Long Run Performance of Ipos Finance Essay

This dissertation focused on the explanatory factors for IPO's performance. In the literature several models had been proposed to explain the factors for which investors required to have the knowledge of them. This study had several objectives among which to offered a theoretical comparison of the most renowned asset pricing models (specifically the CAPM & the three-factor model), to investigated the nature or underlying economic reasons for size and book-to-market factors, and to considered the possibility that risk factors were time-varying over the market cycle. This research tried to present the most important findings in asset pricing from the beginning of modern finance with Markowitz (1959) to the most recent developments. For long time, the CAPM had led the way in which financial economists had thought about the relationship between risk and return.

According to the CAPM, and in the spirit of the modern portfolio theory of Markowitz, investors were rewarded only for bearing systematic risk represented by the market portfolio. Specifically, the CAPM predicted that differences in returns between securities or portfolios of securities were fully explained by differences in market betas. In the 1970's, there was growing evidence that other factors than the market beta could had explanatory power for average returns and that many assumptions of the CAPM were unrealistic. Merton (1973) introduced the I-CAPM, and suggested that investors not only care about the returns of the market portfolio, but also about how market portfolio returns co-vary with labor income and other investment opportunities.

Moreover, Fama and French (1992) showed that the relationship between average return and beta had been historically weak and that portfolios of stocks with high book-to-market ratios and portfolios consisted of small-cap stocks had historically outperformed portfolios of stocks with low book-to-market and portfolios including large-cap stocks respectively. Furthermore, Fama and French (1992) showed that size and book-to-market effect encompassed other variables, such as P/E and leverage that had shown to have had predictive power for future returns. The main result of the academic search for new asset pricing models capable of explaining the anomalies of the CAPM was manifested in the Arbitrage Pricing Theory (APT) proposed by Ross (1976), which modeled the average returns as a linear function of multiple risk factors.

However, the inability of the theory to identify the risk factors was a major limitation to the implementation and usefulness of the APT. In practice, two different approaches to the multifactor model had been used. The first was the use of a microeconomic factor model, by adding some characteristics of the stocks to the market portfolio. Such was the Fama and French three-factor model, which added two variables to the market portfolio: SMB (the return of small-sized portfolios minus the return of large sized portfolios) and HML (the return of high book-to-market portfolios minus the return of low book-to-market portfolios). The second was the use of macroeconomic factors. Such was the model proposed by Chen, Roll, and Ross (1986), which identified the determinants of returns as the following five economic variables: growth rate of industrial production, change in expected inflation, unexpected change in expected inflation, unanticipated change in risk premium, and unanticipated change in the term premium.

1.2 Problem Statement

The objective of the study was twofold: to investigate what were the factors that determined the long-run performance of an IPO and whether size was one of these factors. Specifically, this dissertation aimed to empirically examine the different approaches adopted by the CAPM and the Fama and French three-factor models and investigated the underlying economic reasons for the difference in returns between small and large-sized portfolios and high and low book-to-market portfolios. The ultimate objective of this research was to investigate the underlying economic variables that could explain returns, and also offered some practical advice to portfolio managers with regard to changed the asset allocation according to investment styles and overweighting or underweighting the portfolio beta. In order to do so, different models were introduced, to examine the behavior of asset pricing models in market trend and the behavior of small, large, value and growth stocks were analyzed according to different, volatility and default risk.

1.3 Hypothesis

Size has a significant impact on the long-run performance of an IPO.

1.4 Outline of the Study

In Chapter 2, the theoretical perspective of the CAPM and its main anomalies were discussed. In addition, the Fama and French three-factor model and other proposed multifactor models, as well as the most relevant literature, were explained. Chapter 3, presents the methodology and data used to test the models and the models used in the dissertation were explained in detail. Chapter 4, presents the results of the empirical research that proved the validity of the Fama and French three-factor model and reported the analysis on the stability of the models over time, the explanatory investigation of the underlying variables that could explain SMB and HML. The final chapter, Chapter 5, contained conclusion of the empirical results and integrated the findings of this study with portfolio decisions and offering some advice under what circumstances value, growth, small, and large stocks perform better. Whether it might be useful to derived different specifications of the CAPM according to the market trend versus a single unconditional model definition.

1.5 Definitions

1.5.1 IPO (Initial Public Offering)

The first sale of a company's share to the public and the listing of the share on the stock exchange.

1.5.2 Long-run Performance

It was here referred as beyond one year performance of a share after its floatation.

CHAPTER 2: LITERATURE REVIEW

Extensive studies had been done in various countries to examine specially, the long-run performance of IPO's. One of the significant researches done by Gompers and Lerner (2003) on Pre-Nasdaq IPO's in which they estimated the long-run performance of 3661 listed US IPO's from 1935 to 1972 and measured post five years returns after listing. Their findings supported the proposition that IPO's performance was affected by the method of return measurement. As it was obvious from the results that value weighted buy and holdout returns showed low performance whereas equal weighted buy and hold out returns or cumulative abnormal returns depicted high performance. It was revealed that when cumulative abnormal returns were utilized as a result the underperformance diminishes. CAPM and Fama-French three factor regression model was employed to evaluate the pre-Nasdaq long-run IPO's performance. The model consists of three factors. RMRF; that was value weighted market return minus the risk free rate, SMB; the difference yearly returns of small and big firms, and HML; the return on a portfolio of high book-to-market minus the return of a portfolio of stocks with low book-to-market. Results obtained from simple CAPM regression yielded insignificant intercepts implying zero abnormal performance whereas equal weighted Fama-French three factor regression model, produced significantly positive intercept at one percent confidence level. Ritter (1991) study encompassed long-run performance of 1,526 IPO's on NASDAQ and NYSE from 1975 to 1984. It had been observed that three factors could explain underperformance phenomenon in IPO's that include risk mismeasurement, bad luck, and finally fads and over optimism prevailing among investors.

In addition to it, those companies were more vulnerable to long-term underperformance that went public in high volume years. Thirty one out of thirty six months average adjusted returns showed negative trend including thirteen reflected t-statistics lower than -2.0. There was also declining trend in the cumulative average adjusted returns which after two months of seasoning slightly bounced back then eventually slumped to -29.13 percent at the end of thirty sixth month. This provided reason to believe that underperformance of IPO's under study was both economically and statistically significant. Gopalaswamy, Chaturvedi, and Sriram (2008) conducted study on Indian primary market. The purpose of this endeavor was to critically examine the difference in long-run post issue performance of Indian IPO's through fixed price offer and book building offer. In addition, this study also evaluated the difference in IPO's post performance in particular; the above mentioned two routes of offering. They proposed that IPO's go with book building route performs far better in the long-run than fixed price IPO's. Results suggested that market performance of IPO's not only influenced by their prices but also period of issue and the industry sector in which the company operates. It was noted that the route used for IPO did not influenced the short-run performance but it affected the long-run performance.

Moreover, their performance also depends on the sector to which the company belongs. In a similar study done by Aggarwal, Leal, and Hernandez (1993) on Brazilian, Mexican, and Chilean IPO's investigated both the short-run and long-run performance of IPO's on a sample of 62 Brazilian, 36 Chilean, and 44 Mexican IPO's. It was discovered that investors who purchased and held securities for one year at offering got negative return. Sample companies belonging to Asian emerging markets showed large positive mean and median excess returns between the range of 36.5 percent to 78.5 percent with t- statistics of 6.83 significant at five percent level of confidence. Bessler and Thies (2007) did similar nature of study on IPO's in Germany for the period of 1977 to 1995 in order to found the insight to their inquisitive hypothesis of why some IPO's showed substantial positive and others showed substantial negative long-run buy and hold out returns. It was suggested that long-run underperformance was directly attributed to the size of the firm and this phenomenon was not because of an IPO effect.

They pointed out that the after math financing activity was one of the critically significant factors in determining the long-run health of an IPO that distinguishes out performers and underperformers. Previous evidence suggested that markets for initial public offering (IPO) stocks may resided either of the two conditions which were known as hot-issue or cold-issue regimes. As Ritter (1991) believed corporations could benefit of the timings to go public that could be considered as what he called a window of opportunity and the stakeholders may felt optimistic about the future. At NASDAQ it had been through hot and cold trimming from 2000 to 2002 where shorter incentives were higher in hot issue. However profitability appeared higher on average for cold issue IPO's. Though the riddle as to whether the role of market conditions was important in the IPO activity of new corporation. It was because of the fact; venture capitalists were in good positions to influence the initial pricing of their shares and thereby tried to take advantage of it for their personal interest. Schwartz and Moon (2000) examined volatility of expected young corporations in which he believed that sales as a factor that could drive nubile technology corporations' firm value.

In addition to it, Pastor and Veronesi (2004) deduced a market value to book value of equity valuation model to represent that high level of volatility may justify the observed NASDAQ fluctuations. Here, the uncertainty about future returns was presumed to have a direct connection with return volatility and uncertainty and thus defines both; high stock valuations as well as high return volatility. IPO's performed an imperative role in initial equity financing. Helwege and Liang (2002), suggested that there were normally lower earnings for hot issue IPO's on average but the future prospects were great. A descriptive discussion regarding initial returns and long-run performance of IPO's was in recent studies that figures out the difference between aftermarket and regular return behavior for IPO's in upcoming periods. Boehmer and Fishe (2002) assumed that underwriter activities such as price support may influence aftermath performance because of the influence on aftermarket return behavior. IPO performance in the longer run was generally rather weak when estimated against some market index.

This may be due to the over optimism of investors to the earning potential of new growth firms as belied by (Ritter, 1991). On the other hand, Brav, Geczy, and Gompers (2000) determined that long-run underperformance was not just a common phenomenon to issued companies and could be explained by the risk factor model. Ljungqvist, Nanda, and Singh (2003) model which was based on sentiment investment behavior and short-sale constraints that provides empirical results to the initial under pricing and long-run performance of IPO's. Menyah and Paudyal (2004) used style stock selection methods to identify the aftermarket performance of IPO's. They compared returns for value versus growth IPO's, small-cap versus large-cap IPO's, and IPO's marketed by high-quality underwriters versus those marketed by low-quality underwriters. Interesting facts obtained from this study in which, value and growth IPO's did not showed statistically significant differences in returns for all holding periods and the large-cap IPO portfolios outperformed against the small-cap portfolio. Moreover, IPO's sponsored by recognized underwriters had great credibility in the equity market rendered sufficiently higher returns than IPO's sponsored by unfamiliar underwriters. In this study, after manipulating the degree of the credibility of the underwriter, value and small-cap IPO's marketed by renowned sponsors provided significantly higher aftermarket returns. Chen, Jagadeesh, and Werners (2000) observed that mutual funds showed a propensity for holding small stocks, growth stocks, and momentum stocks in comparison to the market portfolio. The author perhaps believed that the fact that mutual funds and independent investors preferred to had small chunk of IPO's in their portfolios.

Style portfolio selection technique that was mostly used by investment manager therefore it was believed that it could provide great insight into the aftermarket performance of IPO's. Investors would be able to get some important finding from this research by learning the style strategies to attain after market success for IPO's. It also termed with low book-to-market ratios to growth stocks. It was also gleaned from the recent studies that value stocks yielded higher returns against growth stocks. Rosenberg, Reid, and Lanstein (1985), Chan, Hamao, and Lakonishok (1991), Barber and Lyon (1997), and Berk, Green, and Naik (1999) provided a comprehensive framework in which the book-to-market ratio that was considered as a variable that could estimate the firm's risk with respect to the scale of its assets, and thus entailed a fundamental solution for classifying the expected returns on such stocks. Brav and Gompers (1997) also discovered that book-to-market ratios assisted to forecast long-run returns.

LSE also showed favorable returns than growth stocks between 1973 to 1992 (Strong and Xu, 1997). In terms of market capitalization average returns of small capitalization stocks were higher relative to those of high capitalization stocks as noted by (Banz, 1981). This conclusion supports in favor of size as a determining factor for the long-run performance of IPO's. Small companies inherently yielded better returns than large firms according to (Levis, 1985). The instability such phenomenon was found common by sharing knowledge of diversified studies in the domain of IPO's for instance Chan et al. (2000) suggested that growth stocks and large stocks outperformed value and small stocks during the observed period under study. These finding may vary within the specified period of study. This study made an explicit emphasis by providing compelling corroborative evidence to support in favor of style analysis to understanding the aftermarket performance of IPO's. Aftermarket performance of IPO's also ensured the credibility of underwriters. Carter, Dark, and Singh (1998) showed facts that convinced the traditional view that IPO's sponsored by prestigious underwriters incurred a meager loss in the long- run. In support to the previous claim, Jain and Kini (1999) observation made similar connotation that highly known underwriters had their own stake to protect their reputation and reduce the likelihood of being associated with a poorly performing firm by effectively monitoring the managers of firms they take public after the IPO. They also provided evidence to show that both the operating and investment performance of firms taken public by prestigious underwriters were better than those of less prestigious bankers. Some studies were in favor of banks that provided backup to IPO's normally showed positive return up to 1 year after issued (Dunbar, 2000).

IPO's in developing markets for example Malaysia and Thailand had shown successful outcome in the long-run (Corhay, Teo, & Rad, 2000; Allen, Kingsbury, & Boonthanakict, 1999). Finland, Germany, and South African IPO's had also shown poor long-run performance, as in the USA (Lee, Lonhhead, Ritter, & Zhao, 1996; Keloharju, 1993; Ljungqvist, 1997; Page & Reyneke, 1997). Some analysts considered the underperformance and over performance of IPO's was a riddle that had not been ascertained to some unanimous endogenous or exogenous factors in general. There had been some parameters used by the financial industry that forecast the expected returns, one of them was an asset-pricing model, which was an appropriate measure for such purpose, as Banz (1981), Rosenberg et al. (1985), Fama and French (1992), and Brav et al. (2000) suggested that besides beta risk, size and book-to-market ratio were essential determinant of stock returns. Fama-French three-factor model had also been used to measure the long-run performance of Taiwan's IPO's. Some believed that IPO's in developing markets faced stringent regulations therefore considered less efficient than US markets. The reasons behind the anomaly in IPO long-run performance were not clear some believed it was because of market inefficiency either due to the erratic activities of investors or just a glitch caused by wrong selection of a model.

A comprehensive study of ISE IPO's demonstrated that performance was high in the very short-run due to the under pricing; however, results for long-run performance were not cleared. Granger, (1981) and Engle and Granger, (1987) used CAPM for estimating the long-run relationship of the IPO's. Otero and Mendez (2007) study analyzed whether the return of the companies that go public varies with respect to their size. Here long-run stock returns were employed to evaluate the performance of the companies. Consequently interpret the influence of size effect on the financial performance of IPO's. Companies with large size showed a greater initial return to investors and the effect was more felt to smaller companies. One possible reason found for the poor stock price performance after the initial public offering was that investors were over-optimistic about the profit potential of firms, but with the passage of time underperformance occurred as these over-optimistic expectations declined in the post-offering period. A sensible reason for such dramatic change occurred due to error in the overstated expectation of investors because of their over optimism about the earnings management practices around the time of the issue. This led, directors of IPO firms to inflate earnings by manipulating accounting system or financial reporting system. If the market failed to discover that the high earnings reported represent a fictitious increase, negative post offering abnormal returns would be due to a gradual correction of the initial overvaluation as earnings management reverses. The market to book value ratio, also known as the price to book value ratio, was mostly used to evaluate investment forecast.

Here the market value of a company's shares that was price which was divided by its book value per share that was equal to shareholder's funds divided by number of shares outstanding. On the other hand, it was the ratio of market capitalization to shareholder's funds. Some researchers were in favor of this methodology because they believed book value was a relatively stagnant measure that provides flexible comparability over time or across companies. One fascinating factor that supersedes the use of this parameter was that this measure could still be estimated for loss-making companies and companies whose EBIT was negative. On the contrary, there were some criticism lies behind the use of the book value because it did not reflect a firm's earnings power or projected cash flows. It only represents the original cost of a firm's resources and was pretty much influenced by accounting decisions on depreciation. The ratio may not be helpful in the valuation of subjects which did not posses sufficient fixed assets. In addition, growth stock companies may leverage net losses for several years, cutting their debts to make it more compatible in terms of balance sheet.

The fundamental idea underlying all these models was that the average market returns were linear in the risk factors and that the risk factors employed were enough to explain the variance of returns, which was tantamount to saying that no additional factors were needed to further explained the average market returns; The CAPM considers the market portfolio as the sole determinant of average market returns; the Fama and French (1992) multifactor model considers market portfolio, size and book-to-market ratios. On the other hand, the Chen et al. (1986) model considers some macroeconomic factors. Furthermore, as the contribution of this study entailed the consideration of how asset returns behaved in different economic regimes, under the assumption that the prediction and explanatory power of the asset pricing models could be enhanced by introducing the possibility of time-varying parameters (set of coefficients in the model), switching-regimes models and the most important findings in the literature concerning their use were also introduced in this chapter. The CAPM for long time had been the dominant asset pricing model used by financial economists and institutional investors and had led the way economists and practitioners had thought about the relationship between risk and return, specifically the CAPM of (Sharpe, 1964 ; Lintner, 1965; Black, 1972).

The main strength and attraction of the CAPM lies on the simplicity with which it offers a way to measure risk and to explain the relationship between the risk and expected return. The foundations of the CAPM rest on the work of Markowitz (1959), who developed the modern portfolio theory. Markowitz (1959) derived the background for the optimal choice of portfolios by making some assumptions, and specifically: Investors were risk averse; The model lasts for 1 period; mean and variance in the investment returns were the main components considered by the investors. Markowitz's model was called the mean-variance model, because investors select the portfolios that minimize the variance of returns, given the expected return, and maximize the expected return, given the variance. Markowitz (1959) derived a measure of risk and return for a portfolio of assets and he was, therefore, the first to mathematically show that an investor must consider the relationship among assets to build an optimum portfolio. From Markowitz (1959) on, it was accepted that diversification reduces the total risk of a portfolio and that the relevant risk was not the own risk of a single asset, but its average covariance with all the other investments in the portfolio. The natural outcome of Markowitz's (1959) analysis was the identification of the efficient frontier; a set of portfolios that had a given level of risk with maximum return.

The optimum portfolio choice had been depend on the level of risk aversion and was mathematically identified with the portfolio that lies at the point of tangency between the efficient frontier and the investor's highest utility curve. Sharpe (1964) and Lintner (1965) derive the CAPM by adding two important assumptions to the Markowitz model: 1. Investors had homogeneous expectations about the distribution of returns. 2. All investors could borrow or lend at the same rate known as risk-free rate (rf). An introduction of the risk-free asset with zero covariance with the market portfolio allowed deriving a new efficient frontier that was a straight line characterized by totally diversified portfolios perfectly correlated. In the new CAPM world, the efficient frontier became a straight line starting from the risk-free rate (rf) and moving to the tangency portfolio that identified the market portfolio. In the mean-variance efficient world, all the investors invested in the market portfolio and the risk-free asset in proportions that vary according to their level of risk aversion. The fact that all investors own the same risky asset portfolio was known as the separation theorem and was first proposed by (Tobin, 1958). The separation theorem states that the investment decision was separated from the financing decision. In other words, investors first identify the optimal portfolio of risky assets, which was the same for everyone, and then on the basis of their own preferences for risk choose the desired combination of market portfolio and risk-free asset, which determined the position on the straight line efficient frontier.

According to the CAPM, the expected return on any asset was the risk-free interest rate plus asset's market beta times the premium per unit of systematic risk (market premium). Where the excess return over the risk-free rate on a broad-based stock portfolio (proxy of the market portfolio).The CAPM indicated what should be the expected rate of return on risky assets based on their systematic risk or their sensitivity to the market risk (beta). The relevant risk measure for any individual risky asset was its market beta: a standardized measure of risk that related the covariance of an asset with the market to the variance of the market portfolio. According to the CAPM, the expected returns on securities were a positive linear function of the market beta, and the covariance with the market portfolio was enough to explained the returns. Markowitz (1959) outlines that diversification enabled the investor to avoid all the risk apart from the non-diversifiable general economic risks. Since all other risks be avoided by diversification, only the sensitivity of an asset's return to the market risk was relevant. Specifically, there were two types of risks: The diversifiable or idiosyncratic risk. This risk be eradicated through diversification by exploiting the low or not perfect correlation among assets; the non-diversifiable risk that was generated by macroeconomic and general factors affecting the entire market and hence cannot be eliminated. An investor constructing her own portfolio of assets was interested in the contribution of a single asset to the overall variance of her portfolio. To evaluate that contribution, the investor used the market beta; namely the asset's covariance in terms of market divided by the total variance of the market. Investors must carry out a benefit-cost analysis when constructing their portfolios, where the benefit was the marginal increase in portfolio return and the cost was the marginal increase in the portfolio variance. In a Markowitz (1959) efficient world, i.e. dominated by rational agents, investors want to maximize the mean and minimize the variance. Therefore, only the non-diversifiable risk was rewarded.

That lead to the concept of the Security Market Line that defined the required rate of return of an asset as a linear combination of the risk- free rate and the market premium times the asset beta. As a result, the risk less asset, not being correlated with the market return and having zero systematic risk, had beta equal to zero, which implies that it did not contribute to the variance of the market return. In addition, the CAPM predicted that the asset with beta equal to zero must had a return equal to the risk-free rate. Any other risky asset had an expected return larger than the risk-free rate in the measure of the market premium times the asset market beta. In summary, the CAPM suggested that the expected return on any asset was the risk-free interest rate plus asset's market beta times the market premium. Nevertheless, Black (1972) relaxes the assumption of borrowing and lending at risk-free rate and introduced the CAPM with a portfolio of risky assets uncorrelated with the market portfolio. In fact, many of the assumptions of the CAPM were unrealistic, but many be relaxed without major consequences. Reilly and Brown (2006) argued that all models had simplifications, but what really matter was their explanatory power and prediction ability. That was exactly why it was necessary to empirically test the CAPM. According to the CAPM, the only variable that had the ability to explain the assets expected return was the assets own beta. Put differently, market betas did not leaved anything else to explained. In the 1970's, tests on the CAPM showed that there was no relationship exist between expected return and the market beta.

Financial researchers started realizing that variables like size, earnings-price ratios, book-to-market ratios, leverage and momentum could play an important role for the explanation of average returns that goes beyond the market beta. Today, there was large evidence that the CAPM was not capable of explaining the difference in return among portfolios of stocks with different characteristics or when using different styles of investment. These results had important implications for many applications of the CAPM, not only when determining the proper cost of equity, but also when explaining the returns of different strategies and measuring the performance of portfolio managers. The following section presents an overview of the literature and discusses the most important results in relation to testing the CAPM. The CAPM had undergone many tests, amidst the difficulties given by the need of using a market proxy for the theoretical comprehensive market portfolio, which had cast doubts on the validity and applicability of the model itself. According to the CAPM, the efficient frontier was represented by portfolios that were linear combinations of the risk-free asset and the risky assets market portfolio.

Therefore, the CAPM model predicted that the portfolios slope should be equal to the markets expected excess return and it should be plotted along a straight line had an intercept equals to the risk-free rate (rf). The first set of tests focus on the CAPM's prediction about the intercept and slope of the SML. They tried to examine whether the intercept corresponds to the historical average risk free rate and whether the slope applied to the estimates of betas corresponds to the average market premium. In particular, the most famous test was the Fama and MacBeth (1973) test that investigates the CAPM prediction that there was a positive relationship between beta and average expected returns. Specifically, a two-pass technique was applied. In the first stage, the betas for a set of portfolios were estimated and in the second stage the extra returns of portfolios were regressed on the estimated betas. If the CAPM hold, the average value should be an unbiased estimator of the equity premium and should be greater than zero. Whereas, the CAPM refers to the expected market premium, which was always positive, the tests were based on realized market premium, which be negative.

Furthermore, the tests on the validity of the CAPM consider portfolios, rather than individual assets. In fact, betas for individual assets were imprecise and create a measurement error when used to explain average returns, whereas betas for portfolios were more stable and less erratic. The first set of tests, such as Lintner (1965), found that the intercept was larger than the risk-free rate as measured by the monthly return of T-bills. Whereas common stock portfolios average excess return showed that market risk premium was more than the beta's coefficient. Lintner (1965) also found a positive relationship between beta and average return, but flatter than expected theoretically. Similar results were obtained by (Douglas, 1968; Black, Jensen & Scholes, 1972; Miller & Scholes, 1972; Blume & Friend, 1973; Fama & MacBeth, 1973; Fama & French, 1992).Moreover, Reinganum (1981) found that the relationship between beta and cross-sectional returns vary over time. Schwert (1983) argued that there was evidence of a weak risk-return trade-off. Tinic and West (1984) contend that the predictions of the CAPM were inconsistent over time and that the relationship between beta and returns vary with months in a year.

Lakonishok and Shapiro (1986) found a stronger relationship between returns and size than beta. Such empirical findings contradict the theoretical relationship between risk and return advocated by the CAPM. Moreover, Black et al. (1972) used a time-series analysis to verify the relationship between beta and average returns. In order to solve the problem of stability of beta, they use portfolios instead of single assets. The results indicated that when portfolios were selected on the basis of market beta (systematic risk), portfolios with higher systematic risk had lower returns than predicted by the CAPM, whereas higher returns had been observed on portfolios with low systematic risk related to their beta. In addition, Fama and French (1992) showed weak relationship between beta and average return in most recent periods. This indicated that the CAPM did not fully explained the historical realized extra return since a clear positive relationship between beta and return was theoretically expected but not supported empirically.

The second set of tests, the one this study was more interested in, refers to the explanatory power of market betas. If all differences in returns were explained by beta, the coefficient on the additional variables in a multifactor model should not be statistically significantly different from zero. However, the problem was to identified those additional variables that represent an anomaly for the CAPM. According to the CAPM, the rates of return should be entirely explained by the betas. Hence, in order to test the validity of the CAPM researchers had focused on the presence of additional factors to the market risk that had a significant impact in terms of explaining stock/portfolio returns. Furthermore, the CAPM suggested that the variation in the securities and portfolios expected return were solely dependent on market beta's variation. According to the CAPM, the riskiness of the economic activity was entirely captured by the market portfolio. Nevertheless, the empirical findings contradict this assumption. Basu (1977) found evidence that when stocks were sorted on earnings-price ratios, stocks with high E/P (earnings-price ratio) had higher future returns than predicted by the CAPM. Therefore, earnings-price ratios add to the explanation of returns and had predictive power of future returns.

Banz (1981) documents that size could better explained average returns when added to the market portfolio. When stocks were sorted on market capitalization, small stocks showed higher average returns than the CAPM based prediction, whereas average returns on large stocks were lower than predicted by their betas. Therefore, a negative relation between size and average returns was established. Furthermore, Bhandari (1988) found that stocks with high leverage have had higher returns as compared to their market beta's, measured as high debt-equity ratios. That's why investors demanded extra return to recover the risk which wasn't covered by market premium in these stocks. In addition, Stattman (1980) and Rosenberg et al. found that stocks with high book-to-market ratios had high average returns relative to their betas. In the literature that findings was explained as the result of financial distress sensitivity of stocks with high book-to-market. In summary, Extensive evidence proved that beta cannot solely explain the expected returns.

These results led to the market efficiency debate which leads to the conclusion that either market was not particularly efficient for long periods of time or they were efficient, but there was something wrong with the way risk was measured by the CAPM. Fama and French (1992) test the explanatory power when size, book-to-market, leverage and earnings-price ratios were added to the market portfolio. Specifically, Fama and French (1992) found that two variables, size and book-to-market which not only increase the explanatory power of the one-factor market model (CAPM) but also encompass the other variables. They concluded that size and book-to-market were enough to capture the variation in average returns associated with market risk, leverage, earnings-price ratios, size and book-to-market. Furthermore, Fama and French (1992) showed weak relationship was exists between average return and beta's in the period 1963-1990 and they rejected the prediction of the CAPM. One of the possible defenses of the CAPM was the difficulty or impossibility to use the theoretical market portfolio in practice. Along the same lines, Roll (1977) argued  that instead of using the true market portfolios, the tests were based on proxies. One did not know whether the CAPM was valid or not. However, Stambaugh (1982) tested the CAPM using arrange of market portfolios that included not only U.S. common stocks, but also contains bonds issued by corporate and governmental sectors, preferred stocks issued by companies and real estate sector.

He found that tests of the CAPM did not depend on the use of market proxy beyond common stocks because the volatility of market returns was mainly determined by the volatility of stock returns. Whatever the reasons of the weakness of the CAPM, either theoretical or practical, empirical tests showed that most of the applications used in CAPM model were invalid (Fama & French, 2004). The empirical failures of the CAPM pave the way for more complicated asset pricing models. Since 1973, when Merton (1973) proposed the I-CAPM (Intertemporal CAPM), several models had been introduced on the basis that the assumptions of the CAPM were too simplistic and that several variables were needed in order to fully capture the variation of returns. Many unrealistic assumptions had been used in CAPM such as 1: investors only had concerned about their portfolio return's means and variances. 2: how labor income and future investment opportunities co-varies with the investor's portfolio returns. According to the I-CAPM, the marginal value of individual wealth was affected by several factors, not only by the stock market returns. Therefore, the theory suggests that investors require a higher return for those assets that do badly in periods of financial slowdown and they require lower returns for the assets that represent a hedge against the periods of economic downturn. The main result of the academic search for alternative asset pricing models was the Arbitrage Pricing Theory (APT) developed by (Ross, 1976).The theory assumes that the stochastic process generating asset returns be represented as a linear function of K factors of risk. In order to apply the model, it was necessary to select the risk factors and to estimate the  coefficients, which represented the sensitivity of the asset to the risk factors and» risk premia for changes in the risk factors. Examples of the risk factors might be inflation, growth in gross domestic product, changes in interest rates and oil price among others. The basic assumption of the APT was that there were many factors of risk that affect returns unlike the CAPM where the only relevant risk factor was (beta) systematic market risk.

However, the theory did not provide any indication of the relevant factors. Like the CAPM, the APT assumed that the idiosyncratic risk be diversified away and that, in equilibrium, the return on a zero-systematic-risk portfolio was zero. The major difference between CAPM and APT was that the CAPM defined the risk as a single market risk factor, whereas the APT defines the risk as several factors. Moreover, the CAPM had the practical advantage of identifying the single risk factor (the excess return to the market portfolio), whereas the APT requires the specification of the risk factors. The inability to identify the risk factors was a major limitation to the implementation and usefulness of the APT. In practice, two different approaches to the multifactor-model had been used. The first included the use of a microeconomic factor model; such was the three-factor model by Fama and French (1993) that made the use of the size and book-to-market ratio. The second involved the use of macroeconomic factors; such was the model proposed by (Chen et al., 1986). In the following sections the microeconomic approach, the three-factor model by Fama and French (1993), and the macroeconomic approach, the

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