Original paper

SSRN-id3033349.pdf527.8KB

Abstract

This paper proposes and implements an inter-temporal model wherein aggregate consumption and asset-specific dividend growths jointly move with two mean-reverting state variables. Consumption beta varies through time and cross sectionally due to variation in half-lives and stationary volatilities of the dividend signals. Winner (Loser) stocks exhibit high (low) half-lives and stationary volatilities, and thus exhibit high (low) consumption beta commanding high (low) risk-premium. The model also rationalizes the \"momentum crashes\" phenomenon discussed in Daniel and Moskowitz (2014). High half-lives of dividend signals in Winners keep their consumption betas low long after recovering from a prolonged economic downturn, while low half-lives in Losers make their consumption betas grow rather quickly. Thus, coming out of a recession, the long Winner/short Loser strategy reduces in consumption beta and, hence, risk-premia.

Keywords: Momentum, Cross-Sectional Dynamics, Long-Run Risk, Bayesian Filtering

Trading rules

Focus on the largest 20% of stocks listed on NYSE, NASDAQ, and AMEX.
Identify the upper 20% of stocks exhibiting the strongest momentum over a 12-month period.
Form a portfolio giving equal weight to each of the chosen stocks.
Adjust the portfolio composition every month.
Use as a reference: a portfolio with equal weighting of the largest 20% of stocks from NYSE, NASDAQ, and AMEX.

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.

Cross-Sectional Factor Dynamics and Momentum Returns

Original paper

Abstract

Trading rules

Python code

Backtrader