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 paved 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 suggested that investors required a higher return for those assets that do badly in periods of financial slowdown and they required lower returns for the assets that represent a hedged against the periods of economic downturn. The main result of the academic search for alternative asset pricing models was Ross (1976) model known as Arbitrage Pricing theory (APT).The theory assumed that the stochastic processed generating asset returns could 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 β coefficients, which represented the sensitivity of the asset to the risk factors and λ 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 affected returns unlike the CAPM where the only relevant risk factor was (beta) systematic market risk. However, the theory did not provided any indication of the relevant factors. Like the CAPM, the APT assumed that the idiosyncratic risk could 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 defined 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 required 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 factors model and the second involved the use of macroeconomic factors model. Following sections presented the microeconomic approach, the three-factor model, and the macroeconomic approach, the Chen et al. model. The problem of APT and I-CAPM lies in that they did not specified the risk factors to be used in the respective models. Nevertheless, Fama and French (1993) take an indirect approach to the problem. They used size and book-to-market equity. These measures were not proper risk factors but indirectly reflected unidentified state variables that produced non-diversifiable risks not captured by the market beta. They started from the observation that small-cap and value stocks had higher historical average returns than large-cap and growth stocks. Furthermore, they showed evidence that the CAPM was not capable of capturing the abnormal high returns due to the small and value effect. They introduced a three-factor model with the market portfolio and two other factors: SMB (the return of a portfolio of small capitalization stocks minus the return of a portfolio of large capitalization stocks) and HML (the return of a portfolio of stocks with high book-to-market minus the return of a portfolio of stocks with low book-to-market). They showed that their model could better explain the variation in the average return, which wasn't previously captured by the CAPM. Although empirical research had shown the heavy use of the three-factor model even it had some theoretical weaknesses. The size and the book-to-market factors of returns were not themselves state variables of relevance to investors. They were not like consumption, income, or production, for instance, but were variables that indirectly captured some systematic risks. This led researchers to use other multifactor-models to examine the underlying determinants of returns and investigated the economic nature of size and value effects in an attempt to identify the underlying risk factors that were only indirectly assumed by (Fama & French, 1993). As suggested by Cochrane (2001), the three-factor model was presented as an I-CAPM model but had the characteristics of an APT model in that the risk factors were only reflected by mimicking portfolios. In fact, some behavioralists believed that the value effect was linked to an overreaction of investors to stocks with high book-to-market. They contended that value stocks were more exposed or more sensitive to good and bad times and investors overreacted to business cycles by pricing growth stocks too high and value stocks too low. When the overreaction was corrected, the result was an extra return for value stocks and a lower return for growth stocks. This view was advocated by (DeBondt & Thaler, 1987; Lakonishok, Shleifer, & Vishny, 1994; Haugen, 1995). The existent financial literature pointed out that the risk captured by book-to-market was related to the financial distress risk. Firms that were considered riskier and with poor prospects were characterized by low prices, whereas the firms contained low risk and high stability got higher expected returns and were characterized by high prices. Meanwhile, Chan, Chen, and Hsieh (1985) calculated the default risk as, the difference between the high and low-grade corporate bonds monthly return and argued that the size effect accounted for default risk. Keim and Stambaugh (1986) found that the yield spread had predictive power for future stock returns, while Liew and Vassalou (2000) suggested that SMB and HML might help predicted the future GDP growth. Moreover, Rajan and Zingales (1995) showed that debt/equity ratio was a function of size, tangible assets, profitability, and market-to-book ratio. Large companies with tangible assets were less exposed to costs of financial distress and were therefore a good hedged in period of downturn. Firms with low book-to-market tend to borrow less as growth companies face higher costs of financial distress. Therefore, value stocks looked like a better hedged in periods of economic downturn. Moreover, Frank and Goyal (2003) found that smaller, younger, and growth companies were less likely to rely on debt.
In addition, Vassalou and Xing (2002) computed default risk for individual firms by the used the Merton's (1974) option pricing model and found that the size effect was a default effect, and this was largely the case for the book-to-market effect. In conclusion, the work of Fama and French (1993) had changed the way financial economists now think about the relationship between risk and return and had started a thriving research and an interesting debate into the risk factors for which investors required some compensation.
Modern financial theory asserted that through diversification only the systematic risk was rewarded but ignored the identity of the systematic state variables that accounted for it. Macroeconomic multifactor models had been used in an attempt to identify those factors likely to influence the returns of all assets, i.e. the economic variables responsible for the non diversifiable risk. They assumed the market returns as endogenous and as a function of macro variables. As systematic risk was the sole factor, only the general economic state variables influenced market returns.
Chen et al. introduced a macroeconomic multifactor model where they identified the systematic forces that influenced returns as those economic variables affecting the discounted factors and expected cash flows. In fact, according to the fundamentals, the price of a stock should be determined by its dividends present value. Default risk and term structure slopes affected the rate of return used to discount the expected future cash flows and the growth of gross domestic product affected the growth rate of expected cash flows. This approach led to the identification of five factors: (MP) monthly growth rate of industrial production; (DEI) change in expected inflation (changes in short-term T-bill rates); (UI) unexpected inflation (difference between actual & expected inflation); (UPR) unexpected changes in risk premium (difference between the returns on corporate bonds & long-term government bonds); and (UTS) unexpected changes in the term premium (difference between the returns on long-term & short-term government bonds). The authors found that these sources of risk were significantly priced and that neither the market portfolio nor aggregated consumption was separately rewarded by the stock market. Furthermore, Chen et al. found positive and statistically significant risk premium for the growth rate in industrial production as a proxy of non-diversifiable production risks, significant and negative risk premier for unexpected inflation, significant positive risk premier for default risk as a proxy for uncertainty and negative and insignificant risk premium for term structure changed. In order to analyze the determinants of portfolio returns, regime-switching models were introduced. This allowed relaxing the assumption of stable risk premia and evaluating the possibility of time-varying risk premia under the belief that the compensation for some risks was larger at some times and smaller at other times. In so doing, the betas were considered conditional to the market regimes and different from the unconditional betas. Regime-switching models allowed for several sets of parameters into one model depending on the regime in which the stated variable was at a certain time. The importance of using time-varying beta models had been introduced by (Ferson, Kandel, & Stambaugh, 1987).Regime-switching models had been used in several areas, such as the analysis of the business cycle with Hamilton (2005) and asset allocation with (Ang & Bekaert, 2002). Regimes had also been used to measure volatility and change in correlation among assets. Erb, Harvey, and Viskanta (1994) noticed high correlation exists between international equity return's in bear markets as compared to the normal market times. They also noticed that standard models of time-varying volatility failed to capture asymmetric correlations whereas regime-switching models were successful in it. Furthermore, as for the asset behavior, there was wide empirical evidence that asset returns followed complicated non-linear processes with multiple regimes, each of which was associated with a different distribution of asset returns. Ang and Bekaert (2002), Ang and Chen (2002), Connolly, Stivers, and Sun (2005), Garcia and Perron (1996), Gray (1996), Guidolin and Timmermann (2005), Perez-Quiros and Timmermann (2000), Turner, Startz, and Nelson (1989) and Whitelaw (2001) reported evidence of regimes in stock or bond returns. Timmermann (2000) argued that regime-switching models could capture complicated forms of heteroskedasticity, fat tails, and skews in the distribution of returns. In addition, AÑ-t-Sahalia and Brandt (2001) noticed that higher order moments in the distribution of stock and bond returns were time-varying. Meanwhile, Ang and Chen (2002) reported that equity correlations that differed across bull and bear regimes could be successfully captured by a regime-switching model. In fact, regime-switching models typically identified bull and bear regimes with very different mean, variance, and correlations across assets. Ang and Bekaert (2002) found and characterized the international equity returns in two regimes, the bear-market and the normal-market regime. Where pricing model based stock market returns could lead to a more powerful explanation of returns and more profitable portfolio asset allocation decisions. Moreover, there was evidence that asset allocation decisions varied across different regimes. The inspiration for this empirical research was provided by these considerations and, in particular, the work of (Ang & Bekaert, 2002; Guidolin & Timmermann, 2005). Related to switching-regimes and asset pricing models there was a recent fast growing segment of literature that focused on conditional asset pricing models that suggested how conditional versions of asset pricing models could improved the empirical performance of the unconditional versions.
The next section introduced the most important findings of this field of study.
Empirical research had shown that some variables such as size, book-to-market and earnings to price ratios among others, were better able to explain the cross-section of returns than market beta. Financial theory suggested that these variables had explanatory power as they captured information about time-varying risk and that as a result static model or unconditional models were not capable of explaining the cross-section of average returns. Recent empirical research had focused on the role of time-varying betas and factor loadings in the so-called conditional asset pricing models. Ferson and Harvey (1991), Ferson and Koraczyk (1995), Braun, Nelson, and Sunier (1995), and Koutmos and Knif (2002) argued that market betas were time-varying. Ammann and Verhofen (2008) found that time-varying betas in the CAPM and time-varying coefficients for SMB and HML in the three-factor model improved the empirical performance of the models. Hansen and Richard (1987) showed that a conditional CAPM could hold even when the unconditional CAPM was rejected. In addition, Jagannathan and Wang (1996) introduced a conditional CAPM allowing for both betas and market risk premium to vary over time. Ang and Chen (2007) documented time variation in betas of portfolio sorted on book-to-market. Adrian and Franzoni (2005) suggested a conditional CAPM in which time-varying risk was adjusted on the basis of observed realized returns. Pettengill, Sundaram, and Mathur (1995) found a strong segmented relation between beta and returns by introducing a conditional CAPM that distinguished between up markets and down markets suggested that conditional CAPM may hold even when unconditional CAPM was rejected. The most important asset pricing models had been presented, in particular the CAPM and the three-factor model. Whereas the former explained the market returns as a linear function of the systematic market risk (beta), the later one introduced two additional factors, specifically the size and the book-to-market factors. The search for alternative asset pricing models and support for three-factor model introduced by Fama and French (1992) stemmed from the empirical failures of the CAPM. In particular, several findings showed a weak relationship between risk and return as measured by the CAPM on one side and the existence of other risk factors that were rewarded by the market on the other side. In the later part these models would be carefully examined. Moreover, the assumption of constant betas would be relaxed, by the introduction of regime-switching under the belief that the data generation process of returns varied according to the market cycle.
Fama and French (1992) noticed that portfolios of stocks with small size had historically outperformed portfolios of stocks with big size and that portfolios with high book-to-market had historically outperformed portfolios with low book-to-market to an extent that was not explained by their betas. They concluded that size and book-to-market indirectly reflected some common risk factors not captured by the market beta. The result was a model with two additional regressors: SMB and HML The methodology used to determine the coefficients was an OLS time-series multiple regression similar to the CAPM. The only difference was that the dependent variable excess return was a linear function of three independent variables. The factors referred to (1) the excess return on the market (Rm-Rf), (2) the return of small stocks minus the return of big stocks (SMB, Small Minus Big), and (3) the return of value stocks minus the return of growth stocks (HML, High Minus Low). Fama and French (1992) run the time-series regression for a long period of time (1963-1990) used daily returns, which required more data than the CAPM.
Moreover, the time-series regression was applied to the returns of factors such as size and the book-to-market based equity portfolios. Market risk premium, size, and book-to- market factors included in the regressions were taken from the files made available by the SECP. As SMB and HML result was being statistically different from zero, the idea was that the variability of average returns was better explained by this model as it generated higher R-squared values. To test the validity of the Fama and French (1992) model, it was essential to verified whether SMB and HML had a coefficient statistically different from zero. According to the CAPM, the market beta was all that was needed to explained differences in returns, so if SMB and HML were not statistically different from zero and the market premium was significantly priced the validity of the CAPM was upheld. In summary, the empirical results showed that SMB and HML were statistically significant in explaining average market returns and that their addition to the market premium could enhance the explanatory power of the model in terms of higher R-squared.
CHAPTER 3: RESEARCH METHODS
Theoretical Framework & Research Methodology
In the early 1990's and before that CAPM had been widely used and accepted by most of the researchers world wide to measured the average market return. Fama and French (1992) introduced a new model known as three-factor model and declared that their model could better explain the average market return as compared to CAPM.
Basically Fama and French (1992) three-factor model was the extension of CAPM. Size and value factor had been added in addition to the factor market premium to get the accurate results in terms of average market return because CAPM considered the market portfolio as the sole determinant of average market return.
This single hypothesis was applied on 17 different companies for a period of 5 years and results were taken separately year by year for each company. Details of the results were shown in the findings portion of the chapter of results. Here, only the significant and β values were used to test the proposed hypothesis.
In year 2005 total 70 percent, year 2006 total 75 percent, year 2007 total 75 percent, year 2008 total 76 percent, and finally 2009 total 65 percent of the companies showed significant SMB value at 5 percent level of significance. Therefore, the empirical analysis corroborated the hypothesis that the size was one of the factor that affected the long-run performance of an IPO.
CHAPTER 5: DICUSSIONS, CONCLUSION, IMPLICATIONS AND FUTURE RESEARCH
5.1 Conclusion and Discussion
The findings indicated that for small and medium-sized portfolios, the higher excess return was related to higher HML. Moreover, the SMB was positive in most of the cases when considering the large portfolios and the HML was always negative when considering the growth portfolios, with low book-to-market.
In general, the results indicated that the R-squared increased when considering the two additional variables SMB and HML, with values always above 0.80, whereas the difference in terms of beta was much lower compared to the CAPM's results, i.e. without the two additional variables, their effect was partially transferred to the market beta.
The present study had examined empirically the most important asset pricing models in use and had shown their strengths and weaknesses. In particular, it had been underlined how the CAPM, in spite of its simplicity, had many limitations especially in up markets. The three-factor model had been shown to better capture the risk in up and down markets, but it had been said to have had serious limitations concerning the economic significance of the additional factors used in the model. A possible explanation to the success of the three-factor model by had been advanced in this study. The risk might not be linear and investors might be loss averse. If this was the truth, the Fama and French (1993) model success would depend on the adjustment to the betas provided by the two additional factors, SMB and HML, which would proxy the nonlinear betas. The failures of the CAPM and the elusive underpinnings of the three-factor model had even led to cast doubt on the market efficiency. Nevertheless, the overarching result of this study was that the stock market was quite efficient in the way risk factors were rewarded even if the relationship between returns and risk factors was complicated. The existence of time-varying risk premia was actually reasonable for an efficient market, but this study also offered some support to the claim put forward by the behavioralists; it was possible that misalignments of returns could be due to the length of time required by investors to reflect expectations of a dynamic business cycle into the stock market.
Even if the search for an explanation of the risk-return relationship looks still far from reaching a conclusion, the simplicity and the formal elegance of the most renowned asset pricing models makes it likely that the CAPM and the three-factor model would still remained the cornerstone of asset pricing and portfolio management for long time.
5.2 Implications
The empirical results reinforced the point that the three factors were all important to explain the returns of the portfolios. Hence, they offered additional support to the argument that the market portfolio return did not fully captured the risk. Also, the book-to-market appears extremely relevant as it was associated with high average excess returns which showed that how this second factor was particularly important to explain the historical portfolio returns.
A regression for the three-factor model for the six portfolios formed according to size and book-to-market that were representative of the styles was performed. Once the book-to-market attribute was taken into account, the model was not capable of explaining why small-growth had a lower return than large-growth. The relationship between beta and returns seemed weak or absent. As a matter of fact, the introduction of a conditional CAPM might be able to show a significant relationship between beta and returns in up and down markets and explained the apparent anomaly of small-growth and large-growth.
5.3 Limitations and Suggestions for Future Research
The major limitation in this study was represented by the in-sample analysis between the risk and return relationship and the ex-post analysis of the relationship between beta and average excess returns. Nevertheless, the use of a very long period of time, 49 years, with a large number of observations should ensured meaningful empirical results. A second limitation was represented by the reduced number of portfolios examined.
At the end of this study it was worth pointing out as there were still many gaps in the portfolio theory concerning the relationship between returns and risk factors that paved the way for future research projects. For instance, relationship between mergers and acquisitions and SMB effects on them, and between liquidity risk and SMB might be a fascinating area to study. In addition, if the financial literature almost totally agreed on the role played by default risk to explain the small-large premium, the explanation of the value-growth premium was still a moot point.
Fama and French (1992) attributed the value risk premium to the lower prospects of earnings linked to the high book-to-market stocks and to the reflection of financial distress risk. However, the analysis showed that exactly in a bearish market the value risk premium was particularly wide historically. Therefore, it might be useful to study the dispersion of returns within the universe of value and growth stocks. It might well be the case that some growth stocks exhibit high returns whereas some others fail to keep up to the expectations with an overall lower result.
The reality seemed to be more complicated than the models examined here could explain. In particular, the assumption of risk aversion had to be revisited in the light of the different nature of risk-return profile involved by different categories of stocks. Considering the overall period of time, value stocks yield a higher return than explained by their market beta; the conclusion might be that values investors owned a utility function characterized by loss aversion, i.e. beta underestimated their perception of risk. Small stocks yield a higher return than predicted by their beta; this might lead to the conclusion that return was not linear in the risk factors. However, when considering separately up and down markets, the findings showed that beta overestimated the negative return for value in a down market; this suggested that investors presented loss aversion and recognized value as less risky than growth in down markets, therefore required a lower risk premium; the result was that growth were discounted more harshly in down markets than value. Market beta underestimated the return of small stocks in both up and down markets; this suggests that the utility function was much steeper, i.e. investors required much higher return after a given threshold of risk. Moreover, investors who hold growth stocks were most probably risk lover in an up market, i.e. they were willing to take a higher risk in order to take on an opportunity. Therefore, the market beta did not reflect their risk aversion, but overestimates it. An investigation into the relationship between utility function and returns might produce interesting results.
After all, three-factor model might be successful either because it better captured the dynamics of the market or because it corrected the market beta with two factors that partially solved the utility function shape problem. Put differently, the size and value factors adjusted upward the beta. However, it remained unexplained why small-neutral stock portfolios had historically an unexpected positive value effect. The explanation appeared that value was incorporating the part of risk in small not captured by market premium and SMB.
Another interesting field of study was represented by the analysis of time varying betas, where the betas depend on a set of instrumental variables related to the business cycle and with predictive power of returns.
Finally, the search for an economic explanation of SMB and HML was carried out considering the style portfolios as homogeneous, whereas their composition could be quite different over time in terms of industries to which the small, large, growth and value stocks belong. As a result, the analysis looked at the factors that affect styles all else being equal. The ceteris paribus assumption was clearly strong. The style portfolios sensitivity to macroeconomic factors might change in function of the predominant industries to which portfolio stocks belonged at a particular point in time. An industrial analysis might preciously enlighten on the underlying reasons for styles' performance. The underlying hypothesis was that small stocks were more sensitive to the change in macro variables than large stocks.
