Regression Statistics Analysis

1. Introduction The focus of the problem set is two-fold: (i) to introduce you to some datasets widely used in the asset pricing studies; (ii) to help you examine the predictable behavior of stock returns through two classic trading strategies: ? Momentum (Jegadeesh and Titman, 1993): a zero-investment strategy that in each month (?) sorts stocks into deciles on the basis of prior (? ? 12 to ? ? 2) returns, and then buys stocks in the top decile (winners) and sells stocks in the bottom decile (losers). ? Short-term reversal (Jegadeesh, 1990): a zero-investment strategy that in each month (?) sorts stocks into deciles on the basis of prior-month (? ? 1) returns, and then buys stocks in the bottom decile (losers) and sells stocks in the top decile (winners). Sorting variables. The difference among these two trading strategies is that stocks are sorted on past returns with different horizons. The short-term reversal strategy is sorted on previous month return (? ? 1), and the momentum strategy is sorted on the holding period return from month ? ? 12 to month ? ? 2. Asset pricing factors. We will consider a set of asset pricing models and examine how well they could explain these trading strategies. The set of asset pricing models includes: (1) CAPM (2) Fama-French three-factor model All data for asset pricing factors could be downloaded from Ken French’s website: https://mba.tuck.dartmouth.edu/pages/faculty/ken.f… Data. The stock price and return data are from CRSP, which can be accessed through Wharton Research Data Service (https://wrds-www.wharton.upenn.edu). I’ve created a class account: Username: fin550e2022 Password: BehavioralFinance2022! Please do not share the account info with students who are not enrolled in this class. For your convenience, I’ve downloaded and cleaned the data for you. The return data saved in “returns.csv”, and the asset pricing factors (from French’s website) can be found in “factors.csv”, both of which can be downloaded from Canvas. The first row of the file contains the variable names. “return.csv”: the dataset includes monthly returns of stocks trading on the NYSE, NASDAQ and Amex from Jan 1980 through June 2020. Each row represents a stockmonth observation. It contains the following variables: – ??????: company identifier. – ??????: company ticker. – ?: year of time ? – ?: month of time ? – ?????_???: the stock price at the beginning of the indicated month ? – ?????_??????: the number of outstanding shares at the beginning of the indicated month ? (in thousands) – ???: monthly return to holding the security in the indicated month ? – ???_??: a lag of variable ??? where x indicates the number of lagged months. For example, ret_l1 is the monthly return from the previous month ? ? 1, ret_l6 is the monthly return from 6 months ago (month ? ? 6). “factors.csv”: the dataset includes monthly returns of a set of asset pricing factors. Each row represents a month observation. It contains the following variables: – ?: year of time t – ?: month of time t – ?????: market return – risk free – ??b: small – big – ???: high B/M – low B/M (value – growth) 2. Assignment Generally speaking, a coding language is much easier for this type of task and strongly encouraged. Given the size of the dataset, this problem set may be a bit hard to handle in Excel but can still be done. Please feel free to choose the most convenient way for you to complete the analyses. Some useful commands for different programming languages are provided at the end of this document. Software (e.g. Stata, MATLAB) can be accessed through the Virtual Computer Lab. More information can be found: https://sites.wustl.edu/olinit/virtual-lab/ Please submit your code or log file (or your working excel file) along with the write-up for the questions through Canvas by team. In the write-up, you only need to include related information (including related tables and figures) requested in the question subsections. Part 1: data download and summary stats I have downloaded all the data for you to run analyses. This part only serves as a practice for you to download a small sample, clean the data and report the summary statistics. A. Go to WRDS using the log in information listed above, find CRSP ? Quarterly Update ? Stock/Security Files ? Monthly Stock File B. Download the data for stocks of the entire universe from 04/2021 to 06/2021: Step 1: select corresponding period Step 2: select “Search the entire database” Step 3: select the following variables: Price (prc), Number of Shares Outstanding (shrout), Exchange Code (exchcd), Holding Period Return (ret), Share Volume (vol) C. Data cleaning: only keep stocks trading on the NYSE, AMEX and NASDAQ (exchcd: 1=NYSE, 2=AMEX, 3=NASDAQ); remove penny stocks with prc<5. Question: Report the summary statistics (mean, standard deviation, min, p10, p25, median, p75, p90, max) of prc, shrout, ret, vol for the sample. For the remainder of the problem set, use the datasets “returns.csv” and “factors.csv” I have already downloaded for you. Part 2: Momentum strategy For each month, sort the stocks into 10 deciles on past [t-12, t-2] returns (ret_m12_m2): A. Create a variable equal to the return on the stock from t-12 to t-2. That is: ?(?????? 12 ?=2 + 1) ? 1  Or, equivalently, (1 + ???_?2)(1 + ???_?3) … (1 + ???_?12) ? 1 B. Divide the stocks in 10 equal-sized groups, with group 1 being the one with the lowest prior returns and group 10 the one with highest prior returns. The breakpoints for the deciles are determined separately for each month. C. For each month, construct an equal-weighted portfolio within each decile group, compute the return of the equal-weighted portfolio (i.e. for each month, take the average of monthly returns across stocks within each decile group). D. Now, for each month, you have returns for 10 decile portfolios. Next, for each decile portfolio, take the average of returns across all months. Question: (1) Momentum effect: plot the average returns for the 10 decile portfolios. How do you interpret the pattern shown in the figure? (2) Time series pattern of the momentum strategy: Construct a momentum strategy by longing the top decile (group 10) and shorting the bottom decile (group 1), and ?????? = ???????? 10 ? ???????? 1 . Now, you have a time series of returns of the momentum strategy. Plot ?????? against the time line and describe any noteworthy patterns in this graph. Are any of the time periods especially striking? (3) The famous alpha: run the following OLS regression: ??????,? = ? ???? + ???? ? ????? ??????,? = ? ?? + ???? ? ????? + ???? ? ??? + ???? ? ??? The constants of these regressions are the famous alpha. Report the coefficient estimates and t-stats for CAPM alpha (? ????) and Fama-French 3-factor alpha (? ??) for the momentum strategy. You can organize the table like this: CAPM alpha FF 3-factor alpha Coefficient estimate t-stat Are the alphas significant? Can CAPM or Fama-French 3 factor model explain the momentum effect? (4) Value-weighted portfolio: Instead of forming equal-weighted portfolios, we can also form value-weighted portfolios. Follow the same steps A, B and D mentioned above. The only change happens in step C: for each month, instead of taking a simple average of returns across stocks within each decile group, we weigh each stock in the decile on a firm’s beginning-of-month market capitalization (?????_??? × ?????_??????). Report the coefficient estimates and t-stats for the CAPM alpha and Fama-French 3- factor alpha for the value-weighted momentum strategy in a similar table structure illustrated above. Are the alphas significant here? Compare alphas of the valueweighted momentum strategy with alphas of the equal-weighted momentum strategy. Which portfolio creates a higher alpha? What do you think explains the difference?

Only do part 1 and 2.