Original paper

SSRN-id3228116.pdf620.7KB

Abstract

This paper is the second in a series of critiques of the assumption that stable economic relations exist between certain "firm characteristics" and expected returns. The paper explains why this is not the case for past returns and provides theoretical, empirical, and simulated evidence that the stylized facts involving momentum are consistent with traditional risk-based asset pricing, thereby solving the apparent theoretical puzzle. For example, riskier assets tend to be in the loser portfolio after (large) increases in the price of risk: The time-varying correlation between past returns and risk, which determines the risk of momentum portfolios, decreases with the price of risk. Hence, their premiums are approximately negative quadratic functions of the price of risk, theoretically truncated at zero. The best linear (CAPM) function describing this relation unconditionally has the negative slope and positive intercept documented empirically and considered the main momentum puzzle.

Keywords: momentum, risk, puzzle, ranking, conditional

Trading rules

Concentrate on the top quintile of stocks from NYSE, NASDAQ, and AMEX.
Identify the quintile of stocks exhibiting the highest performance over the past year.
Construct a portfolio with uniform weighting from the chosen 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.

A Critique of Momentum Anomalies

Original paper

Abstract

Trading rules

Python code

Backtrader