The proportion of return has varied considerably from the start, ranging from a loss of more than 6% to a gain of more than21%. The average monthly return on this portfolio over the 241 months recorded was 1.8%. Over the entire period, the returns ranged from -31.69% to 37.04%
In the result of the CAPM model regression below, the outcome Y variable is the adjusted value weighted return-risk free rate. The predictor x variable is the market risk premium. Alpha represents the value that a portfolio adds or subtractsfrom the portfolio’s return. In this case alpha is 0.0091, which means the portfolio has outperformed the benchmark index by 0.91%. Beta is a measure of systematic risk of a portfolio in comparison to the market as a whole. The portfolio beta in this case is 1.2139, which means it is 21.39% more volatile than the market.
R-squared, the coefficient of determination is the ratio of the explained sumof squares to the total sum of squares. The higher R square, the closer the estimated regression equation fits the sample data. A value of R square close to one shows an excellent overall fit. R2 measures percentage of the variation of y around Y mean that is explained by the regression equation. In the case of the CAPM regression for the Portfolio A, the value of R-square is 0.3845. Therelationship between X (market risk premium) and Y (portfolio return-risk free rate) is not very strong, which means the regression line is only slightly useful in describing the variation.
The t-values test the hypothesis that the coefficient is different from 0. To reject this, you need a t-value greater than 1.96 (for 95% confidence). In this case the value for t is 2.0493, so the hypothesis can berejected.
Two-tail p-values test the hypothesis that each coefficient is different from 0.To reject this, the p-value has to be lower than 0.05. In this case the p value is 0.0415, so the hypothesis can be rejected. SMB (small minus big) and HML (high minus low) are the variables that have some significant impact on real return.
The significance of F indicates the probability that theregression output could have been obtained by chance. In this case, the significance of F is 0, so there is a 0% chance that the regression output was merely a chance.
Below is the Fama-French 3 factor model regression result for the Portfolio A. The output variable Y is the adjusted value –weighted rate of risk-free return. The predictor x variables in this case are the market risk premium, SMB (smallminus big) and HML (high minus low).
Alpha in this case indicates that the portfolio has outperformed the market by 1.27%.
The beta (measure of systematic risk) of this portfolio is 1.0944, which indicates it is 9.44% more volatile than the market. The other two risk factors, the betas with respect to SMB and HML, are negative. A negative beta means that the asset generally moves opposite thebenchmark: the asset tends to move up when the benchmark moves down, and the asset tends to move down when the benchmark moves up.
The R2 value for the Fama-French 3 factor model in this case is higher than the value for the CAPM model. This possibly indicates the better accuracy of the Fama-French 3 factor model. The relationship between X (market risk premium) and Y (portfolio return-risk freerate), although stronger than in the previous model, is still not very strong. The regression line is perfectly useful in describing the variation, although it does have some accuracy.
Two-tail p-values test the hypothesis that each coefficient is different from 0.To reject this, the p-value has to be lower than 0.05. In this case the p value is 0.0043, so the hypothesis can be rejected. SMB...