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1 Homework: Long-run reversal and value
This homework asks you to check the correlation in returns between a value factor and a long-run reversal factor.
The homework comes with one file in CSV format attached: returns LRR.csv
This file contains monthly returns for the top 1,000 (in terms of market capitalization)
US stocks from 1970 to 2019 (pre-covid). The variables are:
(a) permno: unique stock identifier
(b) date: date of the observation. 19800131 means this observation is for the month of January 1980
(c) prc is the stock price at the close of the last trading day of the month; some prices are negative, which indicates that the stocks did not trade on that day and the price is the midpoint of the bid-ask spread; you can simply take the absolute value
(d) shrout is the number of shares outstanding for the stock on the month
(e) ret corresponds to the stock monthly return (in the case of 19800131, this would be the returns of holding the stock from the close of the last trading day in December up to the close of the last trading day in January).
(f) ret 1 corresponds to the monthly stock return in the previous month (in the case of 19800131, this would be the returns of holding the stock in December), ret 2 two months ago, etc.
(g) ret p1 corresponds to the monthly stock return in the next month (in the case of 19800131, this would be the returns of holding the stock in February).
Questions:
Provide a short document containing your answers and tables for the following questions:
1. At month t, for stock i, define a trading signal sit equal to minus stock i cumulative return from [t-60 month,t-12 month]. This is a long-run return signal, which stops at t-12 to avoid medium-term momentum.
2. Using this signal, construct the LRR factor: for each stock in the cross-section of stocks at date t, define a weight wit = ct N
1
−1
(rank(sit) −
N
2
+1 ), where N is the number of stock in your cross-section, and ct
is such that the portfolio invests $1 in total on on the long-leg and $1 in total on the short. The LRR factor invest $ wit in stock i at the end of month t, holds this position for 1 month, and then rebalance.
3. Merge your dataset with the monthly Fama-French factors. You can find them on Ken French’s website (Ken French’s website)
4. What is the CAPM α of your LRR factor?
5. What is the loading of the LRR factor return on the returns of a value portfolio (constructed using the French dataset)? What is the long-short portfolio α against a 2 factor model that include the market and this value portfolio? What is the correlation between hml and your LRR factor?
6. Would you conclude from this exercise that value is an under-reaction phenomenon? Discuss.