The Capital Asset Pricing Model (CAPM)

Added on - 28 May 2020

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Part 1:1.1IntroductionThe Capital Asset Pricing Model is used to analyze the tradeoff between the risk and the returnof the stock. It is considered as one of the most important and valuable contribution to thefinance. It is known that to earn higher return the investors have to take higher risk, however itis important to know how much risk is optimal. The CAPM model was first introduced by theSharpe in 1964 followed by Treynor in 1961. Furthermore, later academicians such as Mossin(1966), Black in 1972 has also contributed to the Capital Asset Pricing Model(Lee et al., 2016;Pennacchi, 2008).One of the main assumptions of the CAPM model is that the positive tradeoff between risk andreturn asserts that the expected return on any assets/stock is a positive function of only onevariable which is the market beta(Arx and Ziegler, 2008; Tille and Wincoop, 2013).In the current research the Capital Assets Pricing Model has been tested for 6 different portfolios.Monthly return for the entire portfolio and the return on market have been taken intoconsideration. The risk free rate has been used to calculate the excess return for each portfolio.The CAPM model has been tested using the regression model whereas the goodness of fit of themodel has been tested on the basis of R squared and the F statistics. Since the data is time seriesfollowing hypothesis has been tested which is the standard time series CAPM model:1.2HypothesisNull Hypothesis: The intercept is not significantly equal to zero.Alternative hypothesis the intercept is significantly equal to zero.
Correlation matrixResults from the correlation matrix are shown in the table below and the results show that thereturn on the market and the returns on the six different portfolios included in the study arepositively and significantly correlated. In other words, if one variable increases the othervariables also increases. However the correlation do not guarantee the causation .Correlationsmrt_rfSmall lowSmall medSmall highBig lowBig medBig highmrt_rfPearson Correlation1.868**.880**.840**.973**.927**.874**Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492Small lowPearson Correlation.868**1.933**.871**.823**.722**.699**Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492Small medPearson Correlation.880**.933**1.968**.800**.815**.814**Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492Small highPearson Correlation.840**.871**.968**1.739**.799**.837**Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492Big lowPearson Correlation.973**.823**.800**.739**1.866**.789**Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492Big medPearson Correlation.927**.722**.815**.799**.866**1.899**Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492Big highPearson Correlation.874**.699**.814**.837**.789**.899**1Sig. (2-tailed).000.000.000.000.000.000N492492492492492492492**. Correlation is significant at the 0.01 level (2-tailed).1.3Regression analysisFor all six different portfolios six different regression model was performed and the result arediscussed below.
A)Small low and market returnAs the summary output shows the value of R squared is 0.75 which shows that the goodness offit is good. It shows that 75 % of the variation in the dependent variable is explained by theindependent variable and the rest of the variation is due to some other factors.SUMMARYOUTPUTRegression StatisticsMultiple R0.868463R Square0.754228Adjusted RSquare0.753726Standard Error3.306693Observations492Table1Summary output from the regression analysisANOVAdfSSMSFSignificance FRegression116441.9316441.931503.7137141.9872E-151Residual4905357.76610.93422Total49121799.7Table2ANOVA table from regression analysisSimilarly the results from the ANOVA table also shows that the F statistic of 1503.71 isstatistically significant which as the p value is less than 0.05. So the cumulative impact of theindependent variable on the dependent variable is statistically significant.
CoefficientsStandardErrort StatP-valueLower95%Upper95%Lower95.0%Upper95.0%Intercept-0.221110.150452-1.469630.1423048-0.5167197130.074503-0.516720.074502596XVariable11.3030580.03360338.777751.9872E-1511.2370339611.3690821.2370341.369082421Table3Results for regression coefficientsThe results shows that the intercept is not 0 and the p value is also more than 0.05 we cannotreject the null hypothesis. So the CAPM do not hold for this portfolio. The beta in this case ismore than 1 which shows that the return on portfolio is higher than the risk free rate(Çelik,2012).B)Small mid and market returnRegression StatisticsMultiple R0.880209R Square0.774769Adjusted RSquare0.774309StandardError2.454692Observations492Table4Summary output from the regression analysisIn case of small mid portfolio also the R square and the adjusted R squared are both 0.77indicating that the change in the market return explains 77 % change in the return in theportfolio, which is considered to be a very good goodness of fit.ANOVA
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