Original paper

SSRN-id2653680.pdf658.6KB

Abstract

Standard mean-variance optimized momentum outperforms the traditional equally weighted momentum strategy if the expected return vector used reflects momentum's top and bottom only characteristic. This top and bottom only characteristic is the phenomenon that only the stocks in the top decile of momentum's ranking outperform and that only stocks in the bottom decile underperform, while all stocks in the intermediate deciles of the ranking have similar performance. If the optimization does not take this phenomenon into account the portfolio is also long the deciles 2 to 5 and short the deciles 6 to 9, while all these positions thus do not add anything to the return of the strategy. A new simplified bootstrapping methodology shows that the Sharpe-ratio of 52.8 percent of the optimized portfolio is significantly higher (p-value of 0.006) than the Sharpe-ratio of 29.3 percent for traditional equally weighted momentum. The optimized portfolio also exhibit less time-varying equity risk factor return exposures than traditional momentum and as such have more stable returns over the business cycle and have smaller drawdowns.

Keywords: Momentum, Mean-variance optimization, Time-varying risk, Sharpe-ratio, Bootstrap

Trading rules

Focus on the argest 20% of stocks listed on NYSE, NASDAQ, and AMEX.
Choose the top 20% of equities with the strongest 12-month momentum.
Construct a portfolio where all chosen stocks have equal weight.
Adjust the portfolio composition every 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.

Optimization of Equity Momentum: (How) Does it Work?

Original paper

Abstract

Trading rules

Python code

Backtrader