# Chapter 4: Data Analysis and Discussions

## 4.1 Descriptive Statistics

In this section, the descriptive statistics of the data to be used in this dissertation will be presented. Before continuing, it is worth to define naming conventions employed in this chapter. Similar to the discussion presented in previous chapter, a total of six intersection portfolios will be formed. For naming convenience purposes, the two groups of portfolios separated from firm size variables (i.e., market equity, or more commonly known as market capitalization) will be named Small (S) and Big (B). In a similar manner, the three groups of portfolios separated from book-to-market equity ratio will be named high (H), medium (M) and low (L). As such, the six portfolios that are formulated based on firm size and book-to-market equity ratio are: S/L, S/M, S/H, B/L, B/M, and B/H.

With that in mind, the first section will present the total number of companies in the different portfolio formed on size and book-to-market equity from year 2006 to 2010. Specifically, the total amount of companies fall under portfolio S/L, S/M, S/H, B/L, B/M, and B/H will be computed and presented. Then, in the second section, the average return of portfolio S, B, H and L, for the respective years will be presented. Lastly, in a similar vein, the average return of portfolio S/L, S/M, S/H, B/L, B/M, and B/H, for the respective years will be presented. From the average returns figures, meaningful observations can be made to further understand how the different stocks are priced in Malaysian stock market.

In Table 4.1 below, the sample characteristics of this study is shown. Specifically, the specific number of Listed Companies in Portfolio Formed on Size and Book-to-Market Equity from Year 2006 to 2010 are presented. To illustrate, portfolio B/H (i.e., the portfolio formed by inclusion of stocks with big size and high book-to-market equity) has a total sample size of 9 stocks in year 2006; 6 stocks in year 2007; 5 stocks in year 2008 and so on. Overall, for most of the years, it is found that most of the stocks are included in portfolio S/H, followed by portfolio B/L, and then portfolio B/M. Throughout the years, the portfolio with least amount of stocks being included in that particular portfolio is portfolio B/H, followed by portfolio S/L. On closer investigation, it is found that the sequence of the size of these portfolios, are similar to the sequence of the size of portfolio reported by Drew et. al. (2003) in their study on Shanghai Stock Exchange, China.

Overall, Table 4.1 suggests that there are very few stocks being classified under portfolio B/H as stock of larger companies are seldom traded at a high book-to-market equity ratio. On the other hand, the observation that very few stocks being classified under portfolio S/L can be due to the reason that smaller companies are seldom traded at a low book-to-market equity ratio. Then, conversely, it can be observed that most of the stocks of big companies are traded at a low book-to-market equity ratio. Again, it can also be observed that most of the stocks of small companies are traded at a high book-to-market equity ratio.

Such observations suggest that bigger companies are unlikely to be undervalued, in the context of Malaysia. In contrary, smaller companies are likely to be more undervalued, at least, for the research period being investigated, from year 2006 to year 2010 in this dissertation. To explain, it can be perceived that low book-to-market equity ratio suggest that a stock is not really undervalued (indeed, can be overvalued), but a high book-to-market equity ratio suggests that the stock is trading below its book value, and hence, more likely to be undervalued. For small and emerging country such as Malaysia, such observation is justifiable and can be explained. As the stock market of emerging country, particularly for such a small nation such as Malaysia, is frequently illiquid – foreign investors (be it institutional or individuals investors) are less likely interested to invest in the smaller companies, and hence, causing undervaluation of the smaller sized companies in the stock market. Indeed, the smaller companies in the emerging countries can be illiquid, or simply too small a target to be invested by large multinational institutional investors. These smaller sized companies may not fulfill the criteria demanded by the larger players, and hence, due to lack of interests on these stocks, they are likely to be undervalued. Another possible reason is that during the period being investigated, from year 2006 to 2010, the global economy is indeed entering into a recession, and stock market plummeted. In such a situation, smaller sized firms tend to suffer more, as business risks of the smaller firms tend to be greater during recessionary era. This could be the reason contributing to the observation that smaller size firms tend to be undervalued while seemingly larger size firms tend to be overvalued, as measured by book-to-market equity ratio in Malaysia.

In Table 4.2 below, the average return for portfolio S, B, H and L from 2007 to 2010 is shown. To explain, the average portfolio return for portfolio S in year 2006 is 39.2%, while it is a minus 25% in year 2007, and so on. In a similar concept, the average portfolio return for portfolio B is 34.7% in year 2006, and it is a minus 7.6% in year 2007. From the simple observation, it can be seen that the portfolio returns for each of these portfolio has quite similar performance in each of the particular years. For example, in year 2006 and year 2010, these portfolios all recorded encouraging positive returns, ranging from a minimum of 16% per annum to a whopping 45.4% per annum. In contrast, when the market turned bad in year 2007, all of the portfolios recorded negative returns. This suggests that the market sentiment and the economic environment are strong forces affecting the stock market, in a systematic manner. This is consistent with the notion that when the stock market turns bearish, all stocks tend to move downward in tandem, in response to the bad market condition.

Another interesting observation is that except in the year 2006, average returns of portfolio B outperform the average returns of portfolio S throughout the years from 2007 to 2010. As it is understood that the financial market worldwide turned bearish in year 2007 (due to risks of global recession and subsequently happening of global recession in 2008), such a phenomenon can be explained rationally. When market is booming, small sized stocks tend to outperform the bigger sized stocks. However, when recessionary pressures set in, the business risks facing the smaller companies are greater, and this will cause the relative underperformance of the smaller sized companies. Such an explanation is consistent with the notion that business risks for smaller sized firms are higher, and thus, demand greater premium for the stocks.

Then, in Table 4.3 below, the returns for each of the portfolio, namely portfolio S/H, S/M, S/L, B/H, B/M and B/L from year 2007 to year 2010 are shown. In a similar manner, it is observed that all of the portfolio returns tend to be correlated positively with each others. For example, in good market situation, such as in year 2006, all of the portfolios recorded positive returns. In contrast, when the market turned bad in year 2007, all of the portfolios recorded negative returns. Such a trend is obvious even in year 2007 towards 2010. This suggests that the market sentiment and the economic environment are strong forces affecting the stock market, in a systematic manner. This is consistent with the notion that when the stock market turns bearish, all stocks tend to move downward in tandem, in response to the bad market condition. Specifically, there are systematic forces affecting stock returns on large scale in a systematic manner – a notion suggested by the theoretical framework of CAPM as discussed in Chapter 2 above.

## 4.2 Results from Regression Analysis

In this section, the results from the multiple regressions, generated from SPSS will be presented. To do so, the inputs used for each regression will firstly be presented. Then, the three factor model, popularized by Fama and French (1992) will be adopted to generate the respective multiple regression for the six portfolios as follow: portfolio S/H, S/M, S/L, B/H, B/M and B/L.

In Table 4.4 below, the input for the regression analysis for portfolio S/H is provided. To explain, R(port) is the average return of portfolio S/H for the respective years; RFR is the Malaysian risk free rate for the respective years; and R(market) is the stock index returns (proxy by KLCI, or Kuala Lumpur Composite Index) for the respective years. The definition for SMB and HML is same as the definition adopted in Chapter 3 previously. From these inputs, the regression analysis, resemble to Fama and French three factor model for the Malaysian context for portfolio S/H can be simulated.

The results of regression analysis, presented in the format of ANOVA table, for portfolio S/H is presented in Table 4.5 below. Overall, it can be observed that only the first model of regression is statistically significant. The Fama and French three factor model, which is actually regression model 3, is not statistically significant at 5% level.

In Table 4.6 below, the factors loading for each of the factors under Fama and French three factor model, namely, (R_{mt}-R_{ft}), SMB_{t}, and HML_{t}, for portfolio S/H will be presented. As we are only interested on Fama and French three factor model in our analysis, only the factor loadings of the respective risk factors will be investigated. In the table, regression model 3 is actually the Fama and French three factor model. Unfortunately, none of these risk factors have statistically significant factor loadings.

In Table 4.7 below, the input for the regression analysis for portfolio S/M is provided. From these inputs, the regression analysis, or more specifically, the Fama and French three factor model for the Malaysian context for portfolio S/M can be computed.

The results of regression analysis, presented in the format of ANOVA table, for portfolio S/M is presented in Table 4.8 below. Overall, it can be observed that only the first model of regression is statistically significant at 5% level. The Fama and French three factor model, which is actually regression model 3, is not statistically significant at 5% level. However, judging from the p-value for model 3 in the table, it can be concluded that the Fama and French three factor model is statistically significant at 10% level.

In Table 4.9 below, the factors loading for each of the factors under Fama and French three factor model, namely, (R_{mt}-R_{ft}), SMB_{t}, and HML_{t}, for portfolio S/M are presented. As we are only interested on Fama and French three factor model in our analysis, only the factor loadings of the respective risk factors will be investigated. In the table, regression model 3 is actually the Fama and French three factor model. Unfortunately, none of these risk factors have statistically significant factor loadings at 5% level. Nonetheless, factor loadings for risk factors SMB_{t}, and HML_{t} are statistically significant at 10% level.

In Table 4.10 below, the input for the regression analysis for portfolio S/L is provided. From these inputs, the regression analysis, or more specifically, the Fama and French three factor model for the Malaysian context for portfolio S/L can be computed.

The results of regression analysis, presented in the format of ANOVA table, for portfolio S/L is presented in Table 4.11 below. Overall, it can be observed that only the first model of regression is statistically significant. The second model, however, is statistically significant at 5% level. It is noted that for such regression, risk factor (R_{mt}-R_{ft}) is excluded from the regression analysis by SPSS because the risk factor does not contribute anything to explaining the predicted variables (i.e., the portfolio returns of S/L minus risk free rates at the particular year). Only two factors, namely, SMB_{t}, and HML_{t} are included in model 3.

In Table 4.12 below, the factors loading for each of the factors under Fama and French three factor model, namely, (R_{mt}-R_{ft}), SMB_{t}, and HML_{t}, for portfolio S/L are presented. However, as risk factor (R_{mt}-R_{ft}) is found to be contributing zero or very low explanation to the explained variable in the regression, the risk factor is excluded from the regression model. Only two of the other risk factors are included in the regression model. Referring to model 2 in the table, both the factor loadings for risk factors SMB_{t}, and HML_{t} are statistically significant at 5% level.

In Table 4.13 as follow, the inputs for the regression analysis for portfolio B/H are provided. From these inputs, the Fama and French three factor model for the Malaysian context for portfolio B/H can be computed.

The results of regression analysis, presented in the format of ANOVA table, for portfolio B/H is presented in Table 4.14 below. It is noted that the second model is statistically significant at 5% level. Similar to the previous case, in this regression analysis, risk factor (R_{mt}-R_{ft}) is excluded from the regression analysis by SPSS because the risk factor does not contribute anything to explaining the predicted variables (i.e., the portfolio returns of B/H minus risk free rates at the particular year). Only two factors, namely, SMB_{t}, and HML_{t} are included in model 2.

In Table 4.15 below, the factors loading for each of the factors under Fama and French three factor model, namely, (R_{mt}-R_{ft}), SMB_{t}, and HML_{t}, for portfolio B/H are presented. However, as risk factor (R_{mt}-R_{ft}) is found to be contributing zero or very low explanation to the explained variable in the regression, the risk factor is excluded from the regression model. Only two of the other risk factors are included in the regression model. Referring to model 2 in the table, both the factor loadings for risk factors SMB_{t}, and HML_{t} are statistically significant at 5% level.

In Table 4.16 as follow, the inputs for the regression analysis for portfolio B/M are provided. From these inputs, the Fama and French three factor model for the Malaysian context for portfolio B/M can be computed.

The results of regression analysis, presented in the format of ANOVA table, for portfolio B/M is presented in Table 4.17 below. Overall, it can be observed that only the first model as well as the third model of regression is statistically significant at 5% level. The second model is not statistically significant at 5% level, but it statistically significant at 10% level. The third model of regression is actually the Fama and French three factor model.

In Table 4.18 below, the factors loading for each of the factors under Fama and French three factor model, namely, (R_{mt}-R_{ft}), SMB_{t}, and HML_{t}, for portfolio B/M are presented. As we are only interested on Fama and French three factor model in our analysis, only the factor loadings of the respective risk factors will be investigated. In the table, regression model 3 is actually the Fama and French three factor model. Unfortunately, none of these risk factors have statistically significant factor loadings at 5% level. However, in the contrary, the factor loadings for all of the three risk factors are statistically significant at 10% level.

In Table 4.19 as follow, the inputs for the regression analysis for portfolio B/L are provided. From these inputs, the Fama and French three factor model for the Malaysian context for portfolio B/L can be computed.

The results of regression analysis, presented in the format of ANOVA table, for portfolio B/L is presented in Table 4.20 below. It is noted that the second model is statistically significant at 5% level. In this regression analysis, risk factor (R_{mt}-R_{ft}) is excluded from the regression analysis by SPSS because the risk factor does not contribute anything to explaining the predicted variables (i.e., the portfolio returns of B/L minus risk free rates at the particular year). Only two factors, namely, SMB_{t}, and HML_{t} are included in model 2.

In Table 4.21 below, the factors loading for each of the factors under Fama and French three factor model, namely, (R_{mt}-R_{ft}), SMB_{t}, and HML_{t}, for portfolio B/H are presented. However, as risk factor (R_{mt}-R_{ft}) is found to be contributing zero or very low explanation to the explained variable in the regression, the risk factor is excluded from the regression model. Only two of the other risk factors are included in the regression model. Referring to model 2 in the table, both the factor loadings for risk factors SMB_{t}, and HML_{t} are statistically significant at 5% level.

In a nutshell, results from the six different regression models, for the six portfolios as follow: S/H, S/M, S/L, B/H, B/M and B/L are presented. It is noted, for some of these portfolio, SPSS exclude risk factor (R_{mt}-R_{ft}) from the regression model, because the risk factor is found to be contributing zero or very low explanation to the explained variable, i.e., (R_{pt}-R_{ft}). The regression models from the different portfolios have different findings. Not all of the regression models are statistically significant, at the 105 or 5% level. Apart from that, it is found that the factor loadings for risk factors SMB_{t}, and HML_{t} are often statistically significant at the 10% or 5% level. In order to discuss the research findings from a more comprehensive perspective, the factor loadings (i.e., coefficients for the intercepts of the respective risk factors) for the risk factors, in the six different regressions will be compiled and tabulated into a single table. The discussion and the compiled factor loadings are presented in the following section.

## 4.3 Discussion on Results and Findings

In Table 4.22 below, the factor loadings, or also known as the coefficients of intercepts for the respective risk factors for all six portfolios S/H, S/M, S/L, B/H, B/M and B/L from 2007 to 2010 are presented. In the table, the p-value of the respective coefficient of intercept is presented in bracket under the respective coefficient of intercept. To explain, a p-value which is lower than 0.05 indicate that the coefficient of intercepts of that respective risk factor is statistically significant at 5% level. Similarly, a p-value lowers than 0.10 indicate that the coefficient of intercepts of that respective risk factor is statistically significant at 10% level. As discussed before, in some of the regression, specifically, for portfolio S/L, B/H and B/L, risk factor (R_{mt}-R_{ft}) is dropped from the regression model as the risk factor is found to be contributing zero or very low explanation to the explained variable. As such, coefficient of intercept of the risk factors is simply not available (N/A).

A review of the sign of the coefficient of intercept discovered that the sign is indeed similar to the findings presented by Drew et. al. (2003) in their studied on three factor models on Shanghai Stock Exchange in China. It is also similar to the result findings presented by Naughton & Veeraraghavan (2005) in their studied on the validity of three factor models in Taiwan.

To explain, it is discovered that most of the factor loadings (i.e., coefficient of intercepts) for SMB_{t}, and HML_{t} are statistically significant, except for portfolio S/H. Indeed, factor loadings for SMB_{t}, and HML_{t} are statistically significant at 5% level, for portfolio S/L, B/H and B/L. The factor loading for risk factor (R_{mt}-R_{ft}) however is mixed. There is very little empirical evidences supporting that risk factor (R_{mt}-R_{ft}) is capable of explaining the explained variable, namely (R_{pt}-R_{ft}) for the six portfolios. Indeed, only the factor loading of (R_{mt}-R_{ft}) for portfolio B/M is statistically significant at 5% level. Such a findings is consistent with many of the previous researchers, such as by Hearn (2010); Walid (2009); Kassimatis (2008); and Nartea, Ward & Djajadikerta (2009), that the predictive power of beta fall miserably when risk factors such as SMB_{t}, and HML_{t} are added into the regression analysis.

Apart from that, the finding that the factor loading for risk factor SMB_{t} are positive for all of the six portfolios suggest that Fama and French (1992) assertion that smaller firms are generally riskier is true, even in the Malaysian context. To recap, according to them, smaller size firms tend to more susceptible to changes in business cycles, and thus, more risky. The higher degrees of risks facing these firms suggest that higher risk premium is required from the smaller sized firms. Such findings are also consistent with the findings by Drew et. al. (2003) in Shanghai Stock Exchange in China; and by Naughton & Veeraraghavan (2005) in Indonesia, Singapore and Taiwan. Indeed, in our simple observation in section 4.1 above, it is witnessed from the descriptive statistics of average stocks returns of smaller sized firms tend to be more volatile suggest that these smaller firms are indeed riskier investment options. As discussed before, from year 2006 to 2010, the global economy is indeed entering into a recession and stock market plummeted. In such a situation, smaller sized firms are observed to suffer in greater magnitude, as business risks of the smaller firms tend to be greater during recessionary era.

Nevertheless, the finding that the factor loading for risk factor HML_{t} are negative for all of the six portfolios is not consistent with assertion proposed by Fama and French (1992), concerning the observations in United States. To reiterate, Fama and French (1992) observed that stocks traded with higher ratio of book value to market value ratio tend to outperform those stocks with lower book value to market value ratio historically. They explained that firms with higher book value to market value ratio are more likely to be in a financially distressed position, and thus, these securities should have higher expected returns, to compensate for the higher risks associated with them. The negative factor loadings, however, is consistent with Drew et. al. (2003) in their studied on three factor models on Shanghai Stock Exchange in China; and with findings from Naughton & Veeraraghavan (2005) in Taiwan.

The inconsistency of research findings on sign of factor loading for risk factor HML_{t} can be explained by reasons provided by Drew et. al. (2003) in China. Accordingly, such observation suggests that the argument that value firms, as represented by those firms with high book to market value ratio are distressed is not true in emerging countries. In other words, the existence of negative returns indicates that value firms are not riskier than growth firms. Indeed, Drew et. al. (2003) articulated that there are emerging evidences in the international context on the unusual behaviors of the HML portfolio. It is then suggested that such findings in emerging countries are possible due to lack of well developed stock analysis and research in these nations. As such, stock returns could be more subjected to emotional trading and other sort of market sentiment issues, rather than from the fundamentals or attractiveness of the stocks based on financial ratios. Particularly for Malaysia, the reason presented by Drew et. al. (2003) is logical, as it is reasonable to believe that as an emerging countries, the nature of stock market in Malaysia could be similar to the situation in China.

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