Question

A.

Estimating Index Model Coefficients An analyst estimates a security characteristic line using a single index model and finds the following statistics:

	Coefficient	Std. Error	P-value	Lower 95%	Upper 95%
Intercept	0.0112	0.00181	0.1108	-0.017	+0.0277
Rm - Rf	1.027	0.02734	7.661E-07	0.7581	1.559

We know from the results with 95% confidence that the stock's beta is ___________ and is ______________________.

1.12%; insignificantly different from zero

significantly greater than zero, between 0.7581 and 1.559.

between 1.12 and 1.027; significantly different from zero

1.027; between 1 and 2

B.

Estimating Index Model Coefficients An analyst estimates a security characteristic line using a single index model and finds the following statistics:

	Coefficient	Std. Error	P-value	Lower 95%	Upper 95%
Intercept	0.0104	0.0014	0.1114	-0.0163	+0.0228
Rm - Rf	1.067	0.0276	7.673E-07	0.7562	1.53

We know from the results that the estimate of the stock’s alpha is ________ and we know with 95% confidence the alpha is _____________________________.

1.04%; insignificantly different from zero

1.067; between 1 and 2

1.04%; significantly different from zero.

between 1.04 and 1.067; significantly different from zero

C.

Evaluating the CAPM Which of the following statements about the CAPM are valid?

I. As a theory the CAPM is not testable

II. The practicality of the CAPM is testable

III. CAPM betas are not as useful at predicting returns as the Fama-French factors

IV. Even if the CAPM is false, markets can still be efficient

I, II, III, IV

II, III and IV only

II and III only

I, II and III only   

Answer 1

A. We know from the results with 95% confidence that the stock's beta is significantly greater than zero and is between 0.7581 and 1.559

Explanation: low p-value indicates significantly different from zero;  if we see lower & upper limit at 95% interval in the table we see Confidence Interval to be  0.7581 to 1.559 which indicates positive value.

{Note form of equation is: y = Intercept + Beta * (Rm - Rf)}

Choice 1 (1.12%; insignificantly different from zero) is incorrect because - 1.12% irelates to the coefficient for the intercept term.

Choice 3 (between 1.12 and 1.027; significantly different from zero) is incorrect because - if we see lower & upper limit at 95% interval in the table we see Confidence Interval to be -> 0.7581 to 1.559

Choice 4 (1.027; between 1 and 2) is incorrect because - if we see lower & upper limit at 95% interval in the table we see Confidence Interval to be -> 0.7581 to 1.559

B. We know from the results that the estimate of the stock’s alpha is 1.04% and we know with 95% confidence the alpha is insignificantly different from zero

Explanation: Intercept coefficient given in the regression result table as 0.0104 (1.04%). High P-Value off 11.14% fails to reject null that intercept coefficient is not significantly different from zero at 95% Confidence Interval. We also see that the 95% range of -0.0163 to 0.0228 contains zero within this interval.

{Note form of equation is: y = Intercept + Beta * (Rm - Rf); and intercept can be looked upon as alpha}

Other choices provided are not consistent with above explanation.

C. I, II, III, IV

As per Roll's Critique, market portfolio is unobservable. Validity of CAPM is equivalent to market being mean-variance efficient, which is not testable. CAPM may still be a useful predictor of observable returns. Fama French model adds on to CAPM model by considering additional factors like size and book value and can lead to better evaluation of performance. It's possible that the CAPM may be wrong even when the market is efficient.