Question 1 (17 marks) 1. Consider the following Fama-French five factor model rt-rft Bo+B1(rmt - rft) + B2SMBt + B3HMLt + B4CMAt + B5RMWt+ut, (1) where rt denote monthly returns on the Fama-French manufacturing (manuf) portfolio, (rmt - r is the excess market return (the market factor), rft is the risk free interest rate, SMB is the size factor, HML is the value factor, CMA is the investment factor and RMW is the profitability factor. OLS output from estimating (1) over the period January 2000 to February 2022 is shown in Figure 1. (a) You wish to evaluate the probability, p, attached to the manufacturing portfolio return Tt being negative. What random variable would you use to translate this problem into mathematical form? What formula would you use to estimate p from the sample of rt implied by (1)? (3 marks) (b) Interpret the coefficient estimate of the value factor. Test whether this factor has a signif- icant impact on the variation in manufacturing portfolio excess returns. Briefly comment on your conclusion. (2 marks) (c) Test whether the additional four factors are needed in the CAPM specification (1) using the information provided in Figures 1 and 2. What conclusion do you draw? (3 marks) (d) Enumerate the key assumptions of the one factor CAPM model. (2 marks) 2. In the regression results of Figure 1, HAC standard errors have been used. What two properties of the error term does this adjustment correct for? Write the relevant auxiliary regression and details of the testing procedure in each case. (4 marks) 3. The results shown in Figure 3 correspond to the Breusch-Godfrey test applied to residuals of (1). How do you relate these results to the Efficient Market Hypothesis? What other test can be used to verify this hypothesis and why? Briefly explain. (3 marks) (continued) Question 1 (17 marks) 1. Consider the following Fama-French five factor model rt-rft Bo+B1(rmt - rft) + B2SMBt + B3HMLt + B4CMAt + B5RMWt+ut, (1) where rt denote monthly returns on the Fama-French manufacturing (manuf) portfolio, (rmt - r is the excess market return (the market factor), rft is the risk free interest rate, SMB is the size factor, HML is the value factor, CMA is the investment factor and RMW is the profitability factor. OLS output from estimating (1) over the period January 2000 to February 2022 is shown in Figure 1. (a) You wish to evaluate the probability, p, attached to the manufacturing portfolio return Tt being negative. What random variable would you use to translate this problem into mathematical form? What formula would you use to estimate p from the sample of rt implied by (1)? (3 marks) (b) Interpret the coefficient estimate of the value factor. Test whether this factor has a signif- icant impact on the variation in manufacturing portfolio excess returns. Briefly comment on your conclusion. (2 marks) (c) Test whether the additional four factors are needed in the CAPM specification (1) using the information provided in Figures 1 and 2. What conclusion do you draw? (3 marks) (d) Enumerate the key assumptions of the one factor CAPM model. (2 marks) 2. In the regression results of Figure 1, HAC standard errors have been used. What two properties of the error term does this adjustment correct for? Write the relevant auxiliary regression and details of the testing procedure in each case. (4 marks) 3. The results shown in Figure 3 correspond to the Breusch-Godfrey test applied to residuals of (1). How do you relate these results to the Efficient Market Hypothesis? What other test can be used to verify this hypothesis and why? Briefly explain. (3 marks) (continued)
