Original paper
Abstract
The low (high) abnormal returns of stocks with high (low) beta - the beta anomaly - is one of the most persistent anomalies in empirical asset pricing research. This paper demonstrates that investors' demand for lottery-like stocks is an important driver of the beta anomaly. The beta anomaly is no longer detected when beta-sorted portfolios are neutralized to lottery demand, regression specifications control for lottery demand, or factor models include a lottery demand factor. The beta anomaly is concentrated in stocks with low levels of institutional ownership and it exists only when the price impact of lottery demand is concentrated in high-beta stocks.
Keywords:Â Beta, Beta Anomaly, Lottery Demand, Stock Returns, Institutional Ownership
Trading rules
- Use the CRSP database for choosing stocks.
- Calculate the 1-year moving beta of each stock in comparison to the MSCI US Equity Index.
- Organize stocks in increasing sequence based on their projected beta.
- Group stocks into either high beta or low beta collections.
- Distribute weights to stocks according to their beta rankings.
- Adjust the portfolios on a monthly basis.
- Adjust both portfolios to achieve a beta value of one at their inception.
- Construct a no-cost, neutral-beta Betting-Against-Beta portfolio: adopt a long position on low-beta and a short position on high-beta.
Python code
Backtrader
Here’s a Backtrader Python code implementing the trading rules you described:
import backtrader as bt
import backtrader.feeds as btfeeds
import pandas as pd
class BetaRanking(bt.Strategy):
params = (
('lookback', 252),
('rebalance_freq', 21),
('num_long', 10),
('num_short', 10)
)
def __init__(self):
self.betas = {}
self.rankings = []
self.rebalance_day = 0
# Compute beta for each stock
for d in self.datas:
self.betas[d._name] = bt.indicators.Beta(d, self.data0, period=self.params.lookback)
def next(self):
self.rebalance_day += 1
if self.rebalance_day % self.params.rebalance_freq != 0:
return
self.rankings = sorted(
self.datas,
key=lambda d: self.betas[d._name][0]
)
longs = self.rankings[:self.params.num_long]
shorts = self.rankings[-self.params.num_short:]
for d in longs:
self.order_target_percent(d, target=1.0 / self.params.num_long)
for d in shorts:
self.order_target_percent(d, target=-1.0 / self.params.num_short)
for d in self.datas:
if d not in longs and d not in shorts:
self.order_target_percent(d, target=0.0)
if __name__ == '__main__':
cerebro = bt.Cerebro()
# Add strategy
cerebro.addstrategy(BetaRanking)
# Load CRSP database
# Replace this part with your actual CRSP data
for stock_data in CRSP_data:
data = btfeeds.PandasData(dataname=stock_data)
cerebro.adddata(data)
# Load MSCI US Equity Index data
msci_data = btfeeds.PandasData(dataname=pd.read_csv('msci_us_equity_index.csv', parse_dates=['date'], index_col='date'))
cerebro.adddata(msci_data, name='msci_us_equity_index')
# Set initial capital and run
cerebro.broker.setcash(100000.0)
cerebro.run()This code implements a Backtrader strategy that calculates rolling betas for each stock relative to the MSCI US Equity Index, ranks stocks based on their betas, and rebalances the portfolio monthly. Remember to replace the data loading part with your actual CRSP data and the MSCI US Equity Index data in a suitable format.