1) The model has 346 observations (n=346) and 3 independent variables (K=3), 4 i

Question

1)  The model has 346 observations (n=346) and 3 independent variables (K=3), 4 if you include the intercept (alpha) term.  At a 5% significance level, the lower and upper boundaries for the Durbin-Watson statistic are approximately 1.8074 and 1.8419, respectively.  At a 1% significance level, the lower and upper boundaries for the Durbin-Watson statistic are approximately 1.7353 and 1.7697, respectively.  What can be said about first-order autocorrelation given the Durbin-Watson value of 1.8911 calculated from the three factor model residuals?

2)  The CAPM for Apple, which excludes the SMB and HML variables, has a beta (?) value of 1.3699, an R2 of 0.2119 and an F-ratio of 92.52.  Has there been any appreciable gain in predictive power with the three factor model?  Conduct a t-test on the null hypothesis that beta (?) truly equals 1.3699 given the above estimate of 1.2546 and its standard error of 0.1455.  Also, comment on the CAPM intercept term of 1.1758 and its implications for investors given its statistical significance.

Variable - Parameter

Coefficients

Standard Errors

t-Statistics

Intercept - ?

1.1758

0.6505

1.8074

XRMKTt - ?

1.3699

0.1424

9.6186

3)  For August 2011, the actual value of XRMKT is minus 2.65 (-2.65), SMB is plus 0.06 (+0.06) and HML is minus 2.17 (-2.17).  The actual value for XRAAPL is 8.38 for August 2013.  Given the three factor model above, what is the predicted value of XRAAPL for August 2013 in comparison to its actual value?

Variable - Parameter

Coefficients

Standard Errors

t-Statistics

Intercept - ?

1.1758

0.6505

1.8074

XRMKTt - ?

1.3699

0.1424

9.6186

Explanation / Answer

(1) Since the Durbin-Watson value of 1.8911 is larger than upper boundaries for the Durbin-Watson statistic, we can conclude that first-order autocorrelation is statisitcally significant.

(2) Based on the value of R^2, there has been appreciable gain in predictive power with the three factor model

Null hypthesis: beta=1.3699

Alternative hypothesis: beta is not equal to 1.3699

The test statistic is

t=9.6186

Since the t value is larger than the critical value, beta is signifincat different from 1.3699

comment on the CAPM intercept term of 1.1758:

Since CAPM is intercept, it is not meaningful for the whole model even though it is signifcant based on the t-value

(3)predicted value of XRAAPL for August 2013 is

1.1758-2.65+0.06-2.17 =-3.5842

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