Introduction
Stock market undoubtedly plays a significant role in motivating economic growth of a country, so many investors and financial scholars have paid considerable attention on the trends of stock market. However, stock market is a changeable and unstable financial market, in which various factors may influence on the return that investors may obtain from investing in equity shares. The uncertainty of stock market is defined as risks that investors have to undertake while they had invested in stocks, but it is well-known that investors is generally risk-averse, thus a growing number of investors and financial analysts have started looking for the most appropriate and optimal methods to measure the rates of risk from stock market in order to maximize their investing return. Various theories regarding to risk and return have been developed over 60 years.
In the 1970s, Sharpe (1964) and Lintner (1965) deduced the capital asset pricing model (CAPM) on the basis of the framework of Markowitz (1952) and Tobin (1958) Mean-Variance studies. Based on Sharpe-Lintner's creation of a security market line (SML) [1] , an equation for the risk-return line is given by:
to test for a positive risk return trade-off. So as to bear the validity of capital asset pricing model, γ0 is the expected return of a zero-β portfolio, expected to be similar with the risk-free rate and γ1 is the market risk premium, that is importantly different from positive and zero. As well as being a "weapon" of risk management, CAPM is central to investors' understanding of financial risk. If it holds, individual investors will be able to reducing an investing risk from an uncertainty of financial market, thereby increasing their return.
Since it was introduced in the 1960s, economists and financial scholars have been testing the validity of CAPM. Furthermore, the empirical results were strongly supportive of Sharpe-Lintner CAPM during the period of 1970s (Black et al, 1972; Fama et al, 1973). However, greater empirical studies doubted and challenged Black et al (1972). For instance, Fama and French (1992), He and Ng (1994) and Miles and Timmermann (1996) provided feeble empirical evidences on the correlation between the average return and the beta. The debate about the validity of CAPM remains unsettled. Bossaerts and Plott (2002) supported a CAPM's validity, as well as Chen (2003) also claimed that a positive evidence on relationship between return and the beta in Taiwan stock exchange. There still are voices of support on the CAPM's validity, but "the empirical record of the model is poor-poor enough to invalidate the way it is used in application" (Fama and French, 2004).
Henceforth, the aim of the paper is to apply econometric techniques to empirically and systematically estimate the validity of capital asset pricing model in the Singapore stock market. The reason for choosing Singapore is a lot of empirical analyses of CAPM's validity focus mainly on the Western countries such as United Kingdom, United State America and so forth, but the Southeast Asian countries seem to be rarely analysed, particularly in Singapore. Otherwise, closeness of fit, autocorrelation, normality, misspecification, heteroskedasticity and structural changes are tested for avoiding the existence of bias in the paper.
Since CAPM's birth in early 1960s, it has become a crucial issue for the development of financial market. Because of its significance on financial market, the asset pricing theory has always been a disputed topic around the financial economics. Therefore, many econometricians have heavily focused on testing CAPM's validity as well as contributing towards the development and improvement of the models.
Without a doubt the Sharpe-Lintner model, is the earliest model attempting to surmise the expected return of capital asset in the 1960s, which is also the extension of the one period mean-variance model of Markowitz (1952) and Tobin (1958). This earliest model had indicated a linear relationship between market risk (β) and expected return, thus early researches on CAPM were mainly based on individual share return. However, the empirical results were unsatisfactory. Miller and Scholars (1972) pointed out that there are some statistical issues in testing the CAPM's validity while applying individual stocks. Moreover, there is another problem had been discovered by Jensen (1968), who stated that average risk-free rate in CAPM is smaller than the intercept in a time-series regression to test CAPM. According to Friend and Blume (1970), they also found out similar empirical results as well. The above mentioned problems had been overcome under the empirical studies of Black, Jensen and Scholes (1972). Black, et al. (1972) developed the CAPM model with a zero-β version to release the limitation of the intercept term in each period when using all the shares of New York Stock Exchange (NYSE) during the period between 1931 and 1965 to constitute portfolios. In this case, zero beta and non-zero beta portfolios are refereed as two factors CAPM that is given by,
According to this Equation (2), Black et al. (1972) pointed out that there is a linear correlation between β and the portfolio return. In addition to Stambaugh (1982) provided evidence in favour of a zero-beta version of the CAPM model. However, the empirical results of Black et al. (1972) had been disagreed and challenged by many new empirical researches on CAPM. First of all, Fama and MacBeth (1973) extended Black et al. (1972) research by applying monthly data over the period 1926 to 1968 from NYSE to support a linear relationship between the beta and average return, and find out the linear relationship maintains well when the data lays over a long-run period. They (1973) also indicated that the standard CAPM can be denied while using the portfolio as a market proxy is not efficient. Roll (1977) found evidence in support of Fama and MacBeth's (1973) version of the singe-factor CAPM. Even though Ball et al. (1976) also found evidence of a linear relationship between the average return and beta in the Australian Industrial stock market for the period of 1958 to 1970, Reinganum (1981) claimed that there is not a clear relationship between average return and the beta. Furthermore, there is also negative correlation between the beta and average return during a few months in a year (Tinic and West, 1984). On the other hand, Bos and NewBold (1984) provided another argument on β is not stable over time. Therefore, it seems the beta-return relationship in the standard CAPM had been hotly debated in the early mixed empirical findings.
Beside those arguments, the most prominent is to discover that the movements of share return are not only in relation with market, but also connected with other factors such as size (Banz, 1981), price-earnings ratio (Basu, 1983), ratio of book-to-market value (Rosenberg et al., 1985) and so forth. Actually, Banz (1981) found out that large firms have lower expected returns than small firms and behave differently during a long-run period. At the same time, He stated that the expected returns on the U.S. stocks are positively related to the size of firms. Additionally, Basu (1983) indicated that shares with low price-earnings ratio earned dramatically lower than shares with high price-earnings ratio by using a sample period from 1957 to 1971, hence it seems there is a linear relationship between price-earnings ratio and the average return. According to Rosenberg et al. (1985), stocks with high ratio of book-to-market value receive more returns than stocks with low ratio of book-to-market value. In fact, economists did not pay heavily attention on ratio of book-to-market value, but it receive serious attention while Chan, Hamao and Lakonishok (1991) found out that ratio of book-to-market value also play a outstanding role in explaining the cross-section of average returns in the Japanese stock market.
Such factors are named as "anomalies" in the equity market. Many scholars provided various theories for the purpose of explain the "anomalies". Firstly, behaviour financiers such as Debondt and Thaler (1987) and Lakonishok and Vishny (1994) thought that size and book-to-market ratio cannot be the actual risk element but the characters of firm, as well as reflect some fundamental factors of enterprise. On the other hand, some of economists had attempted to apply more complex models in the structure of more rational pricing theory to explain such phenomena (anomalies). For instance, Merton (1973) established Intertemporal Capital Asset Pricing Model (ICAPM), is a linear element model with wealth as well as illustrate variable which predict future movements of income. Another new expansion of the CAPM, had been made by Lucas (1978) and Breeden (1979), is called as Consumption-base Capital Asset Pricing Model (CCAPM). Consumption becomes the main factor in CCAPM for calculating an expected return (Lucas, 1978) and furthermore, Hansen and Singleton (1982) and Jagannathan (1985) found out that CCAPM performed well as compared to the standard CAPM. In addition, Fama and French (1995) established a three factors model that takes size and book-to-market ratio into account and market risk. So as to express these two non-market risk factors above, they applied the return of SMB [4] and HML [5] , and claimed that including SMB and HML in CAPM is more effective to explain the cross-section of stock return, rather than only using market risk factor in CAPM. In the case of Fama-French's three factor model, "the Fama-French (F-F) factors proxy for higher-order co-moments, as the F-F loadings generally become insignificant when higher-order systematic co-moments are including in cross-sectional regressions for portfolio returns" (Chuang, Johnson and Schill, 2001). Due to the empirical results of Chung et al. (2001), many scholars paid serious attention to investigate the validity of the CAPM in the appearance of the third moment - skewness and the fourth moment - kurtosis (higher-order co-moments), especially in the influence of skewness on CAPM. In fact, in the 1970's Kraus and Litzenberger (1976) found out that "when the capital asset pricing model is extended to include systematic skewness, the prediction of a significant price of systematic skewness is confirmed and the prediction of a zero intercept for the security market line in excess return space is not rejected". Nevertheless, Friend and Westerfield (1980) argued that the Kraus-Litzenberger theory is not correct despite there is support that investors may pay a premium for skewness in their portfolios. Moreover, they (1980) also stated that "co-skewness is not significant in either the individual or group regressions". Harvey and Siddique (2000) also tested a CAPM with higher-order-moments, but they found a different result with Friend and Westerfield (1980). They (2000) claimed that the cross-sectional expected return is importantly explained by skewness while CAPM includes size and ratio of book-to-market value. On the other hand, Skewness and kurtosis become a significant role in defining equity valuations. See, for example, Fang and Lai (1997) and Christie-David and Chaudhry (2001).
In fact, when Fama and French (1995) argued that CAPM may incorporate with size, the price-to-earnings ratio as well as market beta Pettengill, Sundaram and Mathur (1995) indicated that "previous studies testing for a systematic relationship between beta and returns find weak and intertemporally inconsistent results, these test results are biased due to the conditional relation between beta and realized returns [6] ". Based on their assumption of a positive or negative correlation between the β and returns over "up market" or "down market", they sampled US shares during the period between 1926 to 1990 and provide a strong evidence in favour of a systematic conditional correlation between the return and the beta. Furthermore, many studies that adopted conditional asset pricing model of Pettengill et al. (1995) to estimate the relation between the beta and return on different data sets provided stronger support for a systematic conditional correlation between returns and the beta. See, for instance, Fletcher (1997), Crombez and Vander Vennet (2000), Elsas et al. (2000) and Sharkrani and Ismail (2001). In addition to Galagedera and Silvapulle (2002) adopted the Pettengill et al. method to test a correlation between the skewness and the returns in the "up and down markets". They (2002) pointed out that the expected return is not only connected to β but also to higher-order co moments. Despite the above criticisms and new developments on the standard CAPM, Bollerslev et al. (1994) constructed a new study on modelling β on the basis of time-varying variance/covariance (time-vary volatility), as well as provided powerful evidence in favour of the relationship between the beta and return by applying the ARCH (GARCH)5 model. Following Bollerslev et al. (1994), Braun et al. (1995), Cho and Engle (1999), Fraser et al. (2000) and Galagedera and Faff (2003) extended the GARCH model to estimate the variability of β under different conditions.
In recent papers, Bossaerts and Plott (2002) claims that "when interpreted as the equilibrium to which a complex financial market system has a tendency to move, the CAPM received support in the experiments reported here". Furthermore, Chen (2003) indicated that there is important correlation between return and the beta under his study in Taiwan share market. This implies that the validity of CAPM is hold. However, according to Yu (2003), there is nonlinear relation between the beta and return in terms of testing the CAPM's validity in the Philippine stock market. In addition to Fama and French (2004) summarized that estimating the CAPM appears a strong rejection of the CAPM while β occur almost zero explanatory power of the variation in mean returns. After the summary of Fama and French (2004), Emanuele (2008) argued that "the evidence has shown that intercepts of regressions are equal to zero, so that the CAPM theory, which assumes the only relevant variable in the regression is the excess return on the market portfolio, has been respected". Different from Emanuele (2008), Nikolaos' (2009) empirical results seems to support the conclusion of Fama and French (2004) and sum up that the validity of CAPM is rejected.
As seen in the above review, it is well-known that there is no one model has absolute capability to forecast the expected share return. When many scholars are questioning the traditional CAPM as well as in support of Fama and French (1995) three factors model or conditional asset pricing model (Pettengill et al., 1995), there are new researches that supported the validity of the traditional CAPM. At this point, it is clear to feel more comprehensive estimations are demanded for further development in the validity of capital asset pricing model.
Data and Methodology
In fact, the paper was planning to sample all of stocks from Singapore stock market, but twelve stocks had started to show their price since 2004. Therefore, the paper only applies monthly adjusted close prices from fifteen companies (Capitaland, Citydev, SIA, SIA Engg, SMRT and so forth) listed in Singapore stock exchange (Strait Time Index) during the period between January 2003 and December 2009. Furthermore, Data has been gathered from the website of www.finance.yahoo.com.sg. In order to better compute the value of the β coefficient, monthly stock returns are utilized by this study. Otherwise, if using high frequency data (e.g. daily or weekly) during this short period, it can possibly lead to the application of very noisy data, and thus generating inefficient measurement on profit.
Moreover, the period of January 2003 to December 2009, that was chosen to test validity of CAPM because Singapore stock market had experienced historically highest and lowest level of return rate, which can be seen from Chart 1. Based on this special volatility in the Singapore security exchange, it may be a better way to estimate the validity and stability of capital asset pricing model.
The Straits Time index (^STI) is utilized as a proxy for the market portfolio. This index represents the value of Singapore market, contains the prices of Singapore 27 general capitalization stocks, and in response to common trends of Singapore share market. This data also had been gathered for monthly intervals between January 2003 and December 2009 and from the website of www.finance.yahoo.com.sg.
The last data have to be collected is the 3-month Singapore Treasury Bill rate (sgtb3m) which is used as the risk-free asset. This data had been collected from the website of Singapore Government Securities (www.secure.sgs.gov.sg) or Monetary Authority of Singapore (www.mas.gov.sg).
After dataset have been systematically presented, it may be the best to generally discuss the methods which were used by this paper. First of all, it is clear that this paper was going to test the significance of the independent variable as well as how risky each stock of 18 firms is in comparison with the market based on the null and alternative hypothesis had been set up. Therefore, the null hypothesis denoted H0 and the alternative hypothesis denoted H1, thus the one-side Hypothesis was conducted as:
In terms of the hypothesis of the CAPM, a share with β > 1 is riskier than the market portfolio (a proxy) as well as has finitely a higher rate of expected return than the market portfolio. In the paper, the p-value approach was used as the unique approach in testing the significance of regression coefficients, in other words, testing the null hypothesis can or cannot be rejected.
Then, so as to estimate a CAPM equation for the Singapore stock, the log return equation was given for transforming the adjusted close price into a series of returns due to it may be not good for directly coping with stock price.
This transformation had been done by using Eview6 software. Actually, all of analytical methods in this paper would be completed by applying Eview6 software. Henceforth, the monthly return rates of 15 firms and the Straits Time index for January 2003 and December 2009. Moreover, the risk-free rate (the 3-month Singapore Treasury Bill rate) shows annual interest rates, thus must convert it into monthly interest rate by dividing 12.
After the price series had been transformed into return, ordinary least squares method (OLS) was applied for testing regression of the CAPM. The main reason for that is OLS method procedures are known as Best Linear Unbiased Estimators (BLUE) which simply implies OLS method is the most efficient among all unbiased linear estimators (Asteriou and Hall, 2007). On the other hand, in order to measure how well regression the standard CAPM really fits the data, goodness of fit statistics was utilized to test it based on the evaluation of R2 and Adjusted R2.
Additionally, it is well-known that the traditional CAPM as the classical linear regression model (CLRM) normally related with five main assumptions. It is because these assumptions were demanded to demonstrate OLS had an amount of desirable properties as well as also thus hypothesis tests concerning the coefficient estimates could validly be established. Therefore, these assumptions were shown as below:
However, such assumptions have high possibility to cause errors such as heteroskedasticity, autocorrelation, misspecification and so on in estimating a CLRM. Henceforth, in order to violate the assumptions of the CAPM, heteroskedasticity, autocorrelation and normality will be tested in this paper.
Firstly, the heteroskedasticity test was performed using the Harvey-Godfrey LM test and White's test (Brooks, 2008). Actually, the main reason for detecting heteroskedasticity is that avoiding the presence of bias in testing CAPM's validity while heteroscedasticity occurs. In other words, if OLS is still applied in the appearance of heteroscedasticity, thus the standard errors could be not correct as well as any inferences made could be misleading. As it was mentioned before, testing for heteroscedasticity using Eview6. Then the Breusch-Godfrey LM test (Brooks, 2008) is the only one test for autocorrelation, because the Durbin-Watson test cannot detects other forms of residual autocorrelation. The reason for testing autocorrelation is similar with testing heteroscedasticity, which avoids the inefficiency of using OLS method. Additionally, if the residuals are non-normally distributed, which will results in the coefficient estimates is wrong. Thus it is important to check for normality of residuals. It is clear that one of the most general tests for normality is the Jarque-Berra (JB) statistic test. According to Brooks (2008), "BJ uses the property of a normally distributed random variable that the entire distribution is characterised by the first two moments - the mean and the variance". This implies that BJ mainly tests the residuals from the model were either significantly skewed or leptokuritic.
Actually, there is a further implicit assumption of CAPM beside those assumptions, is that the correct model is usually supposed to be linear in the parameters, but may not always be agreed. Hence, this paper is also going to test for misspecification of functional form. It is not doubt of that Ramsey's RESET test (Brooks, 2008) is good method for testing general misspecification.
Furthermore, each variable covers 84 observations during five years. From the perspective of long-term trends, this may increase the reliability of the empirical results. On the other hand, economy may experience structural change during a long-run period, which will lead to an invalidity of statistical test. In fact, the world's economy have been suffering a financial crisis after August 2007, thus a structural change test was presented in the paper due to sampling the data from 2003 to 2009. In the paper, a structural change examine is to test for parameter stability because parameter is assumed to constant for the entire sample. Therefore, the paper provides Chow test (Brooks, 2008) for testing parameter stability.
Chapter Four
Empirical Results
The OLS estimated resulted are displayed in Table 1 such as the beta coefficient, the p-value of t-ratio, R-squared and so on. As above mentioned, the p-value approach is used to test significance of coefficients. Thus, it can sum up that the null hypothesis cannot be rejected while the p-value is greater than 0.05, otherwise, if the p-value is less than 0.05 then the study can reject the null hypothesis that the coefficient is importantly different from one at the 5% significance level. Table 1 shows that the p-values of Capitaland, Citydev, DBS, Genting SP, Jardine C&C, NOL, OCBC BK, Semb Corp, SGX, SIA, SIA Engg, SMRT, ST Engg and UOB are less than 0.05 for a 95% confidence interval, signifying the excess return on Singapore stock market has significant explanatory power for the variability of the excess returns of those 14 stocks. It also can be seen from Table 1, there is only one stock (the p-value of ComfortDelGro is equal to 0.0645 > 0.05), indicating that the excess return on Singapore stock exchange has no important explanatory power for the variability of the excess return of ComfortDelGro share.
In order to test whether the value of the population coefficient is equal to one, the Wald-Coefficient Restrictions method is applied. According to Table 1, the CAPM betas of Capitaland stock, Genting SP stock, Jardine C&C stock, NOL stock, OCBC BK stock, Semb Corp stock, SGX stock, SIA Engg stock and UOB stock are 1 cannot be rejected and thus these estimated betas is not significantly different from 1. Table 1 also shows that the p-values of Chi-square in Citydev stock, ComfortDelGro stock, DBS stock, SIA stock, SMRT stock and ST Engg stock are less than 0.05 which rejected the null hypothesis and thence the coefficients of these stocks are significantly different from one at the 5% significance level.
Moreover, Table 1 indicates that betas of Capitaland, Citydev, DBS, Genting SP, Jardine C&C, NOL, OCBC BK, Semb Corp and SGX are greater than 1. This implies that these stocks are riskier than the market proxy (Straits Time index), hence higher expected return rate than Straits Time index. However, ComfortDelGro share, SIA share, SIA Engg share, SMRT share, ST Engg share and UOB share with β < 1 has less risk than Straits Time index, so has a lower rate of expected return than Straits Time index.
Closeness of Fit
Because of 0 < R-square (R2) < 1, if R2 near zero which means regressor is bad at predicting E(Ri). In contrast, R2 close to 1 indicate that regressor is good at predicting E(Ri). It can be seen from Table 1, Capitaland, ComfortDelGro, Genting SP, Jardine C&C, NOL, Semb Corp, SGX, SIA Engg, SMRT and ST Engg are close to zero, particularly in ComfortDelGro, so these stocks are not good at predicting the expected return rate. Additionally, Citydev, DBS, OCBC BK, SIA and UOB are near to one from Table, thus these shares are good at predicting the expected return rate. Therefore, the data of Citydev, DBS, OCBC BK, SIA and UOB seems better to fits the regression equation of CAPM, especially in UOB.
Heteroskedasticity
Based on the Harvey-Godfrey LM test, Table 2 shows that 15 stocks are all bigger than the 5% significant level, which indicates there is no evidence of heteroskedasticity for regression equation of these shares. In order to be sure regarding the results of the Harvey-Godfrey LM test is reliable, White's test is also used for testing heteroskedasticity. Different from the result of Harvey-Godfrey LM test, the tested result of White's test from Table 2 indicates that Capitaland, DBS, SMRT and ST Engg are less than the level of 5% importance, which reject the null hypothesis and summarize the presence of heteroskedasticity. That implies using OLS in the appearance of heteroskedasticity, the beta standard errors from Capitaland, DBS, SMRT and ST Engg might be inappropriate and hence any inferences being make may be equivocal. Furthermore, the result of White's test (Table 2) also indicates that the p-value of Citydev, ComfortDelGro, Genting SP, Jardine C&C, NOL, OCBC BK, Semb Corp, SGX, SIA, SIA Engg and UOB are still greater than the 0.05 for a 95% confidence interval.
Autocorrelation
The paper had decided to choose 5 lags for detecting autocorrelation due to this study uses monthly data. The tested result in p=5 are shown in Table 3. From Table 3 it is possible to know that the p-values of ComfortDelGro, DBS, Genting SP, Jardine C&C, NOL, OCBC BK, Semb Corp, SGX, SIA, SIA Engg, SMRT, ST Engg and UOB are very greater than 5% level of significance, suggesting the rejection of H0 of no serial correlation and summarizing that autocorrelation is not present. The paper also runs 8 lags and 10 lags for confirming the tested results in 5 lags. These results also can be seen from Table 3, pointing out that the p-values of above 13 stocks are still far bigger than 0.05 for a 95% confidence interval, which rejects the null hypothesis. Therefore, it can be sure that serial correlation definitely does not appear in those 13 stocks.
On the other hand, Table 3 also indicates that the p-values of Capitaland and Citydev are smaller than 0.05 for a 95% confidence interval when using 10 lags, 8 lags and 5 lags, thus serial correlation is certainly present. However, if we observe the regression results of Capitaland when using 10 lags, we can see from Table 4 that only the fifth lagged residual term is statistically significant, pointing out, most probably, that the serial correlation is of fifth order. Rerunning the test for a fifth-order serial correlation the results are as shown in Table 5. This time the t-statistic of the lagged residual term (Capitaland) is much bigger, hence the serial correlation is certainly of fifth order. In addition, Table 4 also points out that only the eighth lagged residual term (Citydev) is statistically important, as well as most possibly that the autocorrelation is of eighth order. Thus rerunning the test for an eighth-order autocorrelation the answers are as shown in Table 6. Form Table 6 it is clear that the t-statistic of eighth lagged residual term (Citydev) is much higher, therefore the autocorrelation is surely of eighth order.
Normality
So as to test for normality of residuals in CAPM the paper is going to use Jarque-Berra (JB) which was mentioned before. According to check on the historgram and the p-value (Table 7), Citydev, DBS, Jardine C&C, NOL, Semb Corp, SGX and UOB are bigger than 0.05, thus the null hypothesis for normality of residuals is not rejected, implying that the inferences the study make about the coefficient estimates could be correct. Furthermore, Table 7 also shows that Capitaland, ComfortDelGro, Genting SP, OCBC BK, SGX, SIA Engg, SMRT and ST Engg are less than the 5% important level. It is clear that these residuals are very negatively skewed and are leptokurtic. Therefore, it can strongly reject the null hypothesis that the residuals seem to be normally distributed, especially in ComfortDelGro, Genting SP, OCBC BK and ST Engg.
Misspecification
Whether the model should be linear can be formally estimated utilizing Ramsey RESET test, which is a common test for functional form misspecification. In order to make this test is more accurate, the paper is going to use three different number of fitted term (1, 2 and 3) for testing misspecification of functional form. First of all, the study uses 1 as the number of fitted term for Ramsey's test. The result is shown from Table 8, indicating that the p-values of Capitaland, Citydev, Jardine C&C, SMRT and ST Engg are less than 5% significant level, hence it does reject the null hypothesis of correct specification and summarize that the CAPM is not specified. However, Table 8 also shows that the p-values of ComfortDelGro, DBS, Genting SP, NOL, OCBC BK, Semb Corp, SGX, SIA, SIA Engg and UOB are greater than 0.05 which cannot reject the null hypothesis of no specification error. This also implies that coefficient of the squared fitted term is not statistically important.
This moment is going to change the number of fitted term as 1 to 2 for testing misspecification again. The finding using 2 fitted terms is slightly different with the tested result with 1 fitted term. It can be seen from Table 8, the p-value of OCBC BK is equal to 0.0186 (< 0.05) when the number of fitted term is 2, which can safely reject the null hypothesis of no specification error. On the other side, Table 8 also indicates that the p-value of SMRT is bigger than 5% level of significance and concludes that CAPM is not misspecified. Additionally, the p-value of others with 2 fitted terms holds same position on the result with 1 fitted term.
Finally, 3 fitted terms is used for detecting misspecification. The result with 3 fitted terms changed slightly as being also shown from Table 8. The finding indicates that the p-value of Citydev is bigger than 0.05 and summarize the null hypothesis cannot be rejected. It also can be seen from Table 5, the p-value of DBS, Semb Corp, OCBC BK (which supports the tested result with 2 fitted terms) and SMRT (which is in favour of the results with 1 fitted term) are smaller than 5% level of significance, so the null hypothesis of correct specification can be rejected.
Structural Changes
The study provides Chow test for testing structural stability. First of all, the paper have to break the sample into two or more structures, thus the October 2007 and the January 2009 were applied as break points for testing structural stability. The reason for choosing these two break points is the trend of Straits Time Index has strongly changed on October 2007 and January 2009 is as shown in Chart 1.
According to Brooks (2008), "the first version of the test is the familiar F-test, which computes a restricted version and an unrestricted version of the auxiliary regression and 'compares' the residual sums of squares, while the second and third versions are based on χ2 formulations". In this case, the three versions p-values of Capitaland, Citydev, ComfortDelGro, DBS, Genting SP, Jardine C&C, NOL, OCBC BK, Semb Corp, SGX, SIA, SIA Engg and SMRT are greater than 0.05 for a 95% confidence interval and thus H0 that the parameters are constant across the 2 sub-samples cannot be rejected. This implies that there is evidence of structural stability. This is not an expected result, because these companies should experience a world financial crisis in response to the liquidity shortfall in the United States banking system in 2007 (Ivry, 2008).
Moreover, Table 9 also shows that the three versions p-value of ST Engg and UOB are less than 5% level of significance, which rejected the null hypothesis that the parameters are stable for the whole data set.
Chapter Five
Conclusions
Since the first presence of Sharpe-Lintner CAPM in the 1960s as an approach which helps investors to forecast the expected return from investing in the equity market, many empirical analyses have been executed to test the validity of CAPM in different share markets. Some of empirical results had been in favour of CAPM's validity, for instance, Fama and MacBeth (1973), Ball et al. (1976), Roll (1977), Bossaerts and Plott (2002), Chen (2003), Emanuele (2008) and so forth. However, there are disagreeing empirical evidences that against CAPM's validity, for example, Reinganum (1981), Tinic and West (1984), Yu (2003), Fama and French (2004), Nikolaos (2009) and so on. Additionally, some of scholars extended the standard CAPM to new direction. See, for instance, Merton (1973) - Intertemporal CAPM, Lucas (1978) - Consumption CAPM, Fama and French (1995) - three factors model, Pettengill et al. (1995) - Conditional asset pricing model, Bollerslev et al. (1994) - CAPM conditional time-vary volatility and so forth. Overall, that there is no one model has absolute capability to forecast the expected share return. As such, it is the purpose of this paper to empirically test the validity of the traditional CAPM in the Singapore stock market.
Therefore, this paper is explicit to systematically examine the validity of traditional CAPM in the Singapore share market. By doing so, the paper is going to apply principle econometric techniques to test the standard CAPM's validity. First of all, the paper sampled the prices of 15 stocks and Straits Times Index in Singapore over January 2003 and December 2009, as well as gathered the 3-month Singapore Treasury bills. Secondly, the paper computed the returns of those companies and transformed the interest rate into monthly figures (Table 1).
The empirical findings for testing the regression of CAPM based on the p-value approach show that the p-values of 14 companies (e.g. Capitaland, Citydev, DBS and so on) are smaller than 0.05 for a 95% confidence interval, indicating, most possibly, that the excess return on Singapore share market has important explanatory power for the variability of the excess returns of these 14 firms, except ComfortDelGro. Furthermore, the hypothesis that the value of the population coefficient is equal to one was tested by using Wald-Coefficient Restrictions. The evidences for testing β coefficient claim that Citydev stock, ComfortDelGro stock, DBS stock, SIA stock, SMRT stock and ST Engg stock are less than 0.05 which rejected the null hypothesis that 95% confidence evidences the true value of the beta for expected return rate of these 6 shares. After that, the study used goodness of fit statistic for testing how good regression the standard CAPM really fits the data, and the result shows that only Citydev, DBS, OCBC BK, SIA and UOB are very good at predicting E(Ri).
As a consequence of this, the paper start testing residual by detecting heteroskedasticity, autocorrelation and normality based on various testing methods such as White's test, Chow test and so forth. Firstly, the findings of heteroskedasticity test indicate that 15 firms are all greater than the 0.05, indicating, there is no evidence of heteroskedasticity. Additionally, the tested results of White's test show that only Capitaland, DBS, SMRT and ST Engg rejected the null hypothesis and evidence the presence of heteroskedasticity that means standard errors might be inappropriate for it.
Secondly, the paper analysed autocorrelation by applying Breusch-Godfrey LM test, the findings claims that there is not autocorrelation for testing regression of CAPM in ComfortDelGro, DBS, Genting SP, Jardine C&C, NOL, OCBC BK, Semb Corp, SGX, SIA, SIA Engg, SMRT, ST Engg and UOB. It also indicates that the autocorrelation most possibly appear in 5 orders (Capitaland) and 8 orders (Citydev) while Table 3 claims that they are less than 0.05. According to Jarque-Berra (JB) statistic, the results of testing residual for normality show that the residuals (Citydev, DBS, Jardine C&C, NOL, Semb Corp, SGX and UOB) seem to be normally distributed, but the residuals (Capitaland, ComfortDelGro, Genting SP, OCBC BK, SGX, SIA Engg, SMRT and ST Engg) for is non-normally distributed. It can be generally concluded that approximately 60% companies involve the inferences the paper market about the coefficient estimates may be not correct.
Moreover, functional form has been examined by using Ramsey RESET method. The findings indicates that functional form for ComfortDelGro, Genting SP, NOL, SGX, SIA, SIA Engg and UOB were correct, but for Capitaland, Citydev, Jardine C&C, SMRT and ST Engg, OCBC BK, DBS and Semb Crop were incorrect. In the end, parameters stability also has been examined by investigating structural break. According to Chow approach, the results claims that the null hypothesis can be strongly rejected only for ST Engg and UOB, pointing out, that the parameters are not stable for the whole data set.
Overall, above findings of the paper seem to support the empirical validity of the standard capital asset pricing in Singapore stock market, especially in testing ST Engg, UOB and so on. In fact, the real financial market is complicate, the current concept of CAPM are developing. Therefore, it should be said that there is a long way on the empirical analysis of the CAPM's validity. However, the gapes have been constantly adjusted between theories and reality due to the concept of CAPM has been developed by greater economists. This implies that a steady development of the concept of CAPM. Thus looking forward to a new breakthrough and development of the theory of capital asset pricing model in the future, as well as providing a more comprehensive and profound interpretation.
