SECTION A Answer ALL question in Section A. QUESTION ONE You are investigating the systematic risk for a stock portfolio. The data contains weekly excess returns (in percent) for the portfolio (named ret_ex) and the excess return on the market portfolio (named mkt_ex). The sample size is 150. The regression results in the following output (values in parentheses under each coefficient are standard errors): ret_ex, = 0.20 +1.70 x mkt_ex, R = 0.60,SER = 1.4 (0.10) (1.20) (a) What do the coefficient values, 0.20 and 1.70, mean? (5 MARKS) (b) Calculate the t-statistics of the two coefficients and use them to determine whether the coefficients are statistically significantly different from zero at a 5% significance level. Clearly show how you reach your conclusions. (15 MARKS) (c) Regression Predictions: (i) Brief explain the data type used in your regression. (5 MARKS) (ii) What is the predicted excess return of the portfolio if the excess return of market portfolio is 3%? (5 MARKS) (d) You extend the original model above by including two additional independent variables from the q-factor model: ROE (high-minus-low ROE stocks) and EG (high-minus-low expected growth stocks). The R-squared of the new regression model is 0.65. Use this information to test the null hypothesis that coefficients of the two new variables are jointly statistically insignificant using F-test. Clearly state the null and alternative hypotheses, the value of the F- statistic and the critical value you use. (10 MARKS) QUESTION TWO You are investigating the earnings functions. Using the data of 1,744 individuals, your regression model results show as follows (t-ratios are given in parenthesis under each coefficient): In (Earn,) = 8.50+ 0.03 Age, (5.01) (1.10) where Earn is weekly earnings in GB, and Age is in years. (a) Briefly explain why researchers in general prefer a log-linear specification over a linear specification, in terms of the interpretation of the slope coefficients, and in terms of the distribution of the error term. (18 MARKS) (b) Provide your interpretation on the coefficient on Age, given the regression results. (5 MARKS) You decide to allow the regression line to differ for the below and above 40 years age category. Accordingly you create a dummy variable, Dage, that takes the value of one for age 39 and below, and is zero otherwise. The earnings equation result is provided in the following (t-ratios are given in the parenthesis under each coefficient): In (Earn,) = 6.92- 3.13 x Dage-0.019 x Age, + 0.085 x (Dage, Age) (0.01) (-3.22) (-4.45) (20.01) (c) Using two separate equations, write the estimated regression model: one for the age category 39 years and under, and one for 40 and above. Briefly comment on your findings on the two equations. (15 MARKS) (d) Predict the In(earnings) for a 30 year old and a 50 year old individual. What is the percentage difference between these two individuals? (12 MARKS)