Original paper
Abstract
The strategy of buying safe low-beta stocks while shorting (or underweighting) riskier high-beta stocks has been shown to deliver significant risk-adjusted returns. However, it has been suggested that such “low-risk investing” delivers high returns primarily due to its industry bet, favoring a slowly changing set of stodgy, stable industries and disliking their opposites. We refute this. We show that a betting against beta (BAB) strategy has delivered positive returns both as an industry-neutral bet within each industry and as a pure bet across industries. In fact, the industry-neutral BAB strategy has performed stronger than the BAB strategy that only bets across industries and it has delivered positive returns in each of 49 U.S. industries and in 61 of 70 global industries. Our findings are consistent with the leverage aversion theory for why low beta investing is effective.
Keywords:Â Low Beta, Betting against Beta
Trading rules
- Utilize CRSP database for stock selection
- Compute 1-year rolling beta for each stock relative to MSCI US Equity Index
- Rank stocks in ascending order based on estimated beta
- Allocate stocks to low beta or high beta portfolios
- Weight securities by their ranked betas
- Rebalance portfolios monthly
- Rescale both portfolios to have a beta of one at formation
- Establish zero-cost, zero-beta Betting-Against-Beta portfolio: long low-beta, short high-beta
- Consider simple modifications (e.g., long bottom beta decile, short top beta decile) to enhance performance
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.