Original paper
Abstract
This paper introduces seasonality into a model of expected stock returns. We confirm previous findings that there is no evidence for cross-sectional variation in expected stock returns when we restrict the means to be constant throughout the year. Yet, we show there is substantial variation when considering each month of the year separately. Applying a seasonal structure we estimate an annualized standard deviation of 13.8%. There is strong evidence stocks have distinct expected returns in January, February, ... December. The estimated seasonal variation in expected returns is positive in every calendar month and especially high during October, December, and January. This structure is independent of industry, size, and earnings announcements. These results support the inclusion of seasonal structure into asset-pricing models.
Trading rules
- Select top 30% firms by market cap from NYSE and AMEX
- Monthly grouping into 10 equal-sized portfolios based on performance 12 months prior
- Go long on stocks in top-performing decile, short stocks in bottom-performing decile
- Maintain equal-weighted portfolio composition
- Rebalance portfolio monthly
Python code
Backtrader
import backtrader as bt
import numpy as np
class SeasonalityStrategy(bt.Strategy):
params = (
('top_percent', 0.3),
('num_portfolios', 10),
('lookback_period', 12),
('rebalance_days', 21)
)
def __init__(self):
self.add_timer(bt.timer.SESSION_END, monthdays=[1], monthcarry=True)
self.inds = {}
for d in self.datas:
self.inds[d] = {}
self.inds[d]['market_cap'] = d.close * d.volume
self.inds[d]['past_performance'] = bt.ind.PctChange(d.close, period=self.p.lookback_period)
def notify_timer(self, timer, when, *args, **kwargs):
if self._last_month != self.data.datetime.date(0).month:
self._last_month = self.data.datetime.date(0).month
self.rebalance_portfolio()
def rebalance_portfolio(self):
market_caps = [self.inds[d]['market_cap'][0] for d in self.datas]
past_performances = [self.inds[d]['past_performance'][0] for d in self.datas]
sorted_indices = np.argsort(market_caps)[::-1]
top_percentile = int(len(sorted_indices) * self.p.top_percent)
top_firms = sorted_indices[:top_percentile]
selected_stocks = [self.datas[i] for i in top_firms]
selected_performances = [past_performances[i] for i in top_firms]
sorted_stocks = np.argsort(selected_performances)
num_in_decile = int(len(sorted_stocks) / self.p.num_portfolios)
long_decile = sorted_stocks[-num_in_decile:]
short_decile = sorted_stocks[:num_in_decile]
long_stocks = [selected_stocks[i] for i in long_decile]
short_stocks = [selected_stocks[i] for i in short_decile]
for d in self.datas:
current_position = self.getposition(d).size
if d in long_stocks and current_position <= 0:
self.order_target_percent(d, target=1.0 / len(long_stocks))
elif d in short_stocks and current_position >= 0:
self.order_target_percent(d, target=-1.0 / len(short_stocks))
elif current_position != 0:
self.close(d)cerebro = bt.Cerebro()
# Add data feeds, broker, etc.
cerebro.addstrategy(SeasonalityStrategy)
results = cerebro.run()This is a basic implementation of the trading rules in Backtrader. You’ll need to add your own data feeds, broker settings, and any other desired configurations to complete the implementation.