Original paper

SSRN-id2089466.pdf1827.9KB

Abstract

We examine the role of shorting, firm size, and time on the profitability of size, value, and momentum strategies. We find that long positions comprise almost all of size, 60% of value, and half of momentum profits. Shorting becomes less important for momentum and more important for value as firm size decreases. The value premium decreases with firm size and is weak among the largest stocks. Momentum profits, however, exhibit no reliable relation with size. These effects are robust over 86 years of U.S. equity data and almost 40 years of data across four international equity markets and five asset classes. Variation over time and across markets of these effects is consistent with random chance. We find little evidence that size, value, and momentum returns are significantly affected by changes in trading costs or institutional and hedge fund ownership over time.

Trading rules

Target the top quintile of stocks listed on NYSE, NASDAQ, and AMEX by size.
Select top 20% stocks exhibiting the strongest 12-month momentum.
Create an equally weighted portfolio of selected stocks.
Adjust the portfolio composition each month.

Python code

Backtrader

import backtrader as bt
import backtrader.feeds as btfeeds
import datetime

class Momentum(bt.Strategy):
    params = (
        ('momentum_period', 252),
        ('rebalance_interval', 21),
        ('num_stocks', 0.2),
    )

    def __init__(self):
        self.add_timer(
            bt.timer.SESSION_END, monthdays=[1], monthcarry=True        )  # Rebalance monthly
        self.inds = {}
        for d in self.datas:
            self.inds[d] = bt.indicators.ROC(d.close, period=self.params.momentum_period)

    def prenext(self):
        self.next()

    def notify_timer(self, timer, when, *args, **kwargs):
        if self._getminperstatus() < 0:
            return
        stocks = list(self.datas)
        stocks.sort(key=lambda d: self.inds[d][0], reverse=True)
        selected_stocks = stocks[:int(len(stocks) * self.params.num_stocks)]
        for d in self.datas:
            target = self.broker.getvalue() * (1 / len(selected_stocks)) if d in selected_stocks else 0
            self.order_target_value(d, target)

cerebro = bt.Cerebro()
# Add data for NYSE, NASDAQ, and AMEX stocks
# Replace 'NYSE.csv', 'NASDAQ.csv', and 'AMEX.csv' with appropriate files
for market in ['NYSE.csv', 'NASDAQ.csv', 'AMEX.csv']:
    data = btfeeds.GenericCSVData(
        dataname=market,
        fromdate=datetime.datetime(2000, 1, 1),
        todate=datetime.datetime(2020, 12, 31),
        dtformat=('%Y-%m-%d'),
        openinterest=-1,
        nullvalue=0.0,
        plot=False,
    )
    cerebro.adddata(data)
cerebro.broker.setcash(1000000.0)
cerebro.broker.setcommission(commission=0.001)  # 0.1% commission
cerebro.addstrategy(Momentum)
print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue())
results = cerebro.run()
print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue())
cerebro.plot()

Make sure to replace ‘NYSE.csv’, ‘NASDAQ.csv’, and ‘AMEX.csv’ with the appropriate files containing the stock data for the mentioned exchanges. This code uses the Backtrader framework to implement the trading strategy as described.

The Role of Shorting, Firm Size, and Time on Market Anomalies

Original paper

Abstract

Trading rules

Python code

Backtrader