Applying Capital Asset Pricing Model - Coursework Example

Financial Modeling: Stock Market By: Foundation Course- Tutor: University of: Department of: 15th May 2016 Section A A1. Theoretical Assumptions and implications of Capital Asset Model (CAPM) As stated by Sharpe (1964) and Lintner (1965), Capital Asset Model (CAPM) is a model that describes the relationship between risk and expected return and has a number of assumptions that investors have to be take into consideration while trading in the stock market. These assumptions are as follows:- CAPM assumes that investors have preference for more returns as compared to less return thus they tend to be risk averse so as to maximize their return output. Investors while trading in the stock market tend to be risk takers as long as the anticipated returns output will be as high as possible (Dempsey 2013). Investors can always borrow and lend at risk free rate; although this assumptions is unattainable in reality, it is often believed that the rate at which individual investors borrow funds is never prone to any sort of risks (Dempsey 2013).Therefore, the lowest required return tends to be slightly lower than what the model calculates There are always no market related frictions such as costs for doing transactions, taxes or even restricted short-selling. While trading in the stock market, investors do not take into account other costs associated with the stock trading, for instance, costs such as advertisement expenses, administrative expenses and tax expenses among others are often assumed (Zabarankin, Pavlikov and Uryasev 2014). It is always assumed that investors have accessibility to all the information related to stock trading, which is, they can easily make decisions as to when to buy and sell their stocks in the market (Zabarankin, Pavlikov and Uryasev 2014). . A2. The Extent to which a breach of the assumptions invalidate the CAPM model As a result of the failure of CAPM in empirical tests, its application is often considered invalid in the following ways:- Based on the model’s assumptions of the probability belief that active and potential investors tend to be in agreement with the allocation of returns. However, there is always a conflicting possibility in that active and potential investors’ expectations are biased hence causing the market prices to be inefficient. Therefore, psychological assumption such as overconfidence-based asset pricing model should be used in addition to CAPM (Gospodinov, Kan and Robotti 2014). CAPM fails to adequately illustrate the variation in the stock market, for instance, according to the empirical studies that have been undertaken, it has been confirmed that low beta stocks may offer absolutely higher returns than the model’s prediction (Elbannan 2015). With the model’s assumption that given certain level of expected returns, active and potential investors tend to prefer higher risk (high variance) to lower risks and conversely with a given level of risk will be pleasant with higher returns as compared to lower returns, it does not give adequate consideration to those active and potential investors who have no problem with lower returns at high risks (Ruffino 2014). CAPM’s assumption that all the active and potential investors will take into consideration all their existing assets and optimize them in one portfolio, has an absolutely sharp contradiction to those portfolios that are held by individual investors (Ruffino 2014). This is due to the fact that, traders tend to have fragmented portfolios or even multiple portfolios thus one portfolio may not give the true picture of the expected returns realized by an investor in the stock market. A3: Empirical test of the CAPM: Using the excess return model:  Test:  For the regression result for the first model which runs from the year 1980 to 2009 that is a panel data for 30 years. For the manufacturing industry, Table 1.1: Model Summary (1980-2009) From table 1.1, the r-square for manufacturing is 0.658195 while that for shop is 0.602846 > 0.1 hence the model is fit and good for analysis. The significance level of the market portfolio using manufacturing and shop industry portfolio are shown in appendix 1 and extract are shown in the table 1.2 below Table 1.2: Coefficient analysis for manufacturing and shop (1980-2009)   Coefficients Standard Error t Stat P-value Manufacturing Intercept 0.189993 0.184692 1.028703 0.304314 Mkt-RF 1.049882 0.039986 26.25607 1.82E-85   Coefficients Standard Error t Stat P-value Shop Intercept 0.08297 0.206011 0.402748 0.687374 Mkt-RF 1.042133 0.044602 23.36518 5.37E-74 From the results in table 1.2 above, the p-value for manufacturing is 1.82E-85< 0.05 while for shop is 5.37E-74 < 0.05 hence statistically significance and leading to rejection of null hypothesis of Test: The market beta for manufacturing is 1.049882 while that for shop 1.042133 from table 1.2 above. Since the market beta is greater than one hence risky portfolio. For the year 1990-1999 the model summary are shown below Table 1.3: Model summary 1980-1990 Manufacturing Shop Multiple R 0.823697 0.85477 R Square 0.678477 0.730631 Adjusted R Square 0.675753 0.728349 Standard Error 3.423918 2.939456 Observations 120 120 From the analysis, the R-squared showed 0.678477 and 0.730631 for manufacturing and shop respectively. The model is fit since R-square is greater than 0.1 in both cases. For significance level and beta coefficient the results are shown in the table 1.4 below Table 1.4: regression results (1980-189) Manufacturing   Coefficients Standard Error t Stat P-value Intercept 0.069462 0.315867 0.219909 0.826322 Mkt-RF 1.015103 0.064329 15.77985 7.47E-31 Shop   Coefficients Standard Error t Stat P-value Intercept -0.07943 0.271174 -0.29291 0.770107 Mkt-RF 0.988024 0.055227 17.89026 2.1E-35 From the results in table 1.4 above, the p-value for manufacturing is 7.47E-31< 0.05 while for shop is 2.1E-35 < 0.05 hence statistically significance and leading to rejection of null hypothesis of Test: On the other hand, the market beta for manufacturing is 1.015103 while that for shop 0.988024 from table 1.4 above. Since the market beta is greater than one for the manufacturing, its confirms that the portfolio tends to be risky however for the shop the beta is less than one thus favorable The third empirical review is analysis of the monthly returns for the next 10 years from the year 1990-1999. The SPSS results are shown in appendix 3. Table 1.5: Model fit 1990-999 Manufacturing Shop Multiple R 0.72374 0.705692 R Square 0.523799 0.498001 Adjusted R Square 0.519764 0.493747 Standard Error 3.266003 3.772581 Observations 120 120 The r-square shows that manufacturing is 0.523799 and shop is 0.498001 > 0.1 hence model is fit. For significance level, the results are shown below Table 1.6: Regression results (1990-1999) Manufacturing   Coefficients Standard Error t Stat P-value Intercept -0.1983 0.308635 -0.64252 0.521784 Mkt-RF 0.854563 0.075009 11.39274 9.81E-21   Coefficients Standard Error t Stat P-value Shop Intercept -0.4842 0.356506 -1.35819 0.176993 Mkt-RF 0.937438 0.086644 10.81944 2.26E-19 From the results the p-value is 9.81E-21 0.05 hence is not statistically significance. Gender on the other hand gives a p-value of 5.88E-08< 0.05 hence is statistically significance at 95% significance level, age p-value is 0.691697 which is >0.05, not statistically significance, marital status gives a p-value of 0.259017 >0.05 indicating that it is not statistically significance and lastly union which gives P-value of 0.005088 Read More