Problem 2. Testing Predictability In this problem, you will analyze the predictability of stock returns with respect to the random walk (RW) hypothesis. You will look at this question using both stock index data and stock portfolio data. The stock index data for this exercise is in the file daily_index1988-2023.xslx. The overall period covered by the data is January 1988 through December 2023. You will examine the entire period, as well as three 12-year sub-periods: January 1988 - December 1999, January 2000 - December 2011, and January 2012 - December 2023. The analysis focuses on the CRSP value-weighted index return vwretd and the CRSP equal-weighted index return ewretd. [ ]: idxdata = pd.read_excel('daily_index1988-2023.xlsx', index_col=0) [ ] : [ ]: idxdata['sub1'] = np.int64((idxdata.index >= 19880101) & (idxdata.index = 20000101) & (idxdata.index = 20120101) & (idxdata.index Class Notes) to see what your output should look like. Please briefly comment on the correlograms with respect to the statistical significance and pattern of the autocorrelatios, both within and across the different periods. Question 2.b. Plot correlograms for the daily CRSP equal-weighted returns for our four periods; 198801-202312, 198801-199912, 200001-201112, and 201201-202312. Please see the document return_predict.pdf (on bCourses, under Files > Class Notes) to see what your output should look like. Please briefly comment on the correlograms with respect to the statistical significance and pattern of the autocorrelatios, both within and across the different periods. Compare to the correlograms for the value-weighted returns. [ ]: [ ]: Question 2.c. Reproduce the results in the table from the page titled "Autocorrelation in daily stock index returns, 1988-2023" ( return_predict.pdf). You do not need to reproduce the table as presented on the slide, but you should display the numerical results in some readable fashion. In your submission, you must include the code you used to do this. Interpret the results with respect to the random walk hypothesis, statistical significance, and economic significance. In empirical research, one of the first tasks we often undertake is to try and reproduce results presented in a published paper (or publicly available working paper). This can give you insight into the analysis methods employed by the authors, as well as a jumping off point for verifying assumptions and results. Question 2.d. Reproduce the results in the table from the page titled "Variance ratios for daily stock index returns, 1988-2023" ( return_predict.pdf ). You do not need to reproduce the table as presented on the slide, but you should display the numerical results in some readable fashion. In your submission, you must include the code you used to do this. Interpret the results with respect to the random walk hypothesis, statistical significance, and economic significance. Question 2.e. The stock return data is in the file stockdata_djia.xlsx. The stock return data includes daily reutns for 19 stocks from the Dow Jones Industrial Average (DJIA). These stocks were chosen because they all have a full complement of daily returns over the period January 1988 through December 2023. Hence there are 9,070 return observations for each of these 19 stocks. On each day in the period, each stock is assigned a portfolio number ( PORTNUM) based on market capitalization. Portfolio 1 contains the 6 largest stocks (based on market capitalization at the beginning of each month), portfolio 2 contains the next 6 largest stocks, and portfolio 3 contains the 7 smallest stocks. Daily portfolio returns for each portfolio will be calculated as an equal-weighted return within the portfolio. Note: with this construction, individual stocks can be grouped into different portfolios over the course of the entire sample period. Based on the "raw" data, construct a dataframe that looks like the following, where the portfolio returns are the equal-weighted returns of the stocks in the portfolio, and sub1, sub2, and sub3 refer to the three sub-periods (1) 198801-199912, (2) 200001-201112, and (3) 201201-202312. Int64Index: 9070 entries, 19880104 to 20231229 Data columns (total 6 columns): # Column Non-Null Count Dtype 0 1 2 PORTRET1 9070 non-null PORTRET2 9070 non-null PORTRET3 9070 non-null float64 float64 float64 3 sub1 4 sub2 9070 non-null int64 9070 non-null int64 5 sub3 9070 non-null int64 dtypes: float64(3), int64(3) memory usage: 496.0 KB PORTRET1 PORTRET2 PORTRET3 sub1 sub2 sub3 OBSDATE 19880104 0.037120 0.038363 0.052064 1 0 0 19880105 0.002976 0.015788 0.014205 1 0 19880106 0.004377 0.002232 0.016995 1 0 19880107 0.004002 0.004223 0.006944 1 0 0 19880108 -0.078646 -0.072514 -0.073496 1 0 PORTRET1 PORTRET2 PORTRET3 sub1 sub2 sub3 OBSDATE 19880104 0.037120 0.038363 0.052064 1 0 0 19880105 0.002976 0.015788 19880106 0.004377 0.002232 0.014205 1 0 0 0.016995 1 0 0 19880107 0.004002 0.004223 0.006944 1 0 0 19880108 -0.078646 -0.072514 -0.073496 1 0 0 [ ]: stkdata = pd.read_excel('stockdata_djia.xlsx') stkdata.head() [ ]: [ ]: [ ] : Question 2.f. Plot correlograms for the daily portfolio for our four periods; 198801-202312, 198801-199912, 200001-201112, and 201201-202312. Please see the document return_predict.pdf (on bCourses, under Files > Class Notes) to see what your output should look like. Please briefly comment on the correlograms with respect to the statistical significance and pattern of the autocorrelatios, both within and across the different periods. Compare the correlograms across the three portfolios. Question 2.g. Reproduce the results in the table from the page titled "Autocorrelation in daily portfolio returns, 1988-2023" ( return_predict.pdf ). You do not need to reproduce the table as presented on the slide, but you should display the numerical results in some readable fashion. In your submission, you must include the code you used to do this. Interpret the results with respect to the random walk hypothesis, statistical significance, and economic significance. Question 2.h. Reproduce the results in the table from the page titled "Variance ratios for daily portfolio returns, 1988-2023" ( return_predict.pdf). You do not need to reproduce the table as presented on the slide, but you should display the numerical results in some readable fashion. In your submission, you must include the code you used to do this. Interpret the results with respect to the random walk hypothesis, statistical significance, and economic significance. [ ]: