Original paper

SSRN-id3276334.pdf1509.9KB

Abstract

Stocks tend to earn high or low returns relative to other stocks every year in the same month (Heston and Sadka 2008). We show these seasonalities are balanced out by seasonal reversals: a stock that has a high expected return relative to other stocks in one month has a low expected return relative to other stocks in the other months. The seasonalities and seasonal reversals add up to zero over the calendar year, which is consistent with seasonalities being driven by temporary mispricing. Seasonal reversals are economically large, statistically highly significant, and they resemble, but are distinct from, long-term reversals.

Keywords: seasonalities, seasonal reversals, expected returns

Trading rules

Focus on stocks from NYSE, Amex, and NASDAQ.
Limit to ordinary common shares, excluding other types of securities.
For month t, develop a seasonal reversals factor.

Rank stocks by average other-calendar-month returns (excluding month t) using the past 20 years of data.
Formulate six distinct portfolios.

Take long positions in the two portfolios with the lowest averages.
Take short positions in the two portfolios with the highest averages.
Adjust the strategy on a monthly basis.
Implement a value-weighted portfolio.

Python code

Backtrader

import backtrader as bt
import pandas as pd
import numpy as np
from datetime import timedelta


class SeasonalReversals(bt.Strategy):
    params = (
        ("lookback", 20 * 12),
        ("portfolios", 6),
        ("long_short_ratio", 2),
    )

    def __init__(self):
        self.order_dict = {}
        self.data_dict = {data._name: data for data in self.datas}

    def next(self):
        # Get current date
        current_date = self.datas[0].datetime.date(0)
        if current_date.month != (current_date - timedelta(days=1)).month:
            self.rebalance()

    def rebalance(self):
        # Calculate seasonal reversals factor
        returns = {}
        for stock, data in self.data_dict.items():
            historical_returns = np.array([
                data.close.get(size=-month, ago=-month) / data.close.get(size=-month, ago=-month - 1) - 1
                for month in range(1, 13) if month != data.datetime.date(0).month
            ])
            avg_return = historical_returns.mean()
            returns[stock] = avg_return

        sorted_stocks = sorted(returns, key=returns.get)
        long_stocks = sorted_stocks[:self.params.long_short_ratio]
        short_stocks = sorted_stocks[-self.params.long_short_ratio:]

        # Cancel existing orders
        for orders in self.order_dict.values():
            for order in orders:
                self.cancel(order)

        # Rebalance portfolio
        for stock, data in self.data_dict.items():
            if stock in long_stocks:
                target_weight = 1.0 / (2 * self.params.long_short_ratio)
                self.order_target_percent(data, target_weight, exectype=bt.Order.Market)
            elif stock in short_stocks:
                target_weight = -1.0 / (2 * self.params.long_short_ratio)
                self.order_target_percent(data, target_weight, exectype=bt.Order.Market)
            else:
                self.order_target_percent(data, 0, exectype=bt.Order.Market)


if __name__ == "__main__":
    cerebro = bt.Cerebro()
    # Add data feeds (NYSE, Amex, NASDAQ) for the desired stocks to cerebro
    # Example:
    # data = bt.feeds.YahooFinanceData(dataname="AAPL", fromdate=datetime(2000, 1, 1), todate=datetime(2022, 1, 1))
    # cerebro.adddata(data)

    cerebro.addstrategy(SeasonalReversals)
    cerebro.broker.setcash(100000.0)
    cerebro.run()

Are Return Seasonalities Due to Risk or Mispricing? Evidence from Seasonal Reversals

Original paper

Abstract

Trading rules

Python code

Backtrader