Original paper
Abstract
I examine the momentum anomaly through the prism of higher order risk neutral moments of high and low momentum stocks. I use option prices from 2002 to 2013 to extract time varying ex ante estimates of variance, skewness and kurtosis of high and low momentum stocks. High momentum stocks have lower variance, less negative skewness and lower kurtosis. This is in contrast to studies that use static, ex post estimates of skewness to explain momentum returns as a function of exposure to the higher order moments of the underlying return distribution. These results highlight that momentum returns can not be explained by ex ante estimates of higher order moments and remain dicult to resolve empirically in a rational expectations framework.
Keywords: momentum, risk neutral, skewness, kurtosis, higher order moments, options, derivatives
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.