# THE CONCEPT OF MARKET EFFICIENCY

Capital Market Efficiency, based on its broadest and most commonly used definition, refers to an environment where all information available on any given asset is incorporated into the price of that asset. It is, thus, impossible for any market participant to make supernormal profits from trading that asset in a sufficiently competitive market.

French mathematician Louis Bachelier (1900) was the first to introduce the notion of capital market efficiency with his PhD dissertation 'Theorie de la Speculation'. He is believed to be the pioneer of stochastic process modeling known as Brownian Motion. Using Brownian Motion to evaluate stock options, he observed that "past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes."His observation that prices fluctuate randomly was empirically supported by Cowles (1933) and Cowles (1937) who examined American stock prices, as well as Maurice G. Kendall (1953) who examined British stock and commodity prices. These authors concluded that prices exhibit no correlation between successive changes for any given period of time.

Since Bachelier's thesis, innumerable studies have been conducted on the concept of market efficiency. Paul Samuelson's 1965 article "Proof that Properly Anticipated Prices Fluctuate Randomly" heralded the beginning of modern financial literature on market efficiency. Samuelson uses a 'random walk' model to demonstrate randomness in stock price changes. He notes "...if one could be sure that a price would rise, it would already have risen."

### THE EFFICIENT MARKET HYPOTHESIS

Along with the overwhelming research on portfolio theory, which started with Harry Markowitz (NBED), the efficient market hypothesis is one of the most widely accepted and examined theories in the realm of finance today. The term was coined by Harry Roberts (Roberts, 1967). He also distinguished between weak and strong form efficiency in markets. Using this taxonomy of information sets, markets can be classified as a) Weak form efficient:A market is deemed to be weak form efficient if all past prices and returns on an asset are incorporated into its current price b) Semi strong form efficient: A market is said to be semi strong form efficient if all publicly available information about an asset is fully reflected in its price c) Strong form efficient: A market is strong form efficient if all information about an asset, public as well as private, is incorporated into its price

As can be observed, the criteria for market efficiency gets more stringent as we proceed from definitions of weak form to strong form. Using these definitions suggested by Roberts, Fama (1970) collated a historical review of empirical evidence on market efficiency. He summarises his observations with "A market in which prices always 'fully reflect' available information is called efficient." Burton Malkiel (1992) suggested "A capital market is said to be efficient if it fully and correctly reflects all relevant information in determining security prices."

The initial assumption that the Efficient Market Hypothesis was based on is that expenses charged towards gathering information, conducting analysis as well as costs of transaction are zero. This assumption was clearly incorrect, as in reality, there are costs associated with research, information collation and brokerage. To incorporate these facts into a more relevant definition of the Efficient Market Hypothesis, Fama (1991) revised his initial definition of the Efficient Market Hypothesis and noted "... prices reflect information to the point where the marginal benefits of acting on information (the profits to be made) do not exceed marginal costs." Here, Fama worked on the principle that market efficiency is not a discrete process, but a continuous one. Market efficiency can be thought of as inversely proportional to the costs involved in transactions and information gathering. The lower these costs, the higher the degree of efficiency.Fama (1998) again revised this definition and stated that one may observe in efficient markets that "the expected value of abnormal returns is zero, but chance generates deviations from zero (anomalies) in both directions."

A digression is in order here. Although the Efficient Market Theory is a widely accepted thesis and has been the subject of intense empirical and theoretical scrutiny for almost half a century, financial analysts, econometricians, researchers as well as market participants have not converged on any form of agreement on the validity of market efficiency. Although Fama's definition of the Efficient Market Hypothesis is generally widely regarded within financial circles, even rudimentary internet searches reveal that there are a number of different, and sometimes non-overlapping definitions of the Hypothesis that are accepted by the financial community today.

### ECONOMETRIC DEFINITIONS

Jensen (1978) classifies an 'information set' as ?t where t denotes a time subscript,and defines an efficient market as one where it is not possible for any market participant to earn supernormal profits at time t trading on the basis of information set ?t.. Fama (1970) prescribed that investors generate future expectations for stock prices in the following manner

In (2), E denotes the statistical expectation, pj,t+1 denotes price of security j at time t+1, rj,t+1 represents the returns on prices of security j at time t+1. Finally, both the expectations of price and returns are conditional on the elements of information set ?t., the set of all information that can be accessed by market participants at time t. This equations states that the expected price of an asset j at time t+1, based on the informationavailable on that asset at time t is a function of the price of that asset j at time t, and is proportional to the expected returns on the same asset j at time t+1. The discrepancy between the realized price and the expected price of an asset at time t+1 is equivalent to

where xj,t+1 is equal to the difference between the realized price of asset j at time t+1 and the expected price of asset j at time t+1, conditional on information set t. Thus, by definition, the following condition would hold in an efficient market

which means that the realized price always equals the expected price of an asset in an efficient market.

### EFFICIENT MARKETS AND TIME SERIES MODELLING

A lot of time series modeling in finance is based on the random walk model and the martingale and fair game properties of financial time series.

### THE RANDOM WALK MODEL

The concept of random walk can best be illustrated with an allegory, due to Pearson (1905). He gives an example of an individual, who in a state of inebriation, walks in a random and non-determinable pattern. Pearson suggests that the probability that the individual will end up at the same place he began is equal to the probability that he will end up at any other point on his random path. The most illustrative representation of the random walk model is:

### Pt = Pt-1 + et ,et ~ N (0,s2)t=1, 2.....,T

where Ptis the price of any asset at time t and et is a white noise error term that is independently and identically distributed with zero mean and variance s2. . This equation states that the price of any asset at time t is equal to the price of the asset at time t-1 plus a white noise disturbance term. As is evident from the equation, prices following a random walk model do not have an autoregressive co-efficient.

### MARTINGALES

Consider a random variable, Xt , and an information set ?t at time t. Xt is said to be a martingale if the following condition holds E(Xt+1 l ?t ) = Xt This equation states that our most effective forecast of the value of a variable at time t + 1, given all available information contained within the information set at time t, is exactly the current value of the variable. Applying this interpretation to prices of stocks, it can be stated that our best estimate of stock prices at any given interval in the future is simply the current price of the stock.

### FAIR GAME

A fair game model differs from a random walk model, in a way that, unlike random walk models, returns in a fair game model are not necessarily independent or identically distributed over time. A 'fair game' implies that the stock price at any given time t incorporates all the expectations of investors or speculators given all available information about that stock. Thus, one cannot expect prices to change unless investors' expectations about the future change. Given that investors' expectations are unbiased and rational, changes in stock price are thus random.

Consider a random variable Zt . Ztis said to be a fair game if E(Zt+1 l ?t ) = 0 Let us assume variable Xt is a martingale. Given that such is the case, we can label Zt = Xt - Xt-1 as a martingale difference. This equation states that, given information at time t, our best estimate of the value of a martingale difference at time t+1 is zero. If we consider Xt+1 as the price of a stock at time t+1, then Zt is the change in stock price between time t and time t+1. Thus, a fair game implies that our best guess of the change in price of that stock between any two consecutive intervals is zero.

### EXAMINING MARKET EFFICIENCY

Given that efficiency of markets corresponds to the fair game property of determining asset prices, tests of market efficiency then depend implicitly on the information set used as well as the nature of efficiency being tested. Following Robert (1967) and Fama (1970), markets can be a) Weak form efficient b) semi strong form efficient c) Strong form efficient.

The information set for testing weak form efficiency includes the past history of stock prices, and may also include the magnitude to which trading of that stock occurs. Tests of weak form market efficiency are referred to as 'tests of return predictability'.

Information sets for testing semi strong form market efficiency includes all publicly available information available about that stock at any given time t. The information set used to examine weak form efficiency is a subset of this information set, and incorporates, in addition to past history of the stock, factors such as company announcements, data contained in financial reports, economic fundamentals and forecasts. Taking into account these factors, tests of semi strong form efficiency involve an added degree of fundamental analysis.The most basic form of testing semi strong form efficiency is conducted in the form of an event study, where asset price predictability (or lack of) is examined on the basis of asset price behavior both before and after any information regarding the asset ( in most cases, companies whose stock is under examination ) is announced publicly.

The most stringent form of examining market efficiency is testing for strong form efficiency. In this case, the information sets used to test weak form and semi strong form efficiency are a subset of the information set used to test strong form efficiency. In addition, this information set will contain all privately held information on an asset at any given point of time t. Tests for strong form efficiency are mainly theoretical and serve as a limiting point to testing efficiency. It is illegal and punishable by law, in all regulated exchanges to trade stocks based on any private information or 'tips'.

The Efficient Market Hypothesis holds true whenever prices or returns can be modeled using the random walk theory. However, the converse may not necessarily be true. The random walk model produces independent identically distributed returns, only considering an information set of past prices or returns on a financial asset. Thus, any evidence of prices following a random walk address only a case of weak form market efficiency.

### TESTS OF WEAK FORM EFFICIENCY

Tests of weak form market efficiency use historical realizations of prices and returns to examine the existence of any patterns for those realizations. The presence of patterns in historical prices or returns may then be leveraged to forecast future movements, thus creating opportunities to generate riskless profits. Literature on empirical tests of weak form efficiency is substantial, and it is beyond the scope of this dissertation to list all the studies and results conducted and observed within this realm. Thus, I have presented below, an overview of only the more relevant and important observations from tests of weak form market efficiency.

### Using historical realizations to predict future returns

Tests of asset price / return predictability incorporate tests that verify whether there exists any relationship between the present value of any asset price or returns and the realized values of the same asset over a period of time in the past. Such tests are normally conducted over a short term sample. Relationships are examined using a battery of statistical tests such as correlation tests, which examines the correlation co - efficient between present values and past values. A runs test examines the existence of patterns in the sign of price changes. More sophisticated tests are conducted in the form of filter tests. Filter tests are implemented on the basis of 'rules' that establish patterns of trading ( buying and selling ) over pre defined price limits.

On the basis of correlation and runs tests, Fama ( 1965 ) observed that there does exist a positive relationship between present and past returns. However, the existence of brokerage i.e. transaction costs eliminate any opportunities for profitable arbitrage using such strategies.

### Timing

There is a vast amount of literature that examines the relationship between the returns generated by an asset and the time frame within which the same occur. Such studies have led to conclusions that there does exist a relationship between the magnitude of returns and time periods under study. The most popular of these relationships, known as the 'weekend effect', notes that the average observed returns on an asset are negative over weekends. Weekends here refer to a 48 hour time frame between close of markets on Friday and initiation of trading on Monday. (NBED : see Gibbons and Hess ( 1981 ) and Kenneth French ( 1980 ) ) Harris ( 1986 ) observed that returns continue to decline through the first 45 minutes of trading on the first day of trading each week ( Monday ) after which no discernable patterns were detected.

Another well known phenomenon documenting the relationship between asset returns and timing is known as the ' January Effect '. This hypothesis postulates that asset returns are significantly higher in the month of January, as compared to any other month in the year, especially for stocks with small market capitalization. (NBED : See Fama (1991), Keim (1983) , Reinganum ( 1983 )) . Further to this, Gultekin ( 1983 ) studied the 'January Effect' in the United States of America as well as sixteen other countries. He finds that the January Effect is strongly prevalent in markets other than the United States of America.

No concrete conclusions can be drawn from the myriad tests used to examine the relationship between asset prices and market timing. It is possible that no such patterns actually exist but are a result of data snooping. Data snooping refers to a situation where positively correlated data is used repeatedly to refine the results of such studies. Existence of such phenomena also question the validity of the Efficient Market Hypothesis, as in an efficient market, all opportunities for arbitrage, and thus the ability to profit from 'timing' markets are driven away by competitors exploiting such arbitrage opportunities. One must also consider, as in the case of historical pattern studies, the fact that any arbitrage opportunities that may arise from day of the week or month of the year effects are not feasible for investors to exploit due to negative net profits ( or net losses ) arising on account of transaction and brokerage costs.

### Market anomalies

The most well known cases of market anomalies arise include the momentum effect, the value effect as well as the size effect. Fama and French ( 1992 ) document that stocks with high book to market value ( the ratio of accounting book value to the current market value of a stock ) realize positive abnormal returns.

Jegadeesh and Titman ( 1993 ) investigated the 'momentum effect' and find that stocks with an above average performance in the recent past tend to outperform those with a lower than average performance in the same period.

Banz ( 1981 ) examined the 'size effect' between periods 1931 - 1975. He used the Capital Asset Pricing Model ( CAPM ) to estimate expected monthly returns on stocks. He discovered that the smallest 50 stocks on the New York Stock Exchange ( NYSE ) outperform thelargest 50 stocks on the NYSE by an average of one percentage point. However, the size effect is no longer prevalent or has been drastically toned down, as pointed out by Schwert ( 2003 )

As the Capital Asset Pricing Model had been employed by Banz to estimate expected monthly returns, it can be argued that there may exist misspecifications in the calculation of ߠ( risk parameter of the CAPM ) of small stocks.Small stocks are characterized by infrequent trading, as compared to large firms. As a result of this, their may be underestimated. ( Roll, 1981 and Reinganum 1981 ). Christie and Hertzel ( 1981 ) also show that , being a parameter derived by historical values, does not successfully capture any current economic risks. Due to the fact that for small stocks are underestimated, it is clear that expected returns for small stocks will be underestimated, thus introducing a higher degree of discrepancy between their returns and the returns of large stocks. Perhaps the employment of an adequate and accurate model to estimate expected returns may demonstrate that anomalies such as the size effect do not exist, but are simply the result of inadequate statistical methods.

Other attempts to explain the existence of anomalies include the possibility that there exist no real relationships between the size of the firm and higher than normal returns, but patterns are detected none the less due to the phenomenon of data snooping, as explained in section (NBED). Most anomalies based on size and value effects fail to hold true on examination of different sample periods. For example, Schwert ( 2003 ) finds that many such anomalies disappear or are reverse once they are analysed in economic and financial literature.

### TECHNICAL ANALYSIS

Technical analysis and charting techniques are widely used by foreign exchange and equities traders to develop trading rules. These methods attempt to develop a link between observed patterns in security prices and their subsequent returns