ii) Draw an illustrative graph of the probability distribution of the test statistic and mark on SECTION B: Answer both questions in this section [Total marks: 60] it the following elements: test statistic value, critical value, p-value. [4 marks] Question 2 iii) On the basis of the test outcome, what can we say about the role played by market risk Suppose that it is now January 2004 and that you are interested in estimating the beta of Microsoft and liquidity risk in the excess returns of Microsoft stock over the period under study? (MSFT) stock using daily data from 11/11/1997 to 31/12/2003 (7=1540 days), to inform a stock [3 marks] picking decision. For this purpose, you run the CAPM regression: b) Does liquidity risk play a significant role? To answer this question, you are required to: MSFT,, = a + BUM, +ary, + 5,, &, ~ N(0, 0?) 1. Conduct a two-sided test and a one-sided test for the significance of liquidity risk. Use the 5% significance level for both tests, and discuss the results. [4 marks] where 'MSFT, and I'M are excess returns on Microsoft shares and on the S&P500 market index (a proxy for the market portfolio), respectively, and 7 , are the returns of a liquidity-risk- 2. For each of the above two tests, draw an illustrative graph of the probability distribution mimicking portfolio, so that # provides a measure of systematic (market) risk and 1 provides a of the test statistic and mark on it the following elements: test statistic value, critical value, p-value. measure of liquidity risk. The estimation results are provided in Exhibit 1. [4 marks] Exhibit 1 3. Indicate which test is most reliable (in the event that the two tests provide conflicting Dependent Variable: MSFT answers) and explain your answer. [2 marks] Method: Least Squares c) Address the potential problem of autocorrelation through the following aspects: Sample: 1 1540 Included observations: 1540 1. Using both the information provided in Exhibit 1 in conjunction with the information in Exhibit 2 (shown below) indicate whether there is evidence of autocorrelation in the Variable Coefficient Std. Error t-Statistic Prob regression (indicate the specific information that you are using from each Exhibit). [4 marks] -0.003770 0.044024 -0.085638 0.9318 SP500 1.120008 0.035568 31.48923 0.0000 2. In the context of the test provided in Exhibit 2, write down the expression of the Liquidity 0.650231 0.380345 1.709582 regression run to obtain the test statistic, the expression of the test statistic itself, and indicate the name (and the parameters) of the probability distribution of the test statistic. R-squared 0.391992 Mean dependent var 0.001668 [3 marks] Adjusted R-squared 0.391597 S.D. dependent var 2.214870 S.E. of regression 1.727603 Akaike info criterion 3.932645 3. If there is autocorrelation, explain what are the potential adverse consequences for the Sum squared resid 4590.335 Schwarz criterion 3.939580 inferences in part b) of this question. Which remedies can be applied? [3 marks] Log likelihood 3026.137 F-statistic Durbin-Watson stat 1.972787 Prob(F-statistic) Exhibit 2 a) Conduct a formal hypothesis test at the 5% significance level for the hypothesis Ho: R2 = 0 Breusch-Godfrey Serial Correlation LM Test: versus HA: R 0. i) Write clearly the expression of the appropriate test statistic being used. What is the F-statistic 358.6118 Prob. F(5, ......) 0.0000 probability distribution of the test statistic? What is the critical value of the test at the 5% significance level? What is the p-value of the test? [3 marks]
