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Econometric Analysis of Capm

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Prepared by: Lok Kin Gary Ng, contact email: [email protected] com May, 2009 School of Economic Introduction The analysis of this paper will derive the validity of the Fama and French (FF) model and the efficiency of the Capital Asset Pricing Model (CAPM). The comparison of the Fama and French Model and CAPM (Sharpe, 1964 & Lintner, 1965) uses real time data of stock market to practise its efficacy.

The implication of the function in realistic conditions would justify the utility of the CAPM theory.

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The theory suggests that the expected return demanded by investors on a risky asset depends on the risk-free rate of interest, the expected return on the market portfolio, the variance of the return on the market portfolio, and the covariance of the return on the risky asset with the return on the market portfolio. (Peirson et al, 2007) CAPM can be express as a function; rprf = ? (rmrf)

There is an anticipate relationship between the expected return and risk for the portfolio; a risk factor, observed based on finance and economic theory (Peirson et al, 2007).

This relationship can explain the demand on investing in the financial market; under the economic principle of profit maximization; if the return on investment is greater then interest rate, then people would favor investment (Peirson et al, 2007). Under the CAPM theory, the expected return on investment can be express as;

E(Rp) = Rf + (E(Rm) –Rf) Cov(Rp,Rm) ((m)2 The CAPM risk factor can be estimated with this empirical equation. The risk associate with the CAPM can be divided into two categories; company specific factors (unsystematic risk) and market-wide factors (systematic risk). In order to minimise the risk and fluctuation effect on market, a portfolio of five stocks are choose to stabilise the flux effect and eliminate the unsystematic risk (Peirson et al, 2007).

In 1996, Fama and French (1996) suggested an alternative asset pricing model (AAPM) that extended the application of CAPM. The alternative asset pricing model allows expected returns to be linked to more than a single source of risk. According to Peirson (2007), the returns were related to firm size, leverage, the ratio of the company’s earnings to its share price (E/P) and the ratio of the company’s book value of equity to its market value (BV/MV) (Peirson et al, 2007).

This provides further insight to the CAPM methodology for forecasting. Review of Previous Literature The logic of the CAPM is derived from Markowitz’s (1959) “mean – variance – model”, a model interested in mean and variance of portfolio return with respect to risk. The model acted upon the assumption of all investors as risk averse. The model speculated the minimisation of the variance of portfolio return, given expected return and the maximisation of expected return, given variance. (Fama & French, 1996)

Furthermore, the rise of Sharpe – Lintner CAPM provides an algebraic condition in Markowitz model to predict the relationship between risk and expected return (Perison et al, 2007). This risk relationship is presented as market Beta term ((i) that takes the market variance into account (assumed that market variance is the frontier variance) (Fama & French, 1996). According to Sharpe (1964) and Lintner (1965), the CAPM’s expected return is completely explained by the Beta, meaning to say, other variables should add nothing to the explanation of expected return.

In contrast, Basu’s (1977) evidence that other variables (such as the P/E ratio) has a significant affect on CAPM theory, other scholars (such as Fama and French) developed new methodology to extend the application of the CAPM, called Alternative Asset Pricing Model (AAPM) (Peirson et al, 2007). The rises of an AAPM reflects the inefficiency of the Beta assumption, this is based on the evidence that stock’s price depends not only on the expected cash flows, but also on earnings-price, debt – equity and book-to-market (Peirson et al, 2007).

This realisation demonstrates the shortcomings of the prediction that the market Beta is sufficient to explain expected returns (Ball, 1978). Hence, Fama & French’s three factor model flourished when considering the market book value and the size of business. Additionally, in Fama and French’s (1996) paper, they concluded Sharpe – Lintner’s CAPM has never been an empirical success. According to the current study, the factors that affected the Beta are serious enough to invalidate most applications of the CAPM

Even though there are flaws in the CAPM for empirical study, the approach of the linearity of expected return and risk is readily relevant. As Fama & French (2004:20) stated “… Markowitz’s portfolio model … is nevertheless a theoretical tour de force. ” It could be seen that the study of this paper may possibly justify Fama & French’s study that stated the CAPM is insufficient in interpreting the expected return with respect to risk. This is due to the failure of considering the other market factors that would affect the stock price.

Specification of model The primary estimated model is presented as; rprft = ? 0 + ? 1(rmrf)t + ? 2(smb)t + ? 3(hml)t + ? t This FF three factor model is derived from the CAPM (Peirson et al, 2007); E(Rp)t – Rft = (1(E(Rm) –Rf)t Given that; (i = Cov(Rp,Rm) = risk factor on the portfolio with respect to the market. ((m)2 This leads to the secondary estimated model, this can be rewritten as; rprft = (0t +(1(rmrft) + ? t Under both of these models; • Assume a common pure rate of interest, with all investors able to borrow or lend funds on equal terms. Sharpe, 1964 & Lintner, 1965) • Assume homogeneity of investor expectations: investors are assumed to agree on the prospects of various investments (Sharpe, 1964 & Lintner, 1965) • Assume investors only care about the mean and variance of one-period portfolio return. (Fama & French, 1996) This theory suggests the three factor model approach to explain the return of market to risk free return is most efficient (Fama & French, 1996). Given the five stocks in the market to comply an equally weighted portfolio would allow a simplified analysis. The variables used to estimate the CAPM and FF three factor model are as follow; Variables |Definition | |rprf |Excess return on portfolio with respect to risk free interest | |rmrf |Excess return on market with respect to risk free interest | |smb |First differential of small market capitalization minus the first differential of big market capitalization | |hml |High book to market value stock minus low book to growth value stock |

In application of the model, the data must be first manipulated and arranged to a particular format. The raw data collected has been assembled according to date; further specification is generated in the stata program to fit in the FF three factor model and the CAPM. Derived from finances theory, the increment of the market will result in an increase of investment; therefore the expected sign for every coefficient (? i) is positive. Under the risk-free borrowing and lending assumption, the expected return on assets that are uncorrelated with the market return, must equal the risk free rate (Fama & French, 1996). Consequently, the intercept of the model (? 0) equals to zero.

In the time series approach, Fama and French (2004) stated its FF three factor model has an intercept (? 0) valued zero, as a criteria for the model. In specification of the data, it has covered most of the relevant independent variables according to the theory; therefore there should not be any omitted variables. From further study of the theory, this assumption can never be achieved and there are many difficulties when conducting valid tests to the model that can not be avoided (Fama & French, 1996). Consequently, the CAPM is un-testable in realistic conditions (Peirson et al, 2007). However, the theory is still relevant and will not affect the comparison of the CAPM and the FF model.

Moreover, this data set focus’s on an expansion of the business cycle in the equity market that has a more stable condition. This would be sufficient to conduct comparison test with this data. Ultimately, the focus of this paper is to find the best representation of the asset pricing model, thus this data would sufficiently justify the result. Nevertheless, the large span of data is favourable to test the theory of capital asset pricing. Information that would provide further insight is; • Diversification of asset portfolio, e. g. , bonds, security, houses prices, etc… • Diversification of equity assets, e. g. more stocks, category of assets (ASX50, ASX all ords, etc…). • The data intervals, e. g. (monthly, yearly, quarterly, daily). Structural business cycle data, e. g. (the contraction data, etc…). • Realistic assumptions undertake to measure of data. • International equity market data where government intervention is measured. • Economic or government factors that affect performance of the equity market. Data description The FF three factor model described previously, uses the raw data from varies sources, such that further manipulation is required. The raw data used has been defined below; |Variables |Definition | |meo |Historical data of monthly closing price of stock MEO Australia Limited from Jan 2003 – Dec 2007 inclusive | | |(Yahoo7, 2009d). |nxs |Historical data of monthly closing price of stock Nexus Energy Limited from Jan 2003 – Dec 2007 inclusive | | |(Yahoo7, 2009e). | |sgm |Historical data of monthly closing price of stock Sims Metal Management Limited from Jan 2003 – Dec 2007 | | |inclusive (Yahoo7, 2009g). | |prt |Historical data of monthly closing price of stock Prime Media Group Limited from Jan 2003 – Dec 2007 inclusive | | |(Yahoo7, 2009f). | |ugl |Historical data of monthly closing price of stock United Group Limited from Jan 2003 – Dec 2007 inclusive | | |(Yahoo7, 2009h). |asxsm |Historical data of monthly closing price of stock ASX small businesses ordinaries indexes from Jan 2003 – Dec | | |2007 inclusive (Yahoo7, 2009c). | |asx50 |Historical data of monthly closing price of stock ASX 50 big companies ordinaries indexes from Jan 2003 – Dec | | |2007 inclusive (Yahoo7, 2009a). | |allord |Historical data of monthly closing price of stock ASX all companies ordinaries indexes from Jan 2003 – Dec 2007| | |inclusive (Yahoo7, 2009b). | |cashrate |Historical data of 30 day cash rate interest from Jan 2003 – Dec 2007 inclusive (RBA, 2009). |kfh |Historical data of return on high book value without dividend in local market from Jan 2003 – Dec 2007 | | |inclusive (French, 2009). | |kfl |Historical data of return on low book value without dividend in local market from Jan 2003 – Dec 2007 inclusive| | |(French, 2009). | The raw data collected for stocks and market indices are in varying scalar price units, the data is collected from time series. The elasticity of measurement would be a more desirable presentation of data. To prepare further study, the concept of elasticity of prices generates new variables to normalise problem that can occur within the model. A transformation of data using log function satisfies this condition. Transformed variables are listed below; Variables |Definition | |lns1 |ln(meo) | |lns2 |ln(nxs) | |lns3 |ln(sgm) | |lns4 |ln(prt) | |lns5 |ln(ugl) | |logasxao |ln(allord) | |logasx50 |ln(asx50) | |logasxsm |ln(asxsm) | The raw data collected for a risk-free interest rate (percentage per annum) needs to be converted into monthly basis, which is dividing cash rate (30 days bill rate) by 1200, to have a 1:1 ratio with elasticity data.

So, by generating a variable ‘rf’ on stata; |Variables |Definition | |rf |cashrate/1200 | Similarly, data collected from the Ken French library; the ‘kfh’ and ‘kfl’, needs to be converted into 1:1 ratio with elasticity data. So, by generating a variable ‘hml’ on stata; |Variables |Definition | |hml |(kfh-kfl)/100 | The manipulated data for stock prices are contains serial correlation, as the data is collected from a time series. To prepare further study, new variables have to be introduced to normalise this correlation problem that can occur within the model.

A transformation of data using first derivative satisfies this condition. Transformed variables are listed below; |Variables |Definition | |dlns1 |D1. lns1 (ie. lns1t – lns1t-1) | |dlns2 |D1. lns2 (ie. lns2t – lns2t-1) | |dlns3 |D1. lns3 (ie. lns3t – lns3t-1) | |dlns4 |D1. lns4 (ie. ns4t – lns4t-1) | |dlns5 |D1. lns5 (ie. lns5t – lns5t-1) | |dlogasxao |D1. logasxao (ie. logasxaot – logasxaot-1) | |dlogasx50 |D1. logasx50 (ie. logasx50t – logasx50t-1) | |dlogasxsm |D1. logasxsm (ie. logasxsmt – logasxsmt-1) | By applying the theory of unsystematic risk elimination, risk can be cancelled out by diversification (Peirson et al, 2007).

That is the selected five shares are collected into a portfolio, the effects of company specific factors will tend to cancel each other out; this is how diversification reduces risk (Peirson et al, 2007). For example, taking the un-weighted average on individual stock to create a portfolio cancels out risk. Generating a portfolio variable ‘rport’ on stata; |Variables |Definition | |rport |(dlns1 + dlns2 + dlns3 + dlns4 + dlns5)/5 | The data is in its log differences (supposing the data is stationary and same scale) now. Further arrangement is required to fit into FF three factor model.

The variable included are; |Variables |Definition | |rprf |rport – rf | |rmrf |dlogasxao – rf | |smb |dlogasxsm – dlogasx50 | |hml |(kfh-kfl)/100 | Results From the OLS regression, the model yields; CAPM; rprf = 0. 0176 + 1. 554(rmrf) (0. 0098) (0. 3738)* FF three factor model; rprf = 0. 0154 + 1. 6402(rmrf) + 0. 6994(smb) + 0. 2195(hml) (0. 0098)(0. 3843)*(0. 4070)(0. 3115)

The significance of independent parameters provides an insight into the behaviour of the models, an individual T-test can predict the importance of each parameter under the hypothesis; H0: ? i = 0 (independent variables insignificant at ? /2) Ha: ? i ? 0 (independent variables is significant at ? /2) Where i equal the number of independent variables The result output from stata with student test; Decision rules; P(t) < ? , dismiss H0, P(t) > ? , can’t not dismiss H0 CAPM |Variable |T – stat |p-value |conclusion | |rmrf |4. 6 |0. 000 |significant | |? 0 |1. 80 |0. 077 |insignificant | From the theory of the CAPM, the expected sign for rmrf has a positive relationship, which has now been justified with the result. Under the linear condition of the CAPM, rmrf should be significant to the model; it is evidence from the above table. Another concept stated with the CAPM is that the intercept of the model should be zero, from the model the constant term is close to zero that affirms with the theory (Fama & French, 2004). Furthermore, the significant test for ? concludes with insignificance, it means the constant term should be zero – close to zero, is not sufficient. Thus, the model can dismiss the constant term from the equation, the model can be now rewritten as; rprf = 0 + 1. 554(rmrf) (0. 3738)* FF Three Factor Model |Variable |T – stat |P-value |Conclusion | |rmrf |4. 27 |0. 000 |significant | |smb |1. 72 |0. 091 |insignificant | |hml |0. 70 |0. 484 |insignificant | |? |1. 58 |0. 120 |insignificant | From the theory of the AAPM (FF three factor model), the expected sign for rmrf, smb and hml has a positive relationship, which has now justified with the result. Under the hypothesis of Fama and French (2004), rmrf, smb and hml should be significant to the model; it is evident from the above table, only rmrf has significance to the model. In turn, this contradicts the concept of the AAPM. Similarly with the CAPM, the intercept of the model should be zero, from the model the constant term is close to zero that affirms with the theory.

Furthermore, the significant test for ? 0 is concluded with insignificant. Hence, it means the constant term should be zero – close to zero, is not sufficient. Thus, the model can dismiss the constant term from the equation, the model can be now rewritten as; rprf = 0 + 1. 6402(rmrf) + 0. 6994(smb) + 0. 2195(hml) (0. 3843)* (0. 4070) (0. 3115) By comparing the regression of the CAPM and the FF three factor function, R2 = 0. 2326, and R2 = 0. 2796 respectively, implying there is 23. 24% and 27. 96% of the data explained by independent variables respectively. This demonstrates a weak relationship between dependent variables and independent parameters.

Although, the T – significance test provides undesired result for AAPM, the FF three factor model is still complying with theory (Fama & French, 2004). Further tests to the models conducted, verifies the relevance of theory to practical. To do so, the CAPM and AAPM must satisfy the small sample properties (Gauss-Markov) conditions to provide B. L. U. E. The result must be cross verified with other diagnostic tests. The first test used is the Breusch-Pagan / Cook-Weisberg heteroskedasticity test, if the models suffer heteroskedasticity, the model will be bias. The hypothesis is listed below; H0: constant variance Ha: variance is not constant

The result output from stata with Chi-square test; Decision rules; P(? 2) < ? , dismiss H0, P(? 2) > ? , can’t not dismiss H0 For CAPM |Test |Chi stat |P-value |Conclusion | |Breusch-Pagan / Cook-Weisberg |5. 09 |0. 0241 |Heteroskedasticity | |Breusch-Pagan / Cook-Weisberg, rhs iid |2. 74 |0. 0976 |Homoskedasticity | It is hard to conclude the CAPM model is suffering from heteroskedasticity, which the data is presenting, as theory suggests heteroskedasticity is highly not possible for equity market.

Theory of Autoregressive Condition Heteroskedasticity (ARCH) provides an insight into forecasting the probability of historical trends in the equity market is unrealistic. However, the data collected could coincidentally produce the heteroskedasticity result. In order to justify the hypothesis, a larger span of data is desired. In the result of error term from RHS being distributed independently and identically, the conclusion of homoskedasticity is resulted. For FF three factor model |Test |Chi stat |P-value |Conclusion | |Breusch-Pagan / Cook-Weisberg |2. 64 |0. 241 |Homoskedasticity | |Breusch-Pagan / Cook-Weisberg, rhs iid |2. 17 |0. 0976 |Homoskedasticity | It is comprehensive to conclude the FF three factor model is homoskedastic, which correspond to the expectation and theory. The result has justified the hypothesis, similarly the error term from RHS being distributed independently and identically doesn’t affect the conclusion of homoskedastic. From the finance school of thoughts, the CAPM and AAPM derived the primary linear relationship on the return on investment with respect to the risk factor from the market, that is “rprf = ? (rmrf)” (Peirson et al, 2007).

The primary parameter of ‘rprf’ should explain the relationship sufficiently, so omitted variable is not an issue. Nevertheless, Fama and French (1996), has extended the application of CAPM by adding two market related instrument; smb and hml, to explain the unexplained phenomena embedded within the model. It is knowledgeable to test for any omitted variable that could affect the model. Results are provided below; |Ramsey RESET test |F-stat |P – value |conclusion | |CAPM |0. 28 |0. 8413 |no omitted variable | |FF Three Factor Model |0. 7 |0. 5553 |no omitted variable |

The result for both models affirms with the finance theory; there are no omitted variable. However, by analysing the P – value for both models, the FF three factor model has a higher likelihood to have omitted variable, which contradicts the econometric phenomena that Fama and French suggested (1996). From the raw data, the models are derived from a time series and the sample is taken in the same equity market, it is reasonable to suspect the data implant the inefficiency of serial correlation, which would affect the outcome of model being BLUE. Nevertheless, the procedure and transformation is applied to the data to normalise the serial correlation.

Methodology such as taking the elasticity of price and taking the first derivative of elasticity would break down any correlation. To ensure the efficiency of the model an autocorrelation test is conducted, the hypothesis is listed below; H0: no serial correlation Ha: serial correlation The result output from stata with Chi-square test; Decision rules; P (? 2) < ? , dismiss H0, P (? 2) > ? , can’t not dismiss H0 | |CAPM | | |FF three factor model | |Test |Chi2 stat |P-value |conclusion |Chi2 stat |P-value |conclusion | |Breusch-Godfrey |0. 299 |0. 845 |no serial correlation |0. 027 |0. 8695 |no serial correlation | |Durbin’s alternative test |0. 268 |0. 6049 |no serial correlation |0 |0. 9851 |no serial correlation | The result affirms with the expectation of data manipulation, any implanted serial correlation has been eliminated from the methodology adopted. As mention previously, the data is collected from the same equity market; the model could also be affected by the problem of multicollinearity. Even the sampling techniques should eliminate multicollinearity, it is reasonable to verify the efficiency of the model by conducting a VIF analysis.

Hypothesis is listed below; H0: no multicollinearity Ha: multicollinearity The result output from stata with VIF test; Decision rules; VIFstat ; 10, dismiss H0, VIFstat ; 10, can’t not dismiss H0 |variables |VIF |1/VIF |conclusion | |rmrf |1. 09 |0. 9181 |no multicollinearity | |hml |1. 09 |0. 9208 |no multicollinearity | |smb |1 |0. 9968 |no multicollinearity | |mean VIF |1. 06 | | |

It should be noted that the CAPM will not have a multicollinearity issue, as the model has one independent parameter only, that being a simple regression (such that, it is not possible to correspond to other independent variable by definition)(Verbeek, 2008). From the result, it could be concluded that there is no multicollinearity as expected. As OLS operations could only apply to the estimation of the CAPM and AAPM, if the data is stationary, the transformation of data is therefore necessary. This would constrain the parameters into a stochastic model, that has a integrated data with order 0 [I(0)], consequently could generate an Auto-Regressive model (Verbeek, 2008).

The Auto-Regressive model theory explains that the model could possibly have auto-correlated disturbances that affect the efficiency of the model (Verbeek, 2008), inherited from the transformation of data (which is not cover under the scope of this study). The Dickey Fuller stationary test was undertaken to determine whether the data was stationary. The hypothesis is set out below to conduct the test. H0: ? i = 1, unit root Ha: ? i ; 1, stationary The result output from stata with Dickey Fuller test; Decision rules; P(z(t)) ; ? , dismiss H0, P(z(t)) ; ? , can’t not dismiss H0 |variables |Z(t) stat |p-value |conclusion | |rprf |-7. 495 |0. 0000 |stationary | |rmrf |-8. 230 |0. 0000 |stationary | |smb |-7. 247 |0. 0000 |stationary | |hml |-7. 170 |0. 000 |stationary | As theory suggests (Verbeek, 2008), all the parameters are stationary. It can subsequently be concluded that the parameter is integrated order 1. This could create an Auto-Regressive model, such that, the techniques of the Auto-Regressive model (e. g. ARCH, GARCH etc. ) may apply as instruments for estimates of the CAPM model. Additionally, finding the co-integrative vector in terms of rprf and rmrf does not fall within the scope of this paper, however it is a potential area of interest for further empirical study. For this empirical study, the aim is to justify the validity of FF three factor model compare to CAPM.

It is necessary to conduct a model significant test respectively, using joint significant test. Under the CAPM theory, expected return with respect to risk is explained with the only variable ‘rmrf’, which was early justified, the joint significance test would be on the parameters embedded within FF three factor model. FF three factor model jointly significant test H0: ? 1 = ? 2 = ? 3 = 0 Ha: ? 1 ? ?2 ? ?3 ? 0 Decision rules; P(t) ; ? , dismiss H0, P(t) ; ? , can’t not dismiss H0 | |F – stat |P – value |conclusion | |FF three factor model |7. 12 |0. 0004 |significant |

It should be noted that the FF three factor model is significant to explain the phenomena of excess portfolio return. Another aspect of interest to this paper, is whether smb and hml would add value to explain the phenomena of excess portfolio return. Therefore another significant test is performed. The FF three factor model parameters (smb and hml) jointly significant test H0: ? 2 = ? 3 = 0 Ha: ? 2 ? ?3 ? 0 Decision rules; P(t) ; ? , dismiss H0, P(t) ; ? , can’t not dismiss H0 | |F – stat |P – value |conclusion | |FF three factor model parameter |1. 80 |0. 757 |insignificant | From the result, the insignificance of the two variables contradicts to the recent scholar studies. Furthermore, it could be concluded that the FF three factor model has the tendency of reverting back to the CAPM that it has derived from. This validates the CAPM as a better representation (given the current data) of deriving the relationship of excess return on portfolio with respect to risk. Ultimately, the additional market related variables of FF three factor model can now be dropped; both models can be now presented as; CAPM rprf = 1. 554(rmrf) (0. 3738)* Fama & French AAPM rprf = 1. 6402(rmrf) (0. 3843)* Discussion

From the finance school of thoughts, the CAPM and AAPM derived the primary linear relationship on the return on investment with respect to the risk factor from the market, that is “rprf = ? (rmrf)” (Peirson et al, 2007). The primary parameter of ‘rprf’ should explain the relationship sufficiently. Nevertheless, Fama and French (2004), have extended the application of the CAPM by adding two market related instruments; smb and hml, when trying detail the unexplained phenomena embedded within the model. In the results the CAPM and FF three factor function, there is 23. 24% and 27. 96% of the data explained with the independent variables respectively.

This possibly contradicts the CAPM and AAPM theory, as the explanation of risk phenomena is expressed with one variable (market Beta), which should theoretically has high R2. From the theory of the CAPM, the expected positive relationship has now justified with the results. Under the linear condition of the CAPM, the parameter of the excess market return with respect to the risk-free market (rmrf) has proven significant to the model. Another concept with the CAPM is that under the unlimited lending and borrowing assumption, the intercepts of the model zero, also affirms with the theory (Fama & French, 2004). In contrast to AAPM theory (FF three factor model), the parameters propose a positive relationship as shown in the results.

Under the hypothesis of Fama and French (2004), all parameter should be significant to the model; it is evidence from the result, only rmrf has significance to the model, meaning to say, there is an indication of other influence factors is not possible. Thus, contradicts the concept of AAPM. The CAPM and FF three factor model should not undertake any heteroskedasticity problem, as theory suggests that heteroskedasticity is highly not possible for equity market (Peirson, et al, 2007). This is evidenced with the theory of Autoregressive Condition Heteroskedasticity (ARCH) provides an insight of forecasting probability of following previous trend in equity market is unrealistic (Verbeek, 2008).

From the realization of autoregressive model theory, applying autoregressive analysis as an instrument for estimation of the model would be a potential area of interest for further empirical study. It should also be noted that this analysis has performed under certain constrain, which could possibly alter the result. In order to remove the bias outcome from the data given, instruments that related to other factors should be considered. Few possible instruments that could provide a better insight to CAPM are suggested below; • Using diversification of asset portfolio data, eg, bonds, security, houses prices, etc… • Gather more diversified equity assets data, eg.

More stocks, category of assets (ASX50, ASX all ords, etc…) • Using a larger data intervals, eg 20+ years of equity data • Include structural business cycle data, eg the contraction data, 2008 financial crisis data and 2000 Asian finance market breakdown… • Collect the data under realistic assumptions. i. e. , dividend yield for stock compare to risk • Taking data where government intervention is measured. Eg, Keynesian monetary policy related to market performance – in 1998 HK SARS government has injected funds to stabilise the equity market (HKSAR, 1999) • Economic or government factors that affect performance of equity market. Eg, subsidiary to companies and sectors Conclusions

Overall, the theory contradicts the result from the jointly significance test, it could be concluded that the FF three factor model has the tendency of reverting back to CAPM that it has derived from. This validates the CAPM, could be a better representation (given the current data) of deriving the relationship of excess return on portfolio with respect to risk. Thus, it is an indication of further empirical study is required with the inclusion of addition data and instruments. In addition, another aspect of interest to this paper, is whether CAPM has the Auto regressive model condition, the empirical study would add value to explain the phenomena of excess portfolio return with the market.

Theoretically this is not possible; however, the given data display some interesting phenomena that suggest an insight to Autoregressive model. The analyses of this paper have derived the validity of the Fama and French (FF) model and the efficiency of the Capital Asset Pricing Model (CAPM) using diagnostic tests. It could be concluded that both models provide a BLUE result, meaning to say, both model is efficiently explaining the market phenomena. However, the results have failed to conclude Fama and French alternative asset pricing model (AAPM) has extended the application of CAPM. It should also be noted, the theoretic constrain and human restriction, such as unrealistic assumption and data span, has posted bias outcome of the model.

The undesired conclusion could be eliminated with further study with better instruments and data collection. Furthermore, after the study of ‘smb’ and ‘hml’, it could be stated that; there are some relevant instrument that propose significance to the model, which would be worth to further study. References Ball, R, (1978). ‘Anomalies in Relationships Between Securities’ Yields and Yield-Surrogates. ’ Journal of Financial Economics, Vol. 6, No. 2, p103-26, viewed 16th April, 2009, Basu, S, (1977). ‘Investment Performance of Common Stocks in Relation to Their Price – Earnings Ratios: A Test of the Efficient Market Hypothesis’ Journal of Finance. Vol. 32, No. 3, p633-82, viewed 20th April, 2009,

Fama, EF, and. French, KR, (1996), ‘Multifactor Explanations of Asset Pricing Anomalies’, Journal of Finance, Vol. 51, No. 1, March, p55-84. Viewed 25th of March, 2009, Fama, EF, and. French, KR, (2004), ‘The Capital Asset Pricing Model: Theory and Evidence’, Journal of Economic Perspectives, Vol. 18, No. 3, summer, p25-46, viewed 29th March, 2009, HKSAR, (1999), ‘HKSAR – The Key Issues 1998/99’, viewed 5th May, 2009, Lintner, J. (1965). ‘The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,’ Review of Economics and Statistics. Vol. 47, No. 1, p13-37, viewed 26th April, 2009, Markowitz, H. (1959). Portfolio Selection: Efficient Diversification of Investment’. Cowles Foundation Monograph No. 16. New York: John Wiley & Sons, Inc. Peirson, G, et al (2007), ‘Chapter 7 Portfolio Theory and Asset Pricing’, Business Finance, 9th ed. , McGraw-Hill, Australia, p186-219 Sharpe, WF. (1964). ‘Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk’, Journal of Finance. Vol. 19, No. 3, p425- 42 viewed 21st April, 2009, Verbeek, M. , (2008), A Guide to Modern Econometrics, 3rd ed. , Chichester UK and New York, Wiley. Data Sources French, KR, (2009) ‘Country Portfolios formed on B/M, E/P, CE/P, and D/P [ex. Dividends]’, viewed 14th of April, 2009,

RBA, (2009) ‘Cash Rate – Overnight – Interbank – Securities and Interbank Overnight Cash Rate’ viewed 14th of April, 2009, Yahoo7, (2009a) ‘^ALFI: Historical Prices for S&P/ ASX 50 – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009b) ‘^AORD: Historical Prices for ALL ORDINARIES – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009c) ‘^AXSO: Historical Prices for S&P/ ASX SMALL ORDINARIES – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009d) ‘MEO. AX: Historical Prices for MEO AUST FPO – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009e) ‘NXS. AX: Historical Prices for NEXUS FPO – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009f) ‘PRT.

AX: Historical Prices for PRIME TV FPO – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009g) ‘SGM. AX: Historical Prices for SIM METAL FPO – Yahoo! 7 Finance’, viewed 14th of April, 2009, Yahoo7, (2009h) ‘UGL. AX: Historical Prices for UNITED GRP FPO – Yahoo! 7 Finance’, viewed 14th of April, 2009, Appendices Table 1 Estimates of CAPM |Parameters |Estimates |Standard Error | |rmrf |1. 554 |(0. 3738)* | |constant |0. 0176 |(0. 098) | Table 2 Estimates for FF Three factor model |Parameter |Estimates |Robust Standard Error | |rmrf |1. 6402 |(0. 3843)* | |smb |0. 6994 |(0. 4070) | |hml |0. 2195 |(0. 3115) | |constant |0. 154 |(0. 0098) | *A log file is attached at the end of this paper, and a soft copy of the do file and log file is attached when submitting the soft copy. * ————————————————————————————————————————————————- log: f:uniapplied econometricfinal. log log type: text opened on: 5 May 2009, 17:03:40 . . version 10. 0 . clear all . set more off . . insheet using “f:uniapplied econometricdata. csv”, clear (11 vars, 60 obs) . . /* > Read the data in from a comma delimited file. gt; Assumes data consists of columns of untransformed variables that have > been downloaded (and ordered correctly by date) from the different web sites. > Assumes the following names for variables (all lower case): > 1. The equities meo, nxs, sgm, prt, ugl > 2. allord = the all ordinaries index > 3. asx50 = the S&P ASX 500 index > 4. asxsm = the S&P ASX small ordinaries index > 5. cashrate = the 30 day Bank Bill rate > 6. kfh and kfl are the Ken French High and Low book to market > portfolio returns, (own currency). > These names are included in the first line of the csv file all in lower case > */ . . *get logs of equities and indices . gen lns1 = ln(meo) . gen lns2 = ln(nxs) gen lns3 = ln(sgm) . gen lns4 = ln(prt) . gen lns5 = ln(ugl) . . gen logasxao = ln(allord) . gen logasx50 = ln(asx50) . gen logasxsm = ln(asxsm) . . * Create monthly timeline starting january 2003. . gen time=_n-1 +516 . tsset time, monthly time variable: time, 2003m1 to 2007m12 delta: 1 month . . *Get risk free rate in same scale. . *That is to base 100 and monthly not annually. . gen rf = cashrate/1200 . . * Get log differences. . * That is monthly continuous compond returns . gen dlns1 = D1. lns1 (1 missing value generated) . gen dlns2 = D1. lns2 (1 missing value generated) . gen dlns3 = D1. lns3 (1 missing value generated) . gen dlns4 = D1. ns4 (1 missing value generated) . gen dlns5 = D1. lns5 (1 missing value generated) . . gen dlogasxao = D1. logasxao (1 missing value generated) . gen dlogasx50 = D1. logasx50 (1 missing value generated) . gen dlogasxsm = D1. logasxsm (1 missing value generated) . . *Get return on portfolio; the unweighted average of the five individual stock. . gen rport = (dlns1 + dlns2 + dlns3 + dlns4 + dlns5)/5 (1 missing value generated) . . *Get excess returns on my portfolio and the market portfolio. . gen rprf = rport – rf (1 missing value generated) . gen rmrf = dlogasxao – rf (1 missing value generated) . . *Get the other two Fama French Factors . * 1.

Create hml from Ken French data . gen hml = (kfh-kfl)/100 . . * 2. Create smb . gen smb = dlogasxsm – dlogasx50 (1 missing value generated) . . * 3. Regress the CAPM . regress rprf rmrf Source | SS df MS Number of obs = 59 ————-+—————————— F( 1, 57) = 17. 28 Model | . 086764702 1 . 086764702 Prob > F = 0. 0001 Residual | . 286264845 57 . 00502219 R-squared = 0. 2326 ————-+—————————— Adj R-squared = 0. 2191 Total | . 373029547 58 . 006431544 Root MSE = . 07087 —————————————————————————– rprf | Coef. Std. Err. t P>|t| [95% Conf. Interval] ————-+—————————————————————- rmrf | 1. 553866 . 3738425 4. 16 0. 000 . 8052595 2. 302473 _cons | . 0175815 . 0097607 1. 80 0. 077 -. 0019639 . 0371269 —————————————————————————— . predict e, residual (1 missing value generated) . * 3b. do the diagnostic tests . estat hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of rprf chi2(1) = 5. 09 Prob > chi2 = 0. 0241 estat hettest, rhs iid Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: rmrf chi2(1) = 2. 74 Prob > chi2 = 0. 0976 . estat ovtest Ramsey RESET test using powers of the fitted values of rprf Ho: model has no omitted variables F(3, 54) = 0. 28 Prob > F = 0. 8413 . estat bgodfrey, nomiss0 Breusch-Godfrey LM test for autocorrelation ————————————————————————— lags(p) | chi2 df Prob > chi2 ————-+————————————————————- 1 | 0. 99 1 0. 5845 ————————————————————————— H0: no serial correlation . estat durbinalt Durbin’s alternative test for autocorrelation ————————————————————————— lags(p) | chi2 df Prob > chi2 ————-+————————————————————- 1 | 0. 268 1 0. 6049 ————————————————————————— H0: no serial correlation . estat dwatson

Durbin-Watson d-statistic( 2, 59) = 1. 836838 . estat vif Variable | VIF 1/VIF ————-+———————- rmrf | 1. 00 1. 000000 ————-+———————- Mean VIF | 1. 00 . . * 4. Regress the Fama & French model . regress rprf rmrf smb hml Source | SS df MS Number of obs = 59 ————-+—————————— F( 3, 55) = 7. 12 Model | . 104307825 3 . 034769275 Prob > F = 0. 0004 Residual | . 268721722 55 . 004885849 R-squared = 0. 2796 ————-+—————————— Adj R-squared = 0. 403 Total | . 373029547 58 . 006431544 Root MSE = . 0699 —————————————————————————— rprf | Coef. Std. Err. t P>|t| [95% Conf. Interval] ————-+—————————————————————- rmrf | 1. 640181 . 384265 4. 27 0. 000 . 8700967 2. 410265 smb | . 6993589 . 4070662 1. 72 0. 091 -. 11642 1. 515138 hml | . 2195499 . 3115376 0. 70 0. 484 -. 4047855 . 8438852 _cons | . 0154278 . 0097687 1. 58 0. 120 -. 0041492 . 350048 —————————————————————————— . * 4b. do the diagnostic tests . estat hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of rprf chi2(1) = 2. 64 Prob > chi2 = 0. 1045 . estat hettest, rhs iid Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: rmrf smb hml chi2(3) = 2. 17 Prob > chi2 = 0. 5388 . estat ovtest Ramsey RESET test using powers of the fitted values of rprf Ho: model has no omitted variables F(3, 52) = 0. 70 Prob > F = 0. 5553 . estat bgodfrey, nomiss0 Breusch-Godfrey LM test for autocorrelation ————————————————————————– lags(p) | chi2 df Prob > chi2 ————-+————————————————————- 1 | 0. 027 1 0. 8695 ————————————————————————— H0: no serial correlation . estat durbinalt Durbin’s alternative test for autocorrelation ————————————————————————— lags(p) | chi2 df Prob > chi2 ————-+————————————————————- 1 | 0. 000 1 0. 9851 ————————————————————————– H0: no serial correlation . estat dwatson Durbin-Watson d-statistic( 4, 59) = 1. 965996 . estat vif Variable | VIF 1/VIF ————-+———————- hml | 1. 09 0. 918072 rmrf | 1. 09 0. 920794 smb | 1. 00 0. 996797 ————-+———————- Mean VIF | 1. 06 . . * 5. Test the FF factors as an addition to CAPM . test (smb=0) (hml=0) (rmrf=0) ( 1) smb = 0 ( 2) hml = 0 ( 3) rmrf = 0 F( 3, 55) = 7. 12 Prob > F = 0. 0004 . test (smb=0) (hml=0) ( 1) smb = 0 ( 2) hml = 0 F( 2, 55) = 1. 80 Prob > F = 0. 1757 . . * 6.

Test the data for stationary. . dfuller rprf, trend lags(0) Dickey-Fuller test for unit root Number of obs = 58 ———- Interpolated Dickey-Fuller ——— Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value —————————————————————————— Z(t) -7. 495 -4. 132 -3. 492 -3. 175 —————————————————————————— MacKinnon approximate p-value for Z(t) = 0. 0000 . dfuller smb, trend lags(0)

Dickey-Fuller test for unit root Number of obs = 58 ———- Interpolated Dickey-Fuller ——— Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value —————————————————————————— Z(t) -7. 247 -4. 132 -3. 492 -3. 175 —————————————————————————— MacKinnon approximate p-value for Z(t) = 0. 0000 . dfuller rmrf, trend lags(0) Dickey-Fuller test for unit root Number of obs = 58

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Econometric Analysis of Capm. (2018, Jan 29). Retrieved from https://graduateway.com/econometric-analysis-of-capm/

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