Momentum

This repo is a replication of momentum investing strategy.

Introduction

Jegadeesh and Titman (1993) presented momentum in their seminal paper Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency (Journal of Finance).

Momentum refers to the phenomenon that past winner stocks (based on past 3- to 12-month returns) continue to perform well while past loser stocks continue to have lower returns up to next 12 months.

• Procedures to build momentum strategy

Page 68 of Jegadeesh and Titman (1993)

Motivation

Momentum is a prominent market anomaly that attracts academics and practitioners attention. However, there are some empirical test variations and different authors may make different decisions when dealing with data. And it is not crystal clear in many papers how authors process the data. I would like to see how those decisions affect momentum profits.

Data

• Data is from CRSP between Dec 1925 and Mar 2022.
• Common stocks. shrcd = 10 or 11
• Stock exchanges - NYSE/AMEX/NASDAQ. exchcd is from -2 to 3.

Zero market values

CRSP has zero market values (111 observations and 18 unique stocks). Remove them or not?

permno	date	ret	me
23633	1974-05-31	-0.2778	0
23633	1974-06-30	0.0769	0
23633	1974-07-31	-0.1429	0
23633	1974-08-31	-0.3333	0
23633	1974-09-30	-0.0625	0
23633	1974-10-31	0.4	0
23633	1974-11-30	0.1905	0
23633	1974-12-31	-0.2	0

Month gaps

There are some big gaps between months. Do all authors deal with such cases when calculating lagged returns? If yes, for example, past 6-month return might include returns several years ago.

permno	date	ret	month_diff
64426	1986-10-31	0.0471	1
64426	1986-11-30	0.001	1
64426	1986-12-31	-0.0117	1
64426	1994-01-31	0	85
64426	1994-02-28	0.1	1
64426	1994-03-31	-0.1818	1
64426	1994-04-30	-0.1667	1
64426	1994-05-31	0	1

Missing returns

Some authors fill missing returns with zeros. In the example below, past 6-month return is zero (even there are no valid returns during past 6 months) and the stock will be included when forming portfolios. Does this make sense if including the stock?

In the case below, adding requirement of valid market value will reduce the effect of this issue (but not 100%).

permno	date	ret	me	exchcd
10007	1987-09-30	0.2063	9.804	3
10007	1987-10-31	-0.5263	4.644	3
10007	1987-11-30	-0.3611	2.967	3
10007	1987-12-31	nan	nan	0
10007	1988-01-31	nan	nan	0
10007	1988-02-29	nan	nan	0
10007	1988-03-31	nan	nan	0
10007	1988-04-30	nan	nan	0
10007	1988-05-31	nan	nan	0
10007	1988-06-30	nan	nan	0
10007	1988-07-31	nan	nan	0
10007	1988-08-31	nan	nan	0
10007	1988-09-30	nan	nan	0
10007	1988-10-31	nan	nan	0
10007	1988-11-30	nan	nan	0
10007	1988-12-31	nan	nan	0
10007	1989-01-31	nan	nan	0
10007	1989-02-28	nan	9.3075	3
10007	1989-03-31	-0.1471	7.93875	3
10007	1989-04-30	0.069	8.48625	3

How to use

Python packages

Required packages to run the codes

• pandas
• numpy
• wrds
• statsmodels
• matplotlib
• seaborn
• yaml
• pandas-datareader

Run the code

You can use table.py to produce the results.

For example, options below will try to follow the empirical settings of Jegadeesh and Titman (1993)

j, k, n_port = 6, 6, 10
fill_na = True
skip = False
no_gap = False
size = None
price = None
exchange = [1, 2]
nyse_bp = False
use_duckdb = True
ret_type = 'ew'
start_date = '1965-01-31'
end_date = '1989-12-31'
nw_lag = 3

portew, momew = mom_port(msf, j, k, n_port, fill_na, skip, no_gap,
    size, exchange, use_duckdb, ret_type, start_date, end_date, nw_lag)

There are many options you can configure to test momentum under different settings.

j

Number of month for lagged returns

k

Number of month for holding period

n_port

Number of groups, e.g.10 means deciles

fill_na

If True, fill missing returns with zeros

If False, do not fill missing returns with zeros

skip

If True, skip (exclude) return in formation month when computing lagged j-month return

If False, include return in formation month when computing lagged j-month return

no_gap

If True, replace lagged j-month returns with missing if the difference between formation month and the lagged jth month is not equal to j-1

If False, no control for month gaps

size

If None (ignore this argument), do not require valid market value in formation month for the stocks

If 1, require positive market values

If 2, exclude small stocks (small stocks are defined as stocks with market value less than 20% percentile of NYSE stocks)

price

Minimum stock price, e.g. 5 means that stocks with price less than 5 dollar will be removed

If None, no control for stock price

exchange

If None (ignore this argument), use NYSE(1)/AMEX(2)/NASDAQ(3)

Note - NYSE must be included if use NYSE breakpoints

nyse_bp

If True, use NYSE breakpoints to rank stocks

If False, use breakpoints of all stocks to rank stocks

use_duckdb

If True, use duckdb to perform conditional merge (4x to 5x faster)

If False, use chunk by chunk full merge

ret_type

If 'ew', equal-weighted returns

If 'vw', value-weighted returns

start_date

Start month of portfolio return

end_date

End month of portfolio return

nw_lag

Number of lags when computing t-value with Newey-West standard error

Compare with Fama-French momentum

• Momentum strategy: j=12, k=1
• Sample: 1927-01-31 to 2022-03-31

Equal-weighted

• MOM

port	ret	t	p
1 (loser)	0.0113	3.11	0.002
2	0.0115	3.88	0
3	0.0113	4.42	0
4	0.0124	4.97	0
5	0.0122	5.5	0
6	0.0131	6.13	0
7	0.0134	6.4	0
8	0.0144	6.84	0
9	0.0157	7.4	0
10 (winner)	0.0179	7.29	0
mom (winner-loser)	0.0066	2.89	0.004

• FF MOM

port	ret	t	p
1 (loser)	0.0099	2.76	0.006
2	0.0115	3.83	0
3	0.0114	4.49	0
4	0.0124	4.98	0
5	0.0123	5.56	0
6	0.0132	6.12	0
7	0.0134	6.43	0
8	0.0144	6.81	0
9	0.0158	7.45	0
10 (winner)	0.0179	7.29	0
mom (winner-loser)	0.0079	3.59	0

• Correlation of momentum (winner-loser): 0.997

Value-weighted

• MOM

port	ret	t	p
1 (loser)	0.0037	1.23	0.22
2	0.0074	3	0.003
3	0.0079	3.72	0
4	0.0091	4.74	0
5	0.0092	5.09	0
6	0.0095	5.5	0
7	0.0103	6.46	0
8	0.0112	7.01	0
9	0.0119	7.06	0
10 (winner)	0.0149	7.44	0
mom (winner-loser)	0.0112	4.85	0

• FF MOM

port	ret	t	p
1 (loser)	0.0035	1.15	0.252
2	0.0076	3.05	0.002
3	0.0077	3.69	0
4	0.0092	4.77	0
5	0.0091	5.09	0
6	0.0097	5.54	0
7	0.0103	6.44	0
8	0.0112	7.01	0
9	0.012	7.1	0
10 (winner)	0.015	7.48	0
mom (winner-loser)	0.0115	4.92	0

• Correlation of momentum (winner-loser): 0.998