Financial Economics 2012- Quantitative Methods II, Statistics Project - Essay Example

The CAPM gives an understanding about the kinds of risks that affect the return through assessment of these risks. The model uses the beta of a specific security, the risk-free rate of return, and the market return to compute the required return of an investment to its expected risk. The CAPM Model and its uses The formula for the beta coefficient of stock is given by: Beta Coefficient of Stock (?) = ?rm / ?2m ?rm = the Covariance between the returns on asset i and the market portfolio ?2m = the Variance of the market portfolio This beta value serves as an important measure of risk for individual assets (portfolios) that is different from ?

2m, it measures the non-diversifiable part of risk. It is an indirect measure which compares the systematic risk (risk which cannot be eliminated by portfolio diversification) associated with a company’s shares with the unsystematic risk (risk which can be eliminated by portfolio diversification) of the capital market as a whole. If a beta value of 1 is obtained, the systematic risk associated with the shares is the same as the systematic risk of the capital market as a whole. . = 0.016191667 - -2.205(0.006838583) = 0.03127. Hence the formula is given by: MOBIL =0.

03127 – 2.205 RKFREE Discussion of the regression equations The two regression equations can be interpreted as follows: The first regression equation can be concluded that a unit increase in the market portfolio results into an increase of the monthly returns of Mobil Oil by 0.7135 units. Changing this into monthly percentages, a 10% increase in the market portfolio results into an increase of the monthly returns of Mobil Oil by 7.135%. In the second regression equation, a unit increase in return of the 30 day U.S. Treasury bills leads to a decrease of the monthly returns of Mobil Oil by 2.21 units. The bills are risk free and hence cannot be used to model expected returns.

Hypothesis testing including Null vs Alternative Hypothesis The hypothesis to be tested in this analysis will employ a t-test. This t-test is used because we need to find whether there is a significant difference between the means of MOBIL and MARKET, and between MOBIL and RKFREE. The test will determine whether monthly returns of Mobil Oil (MOBIL) and the market portfolio (MARKET) have a similar mean using a 95% confidence level. Hypothesis 1 Null Hypothesis, H1: Mean of MOBIL = Mean of MARKET Alternative Hypothesis, H­0: Mean of MOBIL ?

Mean of MARKET It is assumed that the variances are unequal. From the analysis, the computed t-statistic (0.2285) is not greater than the tabulated t-statistic (1.9801). Hence we fail to reject the null hypothesis and conclude that the mean of the monthly returns of Mobil Oil is equal to that of the market portfolio at 95% confidence level. The 95% confidence