The fact that stock market investments are important for capital markets and the stability and growth of global economy cannot be gainsaid. They foster higher economic growth rates by injecting capital required for developing innovative and competitive business models. The unprecedented growth and expansion of the stock market has opened up more investment opportunities for virtually all types of investors, attracting significant new capital into the industry. As inventors continue to inject more capital in stock markets, the role of responsibilities of portfolio managers become even greater and complex. In a market that experienced bubbles and a fair share of challenges, portfolio managers have increasingly faced more complex investment decisions to make.

The management of portfolio is essentially a balancing act between risks and rewards while taking cognizance of any form of constraints and restrictions that might be (Parker, 2000). The integration of risk management into the normal portfolio construction of a portfolio manager signifies a positive step towards improvement of equity and financial assets management. In addition, as Parker (2000) expounds, “empowering portfolio managers with the tools to manage risk should allow them to add value in the form of better managing the risk/return characteristics of their portfolio.” However, stock markets are complex, dependant on a wide range of factors, are hard to predict and under strict legal and regulatory frameworks. A complete understanding of the changes in the stock market and the roles and responsibilities of portfolio managers must go beyond the assessment of risk. It is against this background that analyses of stock market investments have attracted considerable interests from a significant number of researchers and from diverse perspectives.

Two key areas that have been exhaustively explored in the literature include market efficiencies and the rational expectations yet, despite these assumptions, it is clear that many investors agree that the market is full of inefficiencies. The consensus in the literature is that availability of information on market trends are costless to access and as such does not add value to portfolio managers. The capacity of any portfolio manager to reap abnormal profits, therefore, does not depend on public available information. Portfolio managers must demonstrate greater intelligence and insights to make use of market dynamics.

Statement of the Problem and Research Questions

Despite the abundant knowledge on assumptions of the efficient market and their influence on investment, a direct relationship between stock market efficiency and portfolio management remains largely unexplored. In fact, research on the relationship between the two key components of the stock market is inconclusive.  After a critical review of the wide dimensional aspects of the topic on stock market efficiency, this research defines the specific boundaries, research objectives, research hypotheses and research questions that were be used and explored in achieving the objectives of this study.

Research Questions

To achieve the objectives of this research, this study seeks to respond to the following questions:

  • What is the concept of stock market efficiency?
  • How does stock market efficiency influence portfolio managers to identify risk-return objectives, develop a well-diversified portfolio and meet the investor’s needs?
  • How can efficient markets help portfolio managers determine if an investment is correctly priced?


The following hypotheses shall guide the current research:

  • There are different types, types, need, and levels of stock market efficiency, which depend on the merits and demerits of new information.
  • Stock market efficiency influences portfolio management.

Objectives of the study

The research paper sought to achieve the following objectives in an exploration of the effect of stock market efficiency on portfolio management. The objectives are:

  • Establish the existence of a concept that at any given time of the efficiency of the stock market, portfolio managers positively identifies risks or return objectives given the investor’s constraints.
  • Make a review of all relevant literature on efficient market hypothesis and compile a report on its relationship or effect to portfolio management.
  • Carry out a critical and comprehensive analysis and present an analytical argument how managers make adjustments based on the information retrieved from stock market efficiency.

Proposed Theory/Theories

The modern financial theory or modern portfolio theory shall comprise of the theoretical foundation of the dissertation. Developed by the University of Chicago and Carnegie-Mellon in the 1950s, the theory has taken over a significant role in financial investment. The relevance of this theory in the current dissertation is that is not only because it places risk at the center of all its constructs, it underlines a wide range of issues in portfolio management. In addition, its interpretation is defined by the desire to apply the concepts to create and defend high returns (Fama, 1970). Despite its shortcomings, the theory has played a significant role in combining Modigliani and Miller (1958) arbitrage principles, the option pricing theory, CAPM, the Portfolio theory and the expected utility maximization.












2.0 Literature Review

2.1. Introduction

The concepts of efficient Stock market and portfolio management have drawn considerable interests among researchers and are widely discussed aspects of capital investments. The reasons behind this are not particularly hard to point out. Stock market efficiency and portfolio management are two critical determinants of economic growth of businesses. The management of the portfolio is essentially a balancing act between risk and rewards while taking cognizance of any form of constraints and restrictions that might be. Portfolio managers have a number of roles and responsibilities even in perfectly efficient markets and as such require insightful information for valuation of financial security, management of business environment risks and development of fiscal and monitoring policy.

On the other hand, the level of efficiency of stocks and their relationship with other market indicators provide important information to investors, who form the backbone of real and long-term capital in a global economy. The following therefore is a comprehensive review of both theoretical and empirical literature that attested to the fact that the concepts of efficient stock market and portfolio management have attracted considerable interests from researchers and present results from past studies on diverse perspectives of these topics. The included behavioural finance, micro-finance, efficient stock market and the efficient market hypothesis, implications of EMH, models of measuring portfolio performance, active verses passive portfolio management and the role of portfolio management in an efficient market.

Behavioural Finance

The Concept of ‘Noise’ Traders and its Relation to Behavioural Finance

People refer to “noise” traders as those whose investment moves and decisions are reliant on mere psychological factors rather than sound principles for investment management (Friedman, 1953).  As the arguments on market rationality says, efficient rational arbitrageurs will not be able to sustain irrational trading unless they first eliminate noise trading.  Moreover, because of the uncorrelated and random nature of trades of noise traders, they end up cancelling each other out thereby leaving the prices of assets unchanged.  Arguments such as those that pertains to the relationship between asset prices and noise traders are familiar due mainly to the studies done on them, fist of which dates back as far as the 1950s and the 1960s (Fama, 1965; Friedman, 1953). Such arguments are in support of the adage that market can be rational, even if the individual investors’ are not.

In response to these arguments, behavioural finance managed to demonstrate that indeed they are valid given that certain assumptions are made.  These assumptions may appear for real markets to be untrue.  Noise investors, as shown by evidences of continuous anomalies, can give serious adverse effects on the equilibrium prices even over a long period of time.  This is attributable to the reality that rational arbitrage, aside from being limited, can also create by itself inefficiency in prices given certain circumstances (Jacobsen, 1999; De Long, Waldman, Summers & Shleifer, 1990). The reasons why “noise” traders are able to affect the prices of stock are due to two rational arbitrageurs’ limitations, i.e., risk aversion and short investment horizons.  Also relevant is the two groups’ relative size.

Should the ability and size of the noise traders in the market be limited, then rational arbitrageurs may not be able to remove entirely their effects in the market (Camerer, 1992).  Also, arbitrageurs aversion to risks alone puts limitations on their ability to cancel out said noise traders.  This is despite the arbitrageurs’ infinite buy and hold horizon (Kyle & Campbell, 1987; Shiller, 1984).  In cases where noise traders overvalue or undervalue industries, markets or stocks over a long period, arbitrageurs’ short horizon becomes limited and their ability to revert asset prices back to its original value (Black, 1986). Thus, noise trading becomes basis for mean reversion’s long-term effects and has the capacity to force asset prices to be diverged from their fundamental values in a long. The claim that noise traders eventually recognizes extreme mispricing which becomes reason for price reversal to fair value over a long period is basis for mean reversion.

“Noise Investor Risk” is a factor that is felt by rational arbitrageurs when noise investors’ beliefs have turned unpredictable and extreme.  This noise investor risk can be priced, is systematic and is non-diversifiable.  Thus, unsophisticated trading could now be taken as a new source of systematic risk that creates added stock market volatility that rational arbitrageurs would normally not consider unless they are ensured of higher returns and compensation (De Long et al., 1990; Figlewski, 1979).  Because of this, arbitrageurs are again limited in their ability to give rational asset pricing.

The noise investor also affects the structure of expected return aside from altering the market’s risk structure.  Due to their willingness to bear the risks that come with holding on to assets, which are over-priced, they consequently get the opportunity to earn much higher returns than their rational counterparts do.  This is because the unorthodox actions of noise traders drive the prices up, which allows them to perform with abnormal profits (De Long et al., 1990).

 Behavioural Finance and Overreaction and Under-Reaction Hypotheses

Under-reaction and over-reaction are two of the most vital hypotheses that explain the anomalies in price equilibrium. These two are quite important in the value effect’s behavioural explanations.  It is each individual’s tendency to overreact and under-react given certain situations.  This is a deviation from optimum Bayesian rational decision making and is perceived to have come from psychological biases, i.e., representativeness heuristic and conservatism (Kaestner, 2005; Daniel, Hirshleifer, & Subrahmanyam, 1998; Tversky, Slovic, & Kahneman, 1982; Tversky & Kahneman, 1973;). The state of conservatism, which is the former psychological bias, is a condition that has investors sticking to their beliefs despite evidence to the contrary (Edwards, 1968).  The implications of this bias in the decision making of investors despite new information are that change is still low and is done under very strict conditions of rationality.  The representativeness heuristic, on the other hand, is an illusion that their order is among chaos (Vishny, Shleifer, & Barberis, 1998).

These biases and their effects were studied some time ago (Hales & Bloomfield, 2001).  The participants in the study were subjected to a series of outcomes, e.g., reversal, continuous, shifting and a combination of reversal and continuous regimes.  The subjects showed over acting behavior after they were exposed to continuous, reversal and then under reactive reversal regimes, which were followed by, added reversal regimes.  What makes such biases important is that conservative investors will only make use of new information partially or even totally disregard them in favor of their own old beliefs.

Investors under-representativeness heuristic take into consideration positive series of company performances that serves as a potential for continuously-grown representative.  They ignore the probability of instant changes given the fact that said performance is by nature possessing of random characteristics.  This can result into over valuation and over-optimism of the prospects of the company. As a result, the existing stable environments may trigger inertia and environments with high volatility will have individuals show excessive impulsiveness (Welch & Hirshleifer, 2000).

The investing public’s heterogeneity is another reason for under-reaction to new information among investors, besides, psychological conservatism. Not all gain equal access to the same wealth of information.  Instead, data is gradually diffused to the public and investors’ ability to gain current prices information has been questioned (Stein & Hong, 1998). In the stock market, investors and players’ reactions to new data are asymmetric and are related to the industry as a whole.

The said asymmetry is vital in value anomaly behavioral explanations (Thaler & De Bondt, 1985; Shleifer, Lakonishok, & Vishny, 1994; Lemmon & Griffin, 2001, Antoniou, Galariotis, & Spyrou, 2003). Given that past successful stocks become subject to negative surprises and large response, the stocks becomes volatile than those which have lost in the past, thus the rational relationship that expected return and risk have is contradicted (Titman & Jegadeesh, 1993; Sloan & Skinner, 2000; Daynes & Andrikopoulos, 2004).

Behavioral Factors in EMH and Portfolio Management

There have been concerted efforts in the past to explore profitability of investment strategies that are primarily based on returns accrued from the past, earnings announcements and stock value. The results of these studies seem to provide evidence that goes against the efficient market hypothesis. However, the relationship between momentum profits and behavioral factors has attracted attention in the recent past because of unexplained common factors and lead-lag relations.

A number of literature in this field agree to the fact that momentum profits can be explained by behavioral factors especially in regards to the nature of the markets. According to Lehmann (1990, p. 14)  “instead of performing a limited search for the maximum momentum returns over arbitrary horizons, biologically-based optimization methods can be helpful in capturing the behavioral biases underlying the observed return momentum and in identifying the return continuations and reversals patterns.” An explorative study on the performance of momentum portfolios within the framework of a generic algorithm by Lo and MacKinlay (1990) also abides in the fact that there exists a strong correlation between momentum profits and behavioral factors. The momentum strategy of as first presented by Jegadeesh and Titman (1993) successfully ranked stocks based on their J month returns.

Whereas most of the studies on momentum profits have focussed on cross-sectional dispersion in mean returns as an important overall aspect, Lo and MacKinlay (1990) and Lehmann (1990) have effectively included industry effects, exchange rates and the overall behavioural biases. The existing literature on the relationship between momentum profits and behavioural factors assert that the latter play a critical part in understanding the scope of the former. According to Barberis and Shleifer (2003, p. 13) “first, once one moves past the very smallest stocks, the profitability of momentum strategies declines sharply with firm size and second, holding size fixed, momentum strategies work better among stocks with low analyst coverage.” This demonstrates that momentum profitability can be explained in both aspects of behavioural actors and size of the firm. However, in the analysis of the available literature on this topic, Jegadeesh and Titman (1993) have presented analysis that is more detailed on the relationship between momentum profits and behavioural factors through an examination of momentum portfolios. Other authors have expounded this by examining the relationship and behaviour between the earnings momentum, price momentum and the price and earnings momentum.

On the other hand, Barberis and Shleifer (2003) assert, “the literature in behavioral finance tries to explain the momentum and contrarian effects as a result of investors’ systematic errors or psychological characteristics.” This issue is well expounded by Jegadeesh and Titman (1993) by explaining, “the short-term contrarian profits can be explained by investors’ over-reactions to firm-specific information.” A congregation among researchers is that momentum profits can be explained by behavioral factors through the analysis of the psychological characteristics of the investors and the analysis of the price and earnings relationship.

Modern Finance

The Concept of ‘Homo Economicus’ as a Crucial Assumption

As early as the 18th and 9th centuries, the role that humans play in economic activity was studied rigorously. Indirectly, the assumption of homo economics into the social sciences resulted. As Pribram pointed out, however, the first person to define this assumption explicitly was J.S. Mill (1983, p.173). The later version of this has its roots in the positivistic doctrine of economic methodologies introduced by Neumann and Morgenstern (1944).

Homo economicus, under the said doctrine, is a model of human behaviour that is deeply simplified, wherein an individual is characterized by absolute rationality, absolutes self-interest, and free access to absolute information concerning a particular situation. This assumption has been developed based on the central reasoning the nature of human behaviour is complex and unpredictable and its incapacity to be efficiently used for the accurate prediction and explanation of human behaviour itself. On the argument of empirical reasoning, mathematical applicability, and simplicity, human behaviour was oversimplified and subsequent quantified methods were developed and used in the realm of the ‘hard’ sciences.

Beginning from its emergence in the literature regarding financial economics, oversimplified human behavior embodied just one portion of the more generic empirical method of deduction that aimed to give a definition for price behavior and formulate a theory for it. This was how modern finance began.

Efficient Stock Market and the Efficient Market Hypothesis

            Analyses of the impact of efficient stock market and the efficient market hypothesis have also dominated the literature. Bachelier (1900) produced a Ph.D. thesis that changed the course of history for financial economics during the commencement of the 20th century. Until now, his thesis denotes a conception of outstanding worth in the field of financial mathematics. He introduced new concepts in the theory of stochastic methods such as that of martingales and Brownian motion soon became starting points for the merging of all finance disciplines, accounting, mathematics, and economics, which produced the foundation of the doctrine of modern finance.

Fama (1970) offers an incisive analysis of efficient market hypothesis. According Fama (1970), a market is considered efficient relative to a given set of information if there exist no abnormal return opportunities for investors that trade based on the said information set. It is, therefore, virtually impossible for an investor to earn abnormal profit consistently based on generally accessible information. During the last 40 years, investment theory was dominated by this proposition. It is depicted mathematically using Fama’s notation  where  is the representation of the difference between j (the security’s actual price) at time t+1and its anticipated price based on the given information set. If the equation above equated to the value of 0, it means that there are no underpriced or overpriced stocks existing at time t; therefore, the investors are faced with no available opportunities for beating the market. It is then regarded that the stochastic process is a fair competition (Le Roy, 1989).

The EMH theory of Fama states that current flows of information are the only factor that can determine the current price movements of assets and that the market prices are the most effective reflectors of the primary values of their principal assets. This theory indicates that a “random walk” exists. A random walk is a stochastic process with independent, equally allocated binomial random variables exist (Morgenstern & Granger, 1970; Osborne, 1959, Roberts, 1959).

Similar to all positivistic theories in economics, the EMH theory itself adheres to specific fundamental assumptions, one of which is the concept of homo economics. Adequate requirements for the EMH can be summed up into four categories. These include self-interest of the investor, the rationality of the investor and the extent to which an investor demonstrates efficient and effective cognitive behavior, the availability of information to the public, and the speed with which this information can be understood and bring about a new price equilibrium.

Among the four assumptions outlined above, the first two are regarded as the most significant as they signify the association between EMH and its positivistic theoretical origins where reality should be oversimplified to allow precise statistical calculations. In this particular case, probable investor irrationality could influence the means of perception of the information, and the process by which the prices of stocks change in order to indicate any new sets of information.

Early scholars used two primary theoretical arguments to undermine any claim that not all investors are rational. According to the first argument, as a group, irrational investors do not have the ability to influence the prices of securities, as their strategies for investment are individually not associated. The second argument asserts that the arbitrage process (Fama, 1965; Friedman, 1953) and the competition among arbitrageurs will guarantee that irrational investors will likely accrue cumulative losses and their wealth will weaken eventually, allowing the rational investors to have the open field to themselves.

The empirical testing of the EMH has proved to be challenging. As EMH supplies the conceptual framework within which the linear asset pricing models are set in, it is impossible to test a model itself critically. The term “joint-hypothesis problem” is frequently used to refer to this difficulty (Fama 1970; 1991). The conceptual linear relationship between risk and anticipated return and the empirical evidence the efficiency of the market, however, may challenge the above adequate requirements and specifically, the arguments for market rationality.

Versions of the Efficient Market Hypothesis

The three versions of efficient market hypothesis have also been the focus of most literature. According to Ball (1991),the three versions of EMH include the weak, the semi-strong and the strong forms.” The author reveals that the versions of EMH differ within the aspect of want is called “all available information.” The weak form of hypothesis advances that stock prices avail all information in the market such as practices deployed in trading platforms, short interest and trading volume, which are available market trading data.

            Farmer (1991) who expounds that weak form of EMH implies that carrying out a trend analysis does not yield any meaningful results supports the assertion. In his analysis, the researcher asserts that trends, history and past shifts in stock market prices are publicly available and as such are not valuable information. This further implies that if these data had the potential to avail information on the future stock prices and expected changes, that information would be in the hands of investors and as such would not constitute any meaningful or valuable information.  However, the signals have no real value because they are widely available and are costless to obtain.

On the other hand, the semi-strong EMH advances that “all publicly available information regard­ing the prospects of a firm must be already reflected in the stock price.” According to Fama (1998), this information includes a range of information not limited to balance sheet composition, accounting practices, patents held, earning forecasts, data on a firm’s product line and quality of management. Back to the previous position, in the event that this information would be publicly available, it would be expected that it would be reflected in a stock process.

Last, the strong-form version of EMH advances that stock process is a reflection of all information available to a firm and includes information that is confidential or available to key stakeholders in the firm. Described by Malkiel (1999) as an extreme form of EMH, a number of people who hold the view that having critical information about a firm would enable corporate managers to exploit the information and make profits before releasing it to the public. Farmer (1998) expounds that this is the underlying reason why SEC emphasizes on preventing insiders from benefiting based on their privileged position. According to Malkiel (1999), “Rule 10b-5 of the Security Exchange Act of 1934 set limits on trading by the corporate officer, directors, and substantial owners, requiring them to report trades to the SEC. These insiders, their relatives, and any associates who trade on information supplied by insiders are considering in violation of the law.”

Implications of EMH

Technical Analysis

            The application of various analyses to predict the trends in stock market has been the subject of broad-based studies on investments and risk management. This has generated the need to develop clear delineations on the implications of Efficient Market Hypothesis. According to Berk and Green (2004), technical analysis refers to the quest for the repeated occurrences and predictable changes in stock prices. Whereas there is abidance in the fact that information plays a key role in examining the future trends in stock prices, technicians believe that the information alone is not sufficient to develop an effective trading strategy.  Berk and Green (2004) expound that “this is because whatever the fundamental reason for a change in stock price, if the stock price responds slowly enough; the analyst will be able to identify a trend that can be exploited during the adjustment period.” This implies that success in technical analysis rests on sluggish response of stock prices to basin supply and demand factors (Berk & Green, 2004). This approach is in contrast to the fundamental notion of EMH.

In the words of Lynch and Musto (2003), “technical analysts are sometimes called chartists because they study records or charts of past stock prices, hoping to find patterns they can exploit to make a profit.” In addition, they employ relative strength approach to carry out a comparative analysis of stock market prices over duration with other stock prices in the same industry. A simple version of this technique involves taking a comparative analysis of stick market prices to an indicator such as S&P 500 index. In the event that a positive increase in ratio is noted over a specified duration, then it is said the stock has exhibited relative strength because it has demonstrated a better performance to the broad market changes. Such a strong relative strength may go on for a long period, enabling investors to make profits. Collins and Mack (1997) on the other injects the aspects of support and resistance levels in technical analysis. These values are driven by market psychology and as such stock process levels are less likely to fall below or rise above.

The Dow Theory

Charles Dow is known as the owner of the brain behind the development of technical analysis. Down Theory is a theoretical perspective upon which portfolio managers and investors identify long-term trends in the stock market. In applying the two indicators driving the theory: Dow Jones Transportation Average (DJTA) and Dow Jones Industrial Average (DJIA), investors gain insights into market trends and confirm or reject the validity of the signals. Dow Theory rests on the fundamental assumption that primary, secondary and tertiary forces simultaneously affect stock market prices.

Other approaches to carrying out technical analysis discussed in literatures include moving averages and volume trading (Jensen, 1968). In moving averages, investors employ the use of averages of stock process collected over several months to arrive at the true value of the stock. If the stock prices fall above the true value, it is expected to rise no further and has higher probability of falling. In addition, moving averages are derived from long run trends. According to Osborne, (1959), “if the trend has been down­ward and if the current stock price is below the moving average, then a subsequent increase in the stock price above the moving average line (a “breakthrough”) might signal a reversal of the downward trend.”

The other aspect of the technical analysis presented by Henriscksson and Robert (1981) focuses on the volume of trading. The assumption is that a price decline in cases of higher trading volumes is an indicator of falling share prices than if the volume traded are lower. This leads to the aspect of trying (trading index), which is a computation of volume and number declining or advancing.

Fundamental Analysis

The second implication of EMH expounded by Hamilton (1922) is the fundamental analysis. In contrast to technical analysis, the fundamental analysis makes use of earnings and dividend prospects of a firm as presented by available data on risk evaluation and future interest rates. According to Hamilton (1922), fundamental analysis is an attempt to generate the accurate analysis of a firm’s prospects through a discounted value of all payments a stockbroker will receive from each share of a stock.  A fundamental analyst will either recommend or disapprove the purchase of a stock if it exceeds or falls below the stock price.

            It is observed that the efficient market hypothesis still holds that fundamental analysis is still poised to fail. This is because a fundamental analyst relies on data that is publicly available to predict the future changes in stock prices.  Whereas analysts make use of these data to gain advantage over other investors and make profits, the complex nature of the market reveals that only unique insights into trends in data presented by stock prices will be rewarded.

Bubbles and Market Efficiency

The analysis of market bubbles and market efficiency have presented interesting findings (Lo, 2002; Lo, 2001). The creation of a widespread expectation that stock prices will rise and continue to rise generates interests from more and more investors who continue to buy stocks. The continued injection of capital in purchasing the stock pushes the prices to rise further. However, naturally, the run-up stalls and the bubbles end up in price crush. The assumption that security prices in bubbles represent the rational and unbiased analysis of the situation is, in fact, impossible to defend. It is based on the analyses that notable economists such as Hyman Minsky, argued that bubbles were because of natural causes. Periods if stability and rise in stock prices are characterized by extrapolation among investors, making them take more risk and purchase more. Against such a scenario, Lo (2002), explains that the risk premiums shrink; generating the further increase in stock prices and the expectations continue to rise. The investors’ confidence continues to rise, they continue to purchase. However, in the end, the risks become unbearable and the bubble crushes.

Are Markets Really Efficient?

On the background knowledge of its limitations, the efficient market hypothesis has failed arouse the enthusiasm among investors and portfolio managers. This implies that for the portfolio managers, the continued search for the undervalued stock is a waste of time. According to Fama and French (1998), the constant search for undervalued securities does not only waste efforts and money, it can lead to an imperfectly diversified portfolio. It is within this understanding that the application of EMH has been limited and scope and the extent to which security analysis can enable portfolio managers to develop portfolios that are more balanced and consequently improve investment performances continue to date. A review of the literature reveals that three key issues that explain why the debate on the degree to which security analysis can improve investment performance will probably continue forever include the magnitude issue, the selection issue, and the lucky event issue.

In an exciting analysis of these three issues, Farmer (2002), expounds that the magnitude view holds that there is “consensus on among players that stock prices are close to their fair values and that only managers of large portfolios can earn enough trading profits to make the exploitation of minor mispricing worth the effort” (p. 899). This implies that better the decisions and actions of efficient and intelligent portfolio managers play the significant role in driving the prices to their fair values. This raises the fact that the quantitative question of “how efficient is the markets?’ is more appropriate than the qualitative question, “are the markets efficient?”

On the other hand, French and Roll (1986) dissect the constructs behind the selection bias issue. In his analysis, the problem with the selection bias issue is that the outcomes presented to the public are a selection of failed attempts. In other words, only portfolio managers and investors who have failed to generate abnormal profits from their selected schemes and strategies will be willing to present such findings. This implies that techniques and arrangements that have been proven to work stay within the confines of the investors. Portfolio managers and investors cannot be trusted in generating schemes and strategies towards generating abnormal returns. Last, the lucky Event Issue is widely captured by Hirshleifer and Luo (2001) in his analysis of the survival of overconfident traders in a competitive securities market According to the researchers, based on the hypothesis that all stocks are fairly priced; any attempt at a selected stock is a gamble. The probability of winning and losing under this hypothesis is equal.

The Empirical Test of the Efficient Market Hypothesis

Against the background of these limitations, a significant amount of literature has focused on the empirical test of the efficient market hypothesis.

Weak-Form Tests: Patterns in Stock Returns

Returns over Short Horizons

According to Jegadeesh and Titman (2001), these are basically returns over short and intermediate horizons. The understanding here is that the tests are essentially on the efficacy of technical analysis. The overriding question around the tests is where there are any chances of speculators discovering past stock trends to make abnormal profits. Jegadeesh and Titman (2001) expound that a common practice is measuring the trends of stock relates to serial correlation of stock market returns. Jegadeesh and Titman (2001) define serial correlation as the tendency of stock returns to be related to past returns. Positive serial correlation (momentum type of property) positive returns follow past positive trends in returns. On the other hand, negative serial correlation (a reversal or “correction” property) implies that positive returns are followed by negative returns.

In an insightful analysis of these correlations, Lo and MacKinlay (1988) examined the weekly correlation of NYSE stocks to discover positive correlation over short horizons. In their findings, both sets of the researchers found out fairly small values of correlation coefficients of weekly returns, for the case of large stocks with reliably up-to-date price data. In their analysis, Lo and MacKinlay (1988) assert that evidence of weak price trends over short periods falls short of presenting any meaningful evidence of trading opportunities and the probability of making substantial profits.

Again, based on the limitations of the weak-form tests, there was the need to develop a complex and comprehensive form of trend analysis. Jegadeesh and Titman (2001) expound on the application of filter rule as a more sophisticated form of trend analysis than the weak-form tests. It provides the guidelines for buying and selling based on past trends of stock prices. Examples of rules that have been availed in the literature include purchasing a stock when at least two past trades have generated profits and buying a security if there is a price increase and holding on to it until the price falls by a similar margin. However, a critical analysis of the filter rules carried out by Fama and Blume (1966) found the contrary and revealed that filter rules have no grounds to help portfolio managers generate profits.

There is the consensus that broad market indexes reveal only weak serial correlations. Based on this knowledge, Fama and Blume (1966) assert, “there appears to be stronger momentum in performance across market sectors exhibiting the best and worst recent returns” (p. 229). Jegadeesh and Titman (1993) in a comprehensive analysis of intermediate-horizon stock price behavior involving the use of three to twelve-month holding periods, revealed that each momentum, whether good or bad for investment, is more likely to continue over time. In concluding remarks, Jegadeesh and Titman (1993) intone, “while the performance of individual stocks is highly unpredictable, portfolios of the best-performing stocks in the recent past appear to outperform other stocks with enough reliability to offer profit opportunities” (p, 88).

Returns over Long Horizons           

After an analysis of patterns of stock prices over short and intermediate horizons that have revealed a momentum in stock prices, an analysis of the same was extended to long horizons. Fama and French (1998) focused on an analysis of stock price behaviors over multi-year periods. In their analysis, the researchers found out that “long-term horizons have found suggestions of pronounced negative long-term serial correlation in the performance of the aggregate market” (p, 251). This has generated the fads hypothesis, which holds that relevant news has the capacity to instigate a market reaction. According to Fama and French (1998), a positive serial correlation (momentum) takes place after an overreaction over short-time horizons. However, subsequent correlation translates to poor runs in stock performances.

This implies that the runs on stock performances will fluctuate with a positive run followed by a negative run translating into negative serial correlation over long-time horizons. These changes in stock prices give the market behavior a picture of constant fluctuations around fair prices.


Besides the studies on market overreaction, a significant amount of focus has been directed towards the analysis of performances of security over long-time horizons. The studies suggest that extreme performances of securities over long-time horizons tend to reverse themselves. This implies that securities that have experienced best performances over long-time horizons are more likely to underperform whereas poor performers over long-time horizons are more likely to present above average levels of performances. Chopra, Lakonishok, and Ritter (1992) and DeBondt and Thaler (1985) in their insightful analysis of stock behaviours over long-time horizons found out poorly performing stock in a particular period are likely to experience a reverse in the trend over the subsequent period. On the other hand, the researchers observed that best performers are more likely to go through a negative reverse and perform poorly in the subsequent period.

            The reversal effect encompassed by varying conditions for best and worst performers seems to point out that relevant news have significant impact on stock process and the behaviours of actors in the market (Cootner, 1964). Upon recognition of an overreaction, performance in extreme investment is reversed. The above therefore holds that investment in recent losers and avoidance of recent winners would generate profits for an investor and would be seen as a viable path for portfolio managers (Cootner, 1964). In addition, the rewards of such a move seem to be plausible enough to be ignored and can be exploited by an investor. Combined with weak-form tests, this assumption would mean that the market might experience a short-run momentum and then go through a long-run reversal in stock behaviour within a particular segment of an entire investment market (Lo, 2002). As postulated by Cootner (1964), “one interpretation of this pattern is that short-run overreaction (which causes momentum in prices) may lead to long-run reversals (when the market recognizes its past error)” (p. 134).

Predictors of Broad Market Returns

The desire to gain insights on the prediction of market returns over easily observed variables has been attracted considerable interests from researchers. Fama and French (1998) in their attempt to predict market returns argue that the aggregate stock market tends to be higher when the dividend/price ratio, the dividend yield, is high. Campbell and Shiller (1988) made the same observation in arguing that earnings yields have the capacity to offer the prediction on market returns. On the other hand, high- and low-grade corporate bonds data retrieved from the bond market and spread between yields have the capacity to offer insights on broad market returns prediction (Keim, 1983).

An analysis of these results and assumptions is that they present a number of difficulties to predict. Keim (1983) presents the picture of these complexities in arguing that even if the data were capable of enabling investors to predict market returns, it would be a violation of EMH. In a different perspective, Keim (1983) argues that these variables are simply illuminating variations that exist in the market risk premium, which, in the analysis of Campbell and Shiller (1988), do not constitute a violation of EMH. According to Fama and French (1998), “the predictability of market returns is due to the predictability in the risk premium, not in risk-adjusted abnormal returns” (p, 257).

Semi-strong Tests: Market Anomalies

Based on the limitations of weak form tests and the consensus that fundamental analysis employs much wider and complex strategies and detailed range of information to develop portfolios than technical analysis does, there is need to develop a better test method. The tests for seeming-strong performances go beyond weak-form tests and ask whether detailed, but publicly available information that goes beyond the trading history of a stock can be exploited towards the improvement of investment performance. These are the underlying frameworks and tests for the semi-strong form of market efficiency.

However, the cross-roads is that information that is publicly available such as a ratio of stock price market and its market capitalization all seem to offer predictions of abnormal risk-adjusted returns. This information available and presented by these positions is very complex to align with EMH and as such are often described as anomalies.

The Price/Earnings Ratio Effect

Basu (1993) in his insightful analysis of the effect of price/earnings ratio revealed that low price/earnings (P/E) ratio stocks provide higher returns than high P/E portfolios. In the in event that the returns are adjusted for portfolios beta, the P/E effect still holds. According to Basu (1977), this issue raises the question of whether the market misprices stocks systematically. This, in essence, would be an alarming issue because the computation of P/E is a very simple process to undertake. Whereas intelligence and much insight would be valuable tools in reaping profits in investments, following such a simplistic process cannot guarantee the generation of abnormal profits.

An interpretation adopted by the ref in the analysis of P/E effect is that “the model of capital market equi­librium is at fault in that the returns are not properly adjusted for risk” (Basu, 1977, p. 671). The interpretation holds that in the event that two stocks have similar expected earnings, the riskier stock will sell at a lower P/E ration. This simply implies that because of the level of the risk, it will generate higher returns because of the low P/E ratio. In the analysis of the same case, Bernstein (1998) intones, “unless the CAPM beta fully adjusts to risk, P/E will act as a useful additional descriptor of risk, and will be associated with abnormal returns if the CAPM is used to establish benchmark performance” (p. 157).

The Small-Firm-In-January Effect

The Size or the small-firm effect has been cited as one of the most common anomalies. Drawn from the work of Branz (1981), dividing stocks into ten portfolios and carryout an analysis based on market indicators and data retrieved from the stock generated interesting findings. The consensus is that smaller-firm portfolios tend to be much riskier than larger-firm portfolios. Even the application of CAPM to adjust the risk, it is ascertained that smaller-firm portfolios registered better performances that larger ones by an average of 4.3% annually (Thaler, 1987).

The small-firm effect are further illuminated in the works and findings Keim, 1983 who in his analysis, revealed that the small-firm effect was more prevalent within the first two weeks of January. A significant number of researchers point out tax-loss selling as the probable cause at the end of the previous year. The hypothetical position is that a higher number of investors download stocks with declined prices to realize their capital losses before the end of the tax year (Keim, 1983). The capital from such sales do not gain entry back into the market until after the full turn of the year, mostly after January (Keim, 1983). The increased demand for stocks at that particular time places an upwards pressure on stock process due to the January effect. Keim and Madhavan (1995) reveal that this is consistent with tax-loss balancing in which the ratio of stock purchases to sales by individual investors is below normal in late December and above normal in early January” (p, 379).  

The Neglected-Firm Effect and Liquidity Effects

An important area that has attracted considerable interests from researchers is the Neglected-Firm Effect and Liquidity Effects (Arbel and Strebel, 1983). This stems from the extended analysis of the small-firm-in-January effect. The fact that small firms tend to find themselves at the periphery indicates that information about them is not readily available. The lack of information about their operations and speculations make them more risky investments and in turn generate higher returns. On the hand, large firms and brand name firms are constantly under the strict lenses of the regulators and subject to consistent regulatory monitoring that assures accurate information and investors shy away from “generic” stock that has no real promise for higher returns.

In efforts to gain insights into the effect of neglected firms, Arbel (1985) in an interesting study divided firms into three categories: neglected groups, the moderately researched and the highly researched based on the number of institutions holding their stock. In his findings, Arbel (1985) intoned neglected firms demonstrated higher levels of January effect. In a related research by Amihud and Mendelson (1991), the researchers revealed, “the effect of liquidity on stock returns might be related to both the small-firm and neglected-firm effects.”

Book-To-Market Ratios      

The book-to-market ratio has been an important area in the semi-strong tests. In a research undertaken by Fama and French (1992), the ratio of the book value of the firm’s equity to the market value of equity is a powerful predictor of returns across securities. In the study, Fama and French (1992) stratified the firms into ten groups based on book-to-market rations. The data on each firm was examined based on average monthly returns for each selected firm. Results of the study revealed that an average annual return of 16.84% was the high­est book-to-market ratio decile whereas the lowest-ratio decile averaged only 10.51%. In the analysis of the researchers, the influence of B/M ratio on returns is not in any way related to beta. This implies that there are only two possible scenarios in this case: either the high B/M ration firms are underpriced or the B/M ratio is acting as a proxy for a risk factor that affects equilibrium expected returns (Fama and French, 1992).

In arriving at the conclusion, Fama and French (1992) found that even after controlling the B/M ratio, there was still no correlation with beta in understanding average security returns. The finding presents yet another interesting but complex issue and challenges the assumption of rational markets. This because it implies that systematic risk, which has been seen to serve as a more significant factor, has not effect on returns, but B/M ratio, which seems insignificant, is capable of predicting future returns.

Post-Earnings-Announcement Price Drift 

In efficient markets, it is normal that any new information is reflected in the stock prices as fast as possible. However, this is not always the case as Ball and Brown (1966) found that the stock prices demonstrate the sluggish response to the announcement of a firm’s earnings. This position has been extended and examined in a number of research findings by examining the effect of news content of earnings announcement on returns expected my market participants (Fama and French, 1988). In the analysis of the same, Fama and French (1988) defined the difference as the “earnings surprise” and presented an insightful study on the sluggish response to the news announcement.

To achieve this objective, the researchers calculated the earnings surprises across a very bid sample of firms, investigated the surprises, divided the selected sampled firms unto ten deciles based on the size of the surprises and obtained the abnormal returns for each decile.  The researchers found a large abnormal return on the day of the earnings announcement (time 0). In summary, positive-surprise firms presented positive abnormal returns whereas negative-surprise firms presented negative abnormal results.       In the analysis of the stock price movements after the announcement day, interesting observations were made. The trend continues with positive-surprise continued with better performances whereas negative-surprise firms continue to undergo negative abnormal returns even after the information was made public. The reason for this as expounded by the researchers is that the market continued to undergo normal adjustments resulting in sustained abnormal returns over a period.

Strong-Form Tests: Inside information

The understanding is that it would not surprise any trader if insiders were to exploit their vantage position to make higher profits while trading in their stocks. This is because it is not expected that the market become strong form efficient. According to Jensen (1968), players regulate trade based on the availability of inside information. Berk and R. Green (2004) explored the ability of an insider to trade profitably in their own stock. There is evidence to support the belief that stock process tend to experience an upward surge after insiders bought shares and the reverse after insiders offload their shares. This raises the question of whether activities of the insiders can enable other investors to make profits. It is based on this that the SEC of USA outlines strict regulation that must be followed by insiders. All insiders must register and publish their trading activities in an official summary of Security Transactions and Holdings.

In an insightful study of the tracking of the release dates of the official summaries, Seylum (1986) found out that relying on insider information to gain the advantage is a waste of time and effort. Whereas there is the tendency for stock prices to rise after the release of insider information, returns made during such periods are insignificant and cannot take care of the costs incurred during transactions.

Interpreting the Evidence

After an analysis of the evidence, the burden lies on how to interpret the ever-growing anomalies in literature. The other question that arises within the same domain is whether the market is too inefficient to allow simplistic trading rules to take precedence. The interpretations of these ever-growing evidence of stock anomalies have attracted considerable interests from researchers and significant attempts have been made.

Risk Premiums or Inefficiencies?   

One attempt to interpret the anomalies in the stock markets was carried out by Fama and French (1993) to interpret the price earnings, small firm, book-to-market and long-term reversal effects. According to Fama and French (1993), these are the most puzzling phenomena in empirical research that have generated varied interpretations. In an expected analysis, the researchers argue that the anomalies are embodiments of risk premiums. In the application of three-factor model, the researchers demonstrate that stock with M/B factors and higher betas have higher average returns. Fama and French (1993) in their analysis argue that three-factor model in which the level of risk is arrived at by

the sensitivity of a stock to a number of factors such as the market portfolio, a portfolio that reflects the relative returns of small versus large firms, and a portfolio that reflects the relative returns of firms with high versus low ratios of book to mar­ket value, does a much better job than one-factor CAPM in explaining security returns

On the other hand, whereas B/M ratios do not obviously fall under risk factors, they may be indicators of more basic determinants of risks. The researchers therefore conclude the patterns observed on returns are a demonstration of an efficient market in which expected returns are relative to the risks.

However, not all researchers concur with the position advanced by Fama and French. In a different and opposite direction, Lakonishok and Smidt (1988) argue that these puzzling phenomena in the stock market are manifestations of efficient markets. The researchers present an opposite result of the analysis in arguing that analysts take the past performance too far into the future. In this position, good performing firms are overpriced and poor performers are under-priced. The general understanding is that prices adjust to their fair values when all market participants realize their mistakes and prices reverse. The position is in line with the reversal effect and to a limited extent, supports the positions adopted by small-firm and book-to-market effects. This is because, as ref intones, firms that experience sharp drops in prices are likely to be small or have high B/M rations.

Anomalies or Data Mining?

The question of whether the anomalies cited in the literature are worth giving the attention they have received or a number of researchers have posed whether they are products of data mining. According to Lakonishok and Smidt (1988), a simply repeated run on the available data from the price of a security repeatedly will definitely generate a criterion that seems to predict stock price behavior and returns. Lakonishok and Smidt (1988) expound that this is the underlying reason why anomalies simply dissipate in literature and fail to find their way into academic literature. The case of the disappearance of the small-firm effect after its wide publication in the 1980s demonstrates this trend. Similarly, the attention paid to the book-to-market strategy in the 1990s dissipated for the rest of the decade after its publication.

            Lo and MacKinlay (1990) proposes that the only way to find a solution to this problem is to find a data that has never been researched and find out if the relationship in question is valid. Such studies by Lo and MacKinlay (1990) have come out to reveal B/M, momentum and size effects in security markets around the world. The consensus is that whereas these puzzling phenomena are embodiments of a systematic risk premium, available information falls short of delineating the precise nature of such risk.

Models for Measuring Portfolio Performance


            Measuring the performance of a portfolio has become a vital subject in the financial markets for investors, portfolio managers, and almost every individual involved the area of finance. This role played by this subject in the financial markets across the globe is extremely important.

Before 1950, investors and portfolio managers have measured the performance of their portfolios almost on the basis of return rate only. They were already aware, during that period, that risk is a crucial factor in determining the success of an investment but they knew no clear or simply method for measuring it.

Markowitz formulated the Modern Portfolio Theory in 1952. He proposed that an investor expects to receive compensation for additional risk and provided a framework for the measurement of risk. During the early 1960s, after the modern portfolio theory was developed as well the as capital asset pricing model (CAPM) during the following years, the variable of risk was incorporated into the process of evaluation. The beginning of asset pricing theory was marked by the creation of the CAPM by William Sharpe and John Litner. The CAPM was attractive primarily because it offers power predictions as regards the measurement of risk and the relationship between risk and the anticipated return.

The first researcher who developed a composite method for measuring the performance of portfolios was Treynor (1965). He evaluated the risk in a portfolio with beta and computed the market risk premium of a portfolio. This method came to be known as the Treynor Index. Subsequently, Sharpe (1966) came up with his own composite index, which has similarities with the Treynor Index; the only difference is that instead of beta, standard deviation was used. This was called the Sharpe Index. It was used in 1967 for evaluating the performance of funds based on both the rate of diversification and the return rate. However, the Treynor Index and the Sharpe index would arrive at an identical ranking for a completely diversified portfolio. In 1968 though, Jensen formulated a method for measuring the performance of a portfolio based on the security market line and was able to successfully show the difference between the anticipated return rate of the portfolio and the anticipated return rate of a benchmark portfolio that would be positioned on the security market line.

The subsequent sections would discuss: (1) the CAPM model, and provide the proof to its theorem and enumerate its assumptions. Some examples would be provided, as well as a detailed explanation of the CAPM as a pricing model, and pricing linearity and the certainty equivalent form and the Treynor Index and how they are used in the evaluation of portfolio performance and their comparisons would be discussed as well.

Capital Asset Pricing Model (CAPM)

History of the Capital Asset Pricing Model (CAPM)

Jack Treynor introduced the capital asset pricing model (CAPM) in 1961. William Sharp and Lintner, meanwhile, presented parallel work in 1964 and 1965 respectively. Sharp was awarded the Nobel Memorial Prize in Economics in 1990, along with Merton Miller and Harry Markowitz in a field of financial economics.

The CAPM is an economic model used for evaluating assets, stocks, and securities by relating risk and anticipated return rate. The anticipated return rate of an efficient portfolio, in the capital market line, relates to its standard deviation but is unable to demonstrate how the anticipated return rates of individual assets relate to their individual risks. The CAPM expresses this relation.

The CAPM is intended in helping to compute the investment risk and what the return on investment is. Two types of investment risk are involved here:

  • Systematic risk
  • Unsystematic risk

Systematic Risk. Systematic risks refer to the market risks that cannot be diversified away; examples of systematic risks include interest rates and wars.

Unsystematic Risk. Unsystematic risks are particular to individual stocks. Unlike systematic risks, it is possible to diversify them away as the investors increase the number of stocks in their portfolios. Unsystematic risks are also referred to as “specific risks”.

Theorem: Suppose that market portfolio M is efficient, I of any asset I satisfy the relationship



where:               rf             =              risk-free rate

ßi             =          beta of the security

                                                M     =          anticipated market return


Proof. Suppose that for any α, the portfolio that consists of a portion α invested in the asset I and the remaining portion (1 – α) invested in the market portfolio M. The anticipated return rate of this portfolio is



The rate of return’s standard deviation is


The illustration below shows how the values of α are traced out.



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