Homework for Chapter 8: This is an exercise on the momentum and long-term contrarian investment strategies. These two strategies are well known challenges for CAPM and the (weak form) of Efficient Market Hypothesis. The strategies are based purely on past stock performance: Momentum strategies are taking a long position in intermediate-term winners and a short position in the intermediate-term losers, whereas the longterm contrarian strategy takes a long position in long-term losers and a short position in long-term winners. As you can see, these two strategies are almost the opposite of each other; however, this exercise will show that they both offer positive and abnormal returns. For simplicity, we skip the procedure of forming portfolios, but the underlying idea is very simple. For instance, to form 10 momentum portfolios, we first calculate the past two-to-twelve month cumulative returns at the end of each month t, and then sorts all the stocks into 10 groups, with group 10 for stocks with best past performance (winners), and group 1 for stocks with worst past performance (losers). Then we calculate the average stock returns for these 10 momentum portfolios at month t+1. We repeat the exercise every month, and we have a time series of momentum portfolio returns for each of 10 momentum portfolios. For details of the portfolio construction, see the following website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_10_port_form_pr_12_2.ht ml Similarly, the procedure for the long-term contrarian strategy can be found here: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_10_port_form_pr_60_13.h tml With the above procedures, we have data in the Excel file "Data_MomContrarian.xlsx". The data sample is monthly from 1931.01-2011.12. The variable definition for each column is described in the following: Column A: Date Column B-K: Monthly returns for Momentum Portfolios, with Column K being the intermediate-term past winners, and Column B being the intermediate-term past losers. Therefore, if you keep buying past winners using past 12-2 month returns, you will generate a time series returns of Column K. Column L-U: Monthly returns for Long-term Contrarian Portfolios, with Column U being the longterm past winners, and Column L being the long-term past losers. Therefore, if you keep buying long-term past winners, you will generate a return time series of Column U. Column V: Time series of market excess return. Column W: Risk-free rate. (Note in CAPM you are regressing "Excess Returns" of a portfolio or stock on the excess return of the market, so you need subtract risk-free rate from the portfolio returns in Column B-U in estimating CAPM. However, Column V is already excess return).

Questions: 1. What are the mean, standard deviation and Sharpe ratio of the 10 momentum portfolio returns? How about 10 Contrarian portfolios? Are there any monotonic patterns in these portfolio returns?

2. Momentum strategy is taking a long position in intermediate-term winner portfolio (Column K) and short position in intermediate-term loser portfolio (Column B), therefore, the strategy return is calculated as the difference between Column K and Column B. What is the average return of momentum strategy? How about standard deviation and Sharpe Ratio? Does momentum strategy offer a higher Sharpe ratio than the market portfolio?

3. Repeat the question 2 for long-term contrarian strategy, where you are taking a long position in long-term losers (Column L) and a short position in long-term winners (Column U). What are the average return, standard deviation and Sharpe Ratio of the 10 contrarian portfolios and the contrarian strategy portfolio (Column L-Column U)? 1

4. What is the correlation between the returns of momentum strategy and long-term contrarian strategy?

5. Now we take a look at the CAPM performance. For each of the 10 momentum portfolio, calculate the alpha and market beta. (Check the slides in Chapter 6 regarding how you can calculate beta. You may need correlation coefficient function in excel) Do you find a pattern in market beta? Does winner portfolio have a higher market beta than loser portfolio? Can CAPM successfully capture the momentum portfolio returns? How about the abnormal return (alpha) of the momentum strategy return (Column K-Column B)? Is it bigger or smaller than the average return of momentum strategy?

6. Repeat the question 5 for long-term contrarian strategy.