What differences do you find in the autocorrelation patterns of the market and the size portfolio stocks ? Are there any differences in the autocorrelation patterns between small and large stocks ? Are your results robust to the choice of the sample period 'P Takeover Announcement Suppose that you wish to statistically test the hypothesis that takeover announcements in- crease the share price of the target company. You have a sample of daily returns data on all traded UK shares, and a sample of takeover announcement dates based on London Times newspaper records. Describe the statistical test that you would use, the key assumptions necessary for the test to be valid, alternative choices in test design , and the limitations of your approach. Power of Event Study Test (From CLM Chapter 4) You are given the following information for an event. Abnormal returns are sampled at an interval of one day. The event-window length is three days. The null hypothesis is that the mean abnormal return over the event window is 0% per day. The alternative hypothesis is that the mean abnormal return over the event window is 0.3% per day' You have a sample of 50 events. The abnormal returns are independent across the event observations as well as across event days for a given event observation. For 25 of the event observations the daily standard deviation of the abnormal return is 3% and for the remaining 25 observations the daily standard deviation is 6%. Given this information, what would be the power of the test for an event study using the cumulative abnormal return test statisticJ1 = _ 2 CAR (T)/\\/F (1')? What would be the power using the standardized cumulative abnormal 1/2 M 337312 (T)? For the power calculations, assume the return test statistic J 2 = L 2 1, standard deviation of the abnormal returns is known . Testing The CAPM Model. Use monthly returns of 10 value-weighted book-to-market portfolios and 10 value -weighted size portfolios and perform the following tests of the Sharpe - Lintner CAPM (In Excel you will need the "Solver" function The matrix functions "mmult' "transpose" and "minverse" may also prove useful): (a) Using the entire sample regress excess returns of each portfolio return on the excess market return , and perform tests with a size of 5% that the intercept is zero . Report the point estimates ,t-statistics , and whether or not you reject the CAPM (b) For each portfolio, perform the same tests over two equi-partitioned subsamplesi (c) Perform the joint tests each with 10 book -to-market portfolios and 10 size portfolios