Question Variable - Parameter Coefficients Standard Errors t-Statistics Intercep

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Question Variable - Parameter Coefficients Standard Errors t-Statistics Intercept - 1.5237 0.6321 2.4108 (Mkt-RF)t - 1.1462 0.1450 7.9023 SMBt - SMB 0.3164 0.2107 1.5015 HMLt - HML -0.8347 0.2236 -3.7323 Adjusted R2 0.2557 F-ratio 39.7390 Number of observations 351 Durbin-Watson 1.8941 a) Interpret the model from a financial perspective. That is, what are these four estimated coefficients telling you about Apple’s systematic stock market performance? Does each make theoretical and intuitive sense? Explain your answers. (Note that a non-zero intercept (alpha ()) denotes the presence of arbitrage opportunities.) b) Comment briefly on the statistical significance of the intercept and each of the independent variables as indicated by their t-ratios and on the statistical significance of the model as a whole as indicated by the F-ratio. What is the interpretation of R2? Running this regression model results in a beta () value of 1.3596, an R2 of 0.2106 and an F-ratio of 93.1237. 1) Has there been any appreciable gain in predictive power with the three factor model? (In other words, did the three factor model do a better job than CAPM of predicting Apple’s stock price?) 2) Conduct a t-test on the null hypothesis that beta () truly equals 1.3596 given the above estimate of 1.1462 and its standard error of 0.1450. (This is basically asking whether or not the Beta estimated by each model are statistically different from one another.) 3) Finally, comment on the CAPM intercept term of 1.2041 which is statistically different from zero. What are the financial or practical implications for investors? Variable - Parameter Coefficients Standard Errors t-Statistics Intercept – 1.2041 0.6432 1.8720 (Mkt-RF)t – 1.3596 0.1409 9.6501 h) For January 2014, the actual value of (Mkt-RF) was minus 3.26% (-3.26), SMB was plus 0.85% (+0.85) and HML was minus 1.83% (-1.83). Given the three factor regression output at the beginning of this document and the actual January values for the variables here, what does the model predict for Apple’s excess return (RAAPL-RF) in January? How does that compare to the actual value for (RAAPL-RF) which was minus 10.77% (-10.77) for January 2014? Is the difference statistically significant?

Explanation / Answer

The Regression model is:

Return on Apple stock=Ri=1.5237+1.1462*(Mkt-RF)+0.3164*SMB-0.8347*HML

a)The returns of the Apple is well explained by the three factors of Market risk premium ,small minus Big companies returns premium SMB and the high minus low Book to market value ratios returns premium .The returns are higher the higher the market risk premium is well explained by positive 1.1462 beta of (Mkt-RF),the smaller firm should earn higher than big firms makes intuitive sense is captured by SMB and the stock returns captures this size effect,stock return also account for the value factor which is HML.

The Apple's market beta is 1.1462 that is for every 1% change in market return the Apple's stock return changes by 1.1462% keeping other factors SMB and HML constant.The intercept not equal to zero indicates that the stock is not trading at fair price therefore there are arbitrage opportunities.

b)For intercept:t-stat=2.4108 >2 is significant at 95% of significance level.Therefore intercept is statistically significant in explaining the returns of the stock Ri.

(Mkt-RF) :t-stat=7.9023 >>2 is significant at 95% of significance level.Therefore (Mkt-RF) is statistically significant in explaining the returns of the stock Ri.

SMB :t-stat=1.5015 <2 is significant at 95% of significance level.Therefore SMB is not statistically significant in explaining the returns of the stock Ri.

HML :t-stat= -3.7323<-22 is significant at 95% of significance level.Therefore HML is statistically significant in explaining the returns of the stock Ri.

The very High F ratio of 39.7390  suggest that model is significant in explaining the returns of the Apple.The returns of the Apple is well explained by the three factors (Mkt-RF),SMB,HML.

R2 of 0.2557 signifies that 25.57% of the variation in the return of the stock is being explained by the independent variables as (Mkt-RF), SMB and HML.

Running the regression model for CAPM results in R2 of 0.2106 that is 21.06% of the variation in the return of the stock is being explained by the independent variables as (Mkt-RF) ,rest of the variation 78.94% is unexplained for.The predictive power for these CAPM model is lesser due to lower R2 value than three factor model. Therefore  there has been appreciable gain in predictive power with the three factor model.

null hypothesis:H0: =1.3596 and alternate:Ha: !=1.3596

t-stat=1.1462-1.3596 /0.1450=-0.2134/0.1450=-1.472

at 95% confidence level:t-stat= -1.472>-2 therefore we accept the null and conclude that the  beta () truly equals 1.3596. Thus Beta estimated by each model are not statistically different from one another.

Investor would earn 1.2041% return when the market risk premium is 0% or that the market returns are equal to the risk free rate of return.Thus the investor would be rewarded with 1.2041% for bearing the unsystematic risk.

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