable. One of the studies is to compute the performance of a "filter rule" used by technical analysts. For example, the 5% filter rule suggests that "buy a stock after it has risen 5% from a low, hold it until the price falls by 5% from its peak, then make a short sale, maintain the short position until the stock rebounds by 5% from its bottom, then take a long position."

Houthakker (1961), Alexander (1961), Fama and Blume (1966) find that this filter rule provided lower returns than a simple "buy-and-hold rule" for the same stock. They suggest that stock prices do not follow consistent cycles over time, and technical analysis cannot predict the price movements. There are exceptions or anomalies to empirical findings: the January and the weekend or Monday effects. Sharpe (1964), Lintner (1965), and Mossin (1966) realize that Osborne's random walk assumptions could not fully explain the market behavior without the assumptions on trader behavior which is rationality. The integration of both price and trader behaviors forms the basis for the EMH which was formalized by Fama.

The Fair Game Hypothesis Back to Top

Fama (1965, 1970) states that the market is a martingale, or fair game. He implicitly assumes that all individuals have the same information functions and, at least conditional on the information under consideration, they share the same beliefs. This allows him to use the terms efficient capital markets without any ambiguity. The fair game means that information cannot be used to profit in the market. It requires that traders be rational in order to achieve general price equilibrium. It does not require independence through time or accept only the independently and identically distributed (IID) observations. If returns are random, then markets are efficient. But, when markets are efficient, the returns are not necessarily random.

The Fair Game Assumptions

1. Equilibrium Expected Returns: Market equilibrium is expressed in terms of expected returns.
2. Complete Markets: All current information is used by the market to form equilibrium prices.

The Fair Game Model

E[p_j,t+1|F_t] = p_j,t(1 + E[r_j,t+1|F])

where:

F_t = information set available at time t

p_j,t+1 = uncertain price of security j at time t+1

r_j,t+1 = (p_j,t+1 - p_j,t)/p_j,t, the one-period return on security j

E[z_j,t+1|F_t] = 0

where:

z_j,t+1 = excess market returns of security j at time t+1

The Fair Game Implications

1. The excess market returns of security is zero.
2. The excess market value of security is zero.
3. The expected total market value of all securities is zero.
4. Martingale: the changes in expected price and returns are zero.
5. Submartingale: the changes in expected price and returns are non-negative.

Samuelson (1965, 1973) combines an assumption equivalent to one of perfect capital markets with the assumption that the security price at any point in time is equal to the market's expectation of all future dividends discounted at a constant rate:

P_jt = S E[x_jt+T(1+r_j) - T]

where:

P_it = equilibrium price of security j at time t

x_jt+T = uncertain dividend paid on security j at time t+T

r_j = discount rate appropriate to security j

E[.] = conditional expectation on the information available at t

The martingale property of security price states that at any point in time the equilibrium price is set such that the expected one-period security return is equal to the discount rate. That is, the expected security return conditional on the information available at time t is equal to the unconditional discount rate. Alternatively, the current price is a sufficient statistic for the next-period expected price in the sense that the latter is equal to the former compounded at a rate that is independent of the realization of the information available. Martingale also implies that past price series was not related to future prices. The current prices fully reflect all past price series so that a knowledge of that series has no value in forming expectations about future prices. The fair game model does not require IID assumption like the random walk. Price changes will be random only because of the evaluation of the random changes in fundamentals of a firm, not the random pattern of price changes.

In the semistrong-form EMH, prices reflect all publicly available information. Security analysts formulate security value base on information that is available to all investors. A large number of independence estimates results in a fair value by the aggregate market. Security analysts become the reason why markets are efficient; they form a fair price by consensus. However, fundamental analysis is not a method through which windfall profits are obtained, but a segment of the information-producing industry. Each investor must ask himself whether the additional information produced by security analysts is worth its costs (commissions and fees).

Ball and Brown (1968) test the semistrong-form EMH by studying the equation used to forecast the EPS of each of 261 firms over the period. The forecast was based on the average trend in earnings in the past plus a deviation from this trend caused by the cycle of average corporate profitability for all other stocks. This forecast was then subtracted from the actual earnings reported at the end of the year. Firms with reported earnings greater than the forecast were placed in one group, while those reporting less than forecast were placed in another group. If stock price responds rationally to public information, we would expect the stocks of firms reporting unexpectedly high earnings to show above-average returns, and vice versa. They found that most of the good or bad information contained in the earnings reports was already anticipated by the market. This section can be concluded that most of the information contained in the earnings reports had already been quite accurately estimated on the basis of fundamental data and that the market adjusts very quickly to reflect new information in the price after receiving it. Therefore, the market appears to be informationally efficient in the semi-strong form sense, so that abnormal returns cannot be made simply by security analysis net of costs.

The Strong-Form Hypothesis Back to Top

Under the strong-form EMH, investors who acquire inside information act on it and quickly force the price to reflect the information. The initial acquisition of new inside information is largely a matter of chance, and since stock prices already reflect the existing inventory of inside information, efforts to seek out inside information to beat the market are costly. The professional investors truly have zero market value because no form of search or processing of information will consistently produce superior returns.

Within this strong-form environment, it is possible to realize abnormal returns by obtaining new information and trading on it ahead of the market. In doing so is to compete in the "information producing industry" against other security analysts. This industry is highly competitive, so the excess returns on producing new information are likely to be driven down to the point where they closely approximate the costs. The inside information generated by the industry is likely to be worth its cost to large institutional investors, but its value to the small individual investors is more doubtful.

Empirical Tests of Capital Markets Efficiency Back to Top

Haugen (1986) delineates four criteria against which the actual capital markets can be empirically tested. These criteria do not distinguish among the three forms of EMH as Fama suggests, but are grouped according to the behavior of security prices and returns as well as market participants. The markets are said to be efficient if they exhibit the following characteristics:

1. Security Prices' Responsiveness to New Information: Security prices should respond quickly and accurately to the receipt of new information that is relevant to valuation. The empirical tests related to this criterion include the measurement of stock price response, the stock price response to the announcement of dividends and stock split, the stock price reaction to earnings reports, and the stock price reaction to positive and negative events.
2. Security Returns' Responsiveness to Term- and Risk-Premia: The changes in expected security returns from one period to the next should be related only to changes in the level of the risk-free interest rate and changes in the level of the market risk premium associated with the security. Returns associated with factors other than these should be unpredictable. Under this criterion, serial correlation and cross-sectional studies and conducted.
3. Trading Strategies' Ability to Discriminate Profitable Investments: It should be impossible to discriminate between profitable and unprofitable investments in the future by examining the characteristics of current investments. This implies that trading rules should fail to earn abnormal returns from buying profitable stocks and selling unprofitable stocks under the efficient market conditions. In this criterion, neither contrarian nor momentum trading strategies should outperform the traditional buy-and-hold strategy. Empirical tests of trading rules include various studies on filter rules and the contrarian strategies.
4. Professional Investors' Ability to Forecast Future Earnings: There is no significant difference between the average investment performance of the well-informed and the uninformed investors. If there were, the differences in performance between and within the two groups of investors should be due to chance. There are tests of security prices and returns predictability based upon several explanatory variables such as dividend yields, term-structure of interest rate, quarterly earnings reports, calendar effect, day-of-the-week effects, price-earnings ratios effect, price-to-book ratios effect, size effect, and trading volume effect.

Fama (1970, 1991), on the other hand, categorizes the empirical approaches to test markets efficiency differently using his proposed three forms of EMH as guidelines:

1. Tests of Returns Predictability: This group is catered to test the weak-form EMH and the random-walk model which consists of the tests of independence, tests of trading rules, tests of contrarian strategies, and the cross-sectional and time-serial tests of capital asset pricing models.
2. Event Studies: Semistrong-form EMH and the fair-game model are tested under the event studies to see how security prices and returns adjust to the arrivals of public information related to the specific firms' past earnings performance and the general economic, political, and social conditions and events.
3. Tests of Private Information: The tests in this group are applicable to the strong-form EMH whether investors' possession of private information which is not reflected in security prices can result in abnormal returns.

Tests of Returns Predictability

Currently, there have been five areas of tests conducted under this category:

Statistical Tests of Independence

Alexander (1961), Fama (1965), Fama and Fisher (1966), Neiderhoffer and Osborne (1966), and Fama and MacBeth (1973) conduct serial correlation studies of price changes over time and find that there is statistical insignificant correlation among prices changes. Their findings confirm that the weak-form EMH holds. French and Roll (1986) test variability in price changes during the trading hours and find that the first-order autocorrelations of daily stock returns are positive which go against the random walk hypothesis. The serial correlational studies on short and long horizons are done by Shillers (1984) and Summers (1986) with the conclusions that long-horizon returns are negatively autocorrelated. Lo and MacKinley (1988), Conrad and Kaul (1988), and Jegadeesh (1990) consider stock portfolios of different sizes and find that small stock portfolios have a stronger autocorrelation than large ones which also earn more than 2% in excess returns. Christie and Huang (1995) include market overreaction and fads into the study and do not find evidence against the EMH. The tests of random walk conducted by Fama (1965) and Hagerman and Richmond (1973) cannot reject the null hypothesis that the runs tests fall within the expected range for random series and that OTC stock prices change independently over time, respectively.

Tests of Trading Rules

Alexander (1961) performs a test of "one security and cash y% filter rule" and finds that it cannot beat the buy-and-hold strategy after deducting the transaction costs. Fama and Blume (1966) and Pinches (1970) test various filter and trading rules and have the same conclusion as Alexander's. However, Brush (1986) and Pruitt and White (1988) find that "three-part filter rule" or adjustments relative strength for January effect exhibits the ability to generate abnormal returns after taking transaction costs into account.

Tests of Contrarian Strategies

Under the contrarian strategies, all tests done by Dreman (1982), DeBondt and Thaler (1985, 1987), Jegadeesh and Titman (1993), and Lakonishok, Shliefer, and Vishney (1994) show that stocks of losing firms outperform stocks of winning firms. Losing stocks can be viewed as being ones which are out of favor or belong to small firms (value stocks) whose growth potentials are lower than larger firms (growth stocks).

Tests of Cross-sectional Returns Predictability

The studies in this area attempt to test both the market efficiency hypotheses and the capital asset pricing model (CAPM), or the so-called "joint hypothesis". Four groups of cross-sectional tests are conducted according to the parameters used. First, Basu (1975, 1977), Peavy and Goodman (1983), and Fuller, Huberts, and Levinson (1993) use price-earnings (P/E) ratios as the parameter to predict stock price and returns movements. They find that stocks with low P/E ratios have lower risk but higher returns than those with higher P/E ratios. Second, Banz (1981), Reinganum (1981), and Basu (1983) test on both the NYSE and AMEX stocks using the size parameter (i.e, the market capitalization of stocks) and find evidence against the semistrong-form EMH. Third, the joint hypothesis is tested by Roll (1981), Reinganum (1982), Stoll and Whaley (1983), Reinganum (1983), Brown, Kleidon, and Marsh (1983), Chan, Chen, and Hsich (1985), and Reinganum (1992) using the market capitalization as parameter. All of their results turn out to be inconsistent with what EMH and CAPM predict them to be. Fourth, Rosenberg, Reid, and Lanstein (1985), Chan, Hamao, and Lakonishok (1991), and Fama and French (1992) use both market capitalization value and book equity value as test parameters and find significant predictability of future stock returns. Finally, the tests using trading volume as parameter are studies by Arbel and Strebel (1983), James and Edmister (1983), Campbell, Grossmand, and Wang (1993), Blume, Easley and O'Hara (1994), and Conrad, Hameed, and Niden (1994) show that high-trading-volume stocks experience price reversals while low-trading-volume stocks are positively autocorrelated.

Tests of Time-serial Returns Predictability

There are four groups of time-series study using dividend yields, term structure, earnings reports, and calendar effects (January, weekend, Monday, and intraday) as testing parameters. Predictability of price movements due to dividend yields is tested by Rozeff and Shiller (1984), Fama and French (1988), Balver, Cosimano, and McDonald (1990), and Fuller and King (1990), of which two studies confirm that this parameter cannot be used to forecast future returns. Using the term structure of interest rate as forecaster, Keim and Stambaugeh (1986) and Campbell (1987) find that stock and bond returns are predictable from a common set of stock market and term-structure variables. Latane, Joy, and Jones (1970), Joy, Litzenberger, and McEnally (1977), Ball (1978), Watts (1978), Joy and Jones (1979), Rendleman, Jones, and Latane (1982), and Foster, Olsen, and Shevlin (1984) test the predictive power of the use of quarterly earnings reports and unexpected changes from the previous quarters. They find that good earnings reports are not quickly reflected in stock prices and there is a positive relationship between the unexpected earnings announcement and the post-announcement stock price changes. The January effect studies are conducted by Branch (1977), Dyl (1977), Roll (1983), Keim (1983), and Reinganum (1983) who find evidence against EMH that tax selling and size are related to the January effect. Chang and Pinegar (1986, 1988), Keim (1985,1986), Lakonishok and Smidt (1984, 1986), and Giffiths and White (1993) test the January effect by incorporating long-term government and corporate bonds with stocks and find a nonlinear relationship between tax selling, dividend yields, trading volume, and behavior of fund and money managers and the January effect. The weekend effect, to a lesser extent, is studied by French (1980), Gibbon and Hess (1981), and Keim and Stambaugh (1984) who conclude that market opening's stock returns on Monday are significantly negative following the weekend market closure. Rogalski (1984) tests the Monday effect and find that the negative returns after adjusting for the weekend effect and Monday's trading turn out to be positive. And finally, Smirlok and Stacks (1986) and Harris (1986) observe the intraday stock price movements and find a shift in the weekend and Monday effects before and after 1974 and that large stocks tend to have the weekend effect while small stocks experience the Monday effect.

Event Studies 

Four areas of event studies have been examined including the initial public offerings (IPOs), the stock's exchange listing, the unexpected economic events, and the announcement of accounting changes.

In the IPOs area, Miller and Reilly (1987) find that the price adjustment due to IPO underpricing takes place within one day after the offering. Van Horne (1970), Goulet (1974), Ying, Lewellen, Schlarbaum, and Lease (1977), Sanger and McConnell (1986), and Howe and Kelm (1987) test the predictability of price movements due to the stock's exchange listing and find mixed results. The unexpected economic news and world events do reflect quickly into the prices as confirmed by Reilly and Drzycinski (1973), Pierce and Roley (1985), and Jain (1988). Brown and Ball (1968), Archibald (1972), Kaplan and Roll (1972), and Sunder (1975) find the announcements of accounting changes are also rapidly incorporated into stock prices of the firms making such announcements.

Tests of Private Information

The tests have been done on four groups of market participants who are assumed to have access to private information affecting stock prices: i) the corporate insiders, ii) the stock exchange specialists, iii) security analysts, and iv) professional fund and money managers.

Corporate Insider Studies

Pratt and DeVere (1960, 1966), Lorie and Niederhoffer (1968), Finnerty (1976, 1978), and Lorie and Brealey (1978) find that corporate insiders consistently outperform the markets on the long position. Kerr (1980) argues that the markets have eliminated this inefficiency. Trivoli (1980) find the by combining inside information with key financial ratios, the corporate insiders can improve their stock returns substantially. Nunn, Madden, and Bambola (1982) note that traders should distinguish buying insiders from selling insiders since their returns differ.

Stock Exchange Specialist Studies

A study conducted by the Securities & Exchange Commission (SEC) in 1963 concludes that specialists' returns are substantially abnormal. Niderhoffer and Osborne (1966) find that specialists' monopolistic power over information provides an edge for them to earn abnormal returns.

Security Analyst Studies

The analysts' published reports such as Value Line's stock rankings and their recommendations are tested by Black (1973), Holloway (1981), Copeland and Mayers (1982), Stickel (1985), and Peterson (1987) with mixed results. Three of the studies find that after adjusting for transaction costs, abnormal returns disappear. Lloyd, Davies, and Lanes (1978) and Lin, Smith, and Syed (1990) find that analysts' opinions such as those mentioned in the Wall Street Journal have a significant impact on stock price movements.

Professional Fund and Money Manager Studies

Earlier tests done by Treynor (1965), Sharpe (1966), and Jensen (1968) find that most mutual funds managers do not improve their performance by straying from with the buy-and-hold strategy. Ippolito (1989) concludes that funds during 1965 to 1984 outperform the markets after adjusting for research and transaction costs. Munnell (1983), Brinson, Hood, and Beebower (1986), and Ippolito (1987) find that pension fund managers are not able match their funds performance with that of the markets. More recently, Coggin, Fabozzi, and Rahman (1993) find that the best equity pension fund managers can earn substantial risk-adjusted returns.

Conclusions Back to Top

My conclusions for the area of informationally efficient capital markets are the following. There is little evidence that stock prices exhibit consistent patterns that could be used to predict their future movements. However, stock prices tend to follow a long-run upward drift (or deterministic trends) with random fluctuations (stochasticity) around these trends. This does not imply that stock prices fluctuate in an irrational manner since they tend to respond to new information quite rapidly. Since good or bad new information sets arrive randomly over time, there should not be any time-serial patterns in the price movements.

Therefore, new information sets that are not yet reflected in stock prices have tremendous value for those acquirers to be able to realize abnormal returns. This is supported by the evidence of semistrong-form EMH which shows that capital markets are not informationally efficient in terms of returns predictability. Yet, acquisition of relevant and valuable information is costly and highly competitive. The abnormal returns generated from such information may not worth the cost and time of individual investors, but may be worthwhile of large institutional investors who are able to reduce their cost of information through voluminous trading transactions.

With the evidence of serially-uncorrelated trend in stock prices and statistically significant predictability of stock returns, I believe that capital markets are not informationally efficient in the long run. On the other hand, I am certain that, for shorter horizons and given a high competition for information, efficiency in capital markets still remains high and that professional traders who employ certain trading rules should not consistently outperform the markets.