Original paper
Abstract
The leverage aversion theory implies that returns to the betting-against-beta (BAB) strategy are predictable by past market returns: An outward shift in investors' aggregate demand function simultaneously increases market prices and increases the expected future BAB return. I confirm the prediction empirically and find that the BAB strategy performs better in times when and in countries where past market returns have been high. I construct timing-strategies that are long BAB half the time and short BAB half the time, based on past market returns, and show that these timing strategies have realized strong historical performance.
Keywords:Â Asset Pricing, Leverage Constraints, Factor Timing, BAB
Trading rules
- Target assets:All country ETFs.
- Beta computation: Using a 1-year rolling timeframe, compared to the MSCI US Equity Index.
- Sorting of ETFs: List in order of increasing beta.
- Categorize into two groups: Those with lower beta and those with higher beta.
- Allocate weights: Based on their beta rankings.
- Monthly adjustments: Revise portfolios at each month's end.
- Adjust portfolios: Ensure both high and low-beta groups have a beta of one upon creation.
- Betting-Against-Beta strategy: Long on low-beta, short on high-beta (zero-cost, zero-beta)
- Potential enhancements: Boost performance by taking long/short positions in ETFs within the top and bottom beta deciles.
Python code
Backtrader
import backtrader as bt
import pandas as pd
import numpy as np
class BettingAgainstBeta(bt.Strategy):
params = (
('beta_window', 252), # 1-year rolling window for beta calculation
('rebalance_freq', 20) # Monthly rebalancing
)
def __init__(self):
self.etfs = self.datas[1:] # All country ETFs
self.msci_index = self.datas[0] # MSCI US Equity Index
self.counter = 0
def next(self):
self.counter += 1
if self.counter % self.params.rebalance_freq == 0:
etf_betas = []
for etf in self.etfs:
returns_etf = pd.Series(etf.get_array('close')[-self.params.beta_window:]).pct_change().dropna()
returns_index = pd.Series(self.msci_index.get_array('close')[-self.params.beta_window:]).pct_change().dropna()
beta = np.cov(returns_etf, returns_index)[0][1] / np.var(returns_index)
etf_betas.append((etf, beta))
etf_betas.sort(key=lambda x: x[1]) # Sort ETFs in ascending order by beta
low_beta_etfs = etf_betas[:len(etf_betas) // 2]
high_beta_etfs = etf_betas[len(etf_betas) // 2:]
# Adjust positions - long on low-beta, short on high-beta
for etf, beta in low_beta_etfs:
self.order_target_percent(etf, target=1 / len(low_beta_etfs))
for etf, beta in high_beta_etfs:
self.order_target_percent(etf, target=-1 / len(high_beta_etfs))
if __name__ == '__main__':
cerebro = bt.Cerebro()
# Load data for MSCI US Equity Index and Country ETFs
# Assuming historical data is available as csv files
msci_index_data = bt.feeds.YahooFinanceCSVData(dataname='path_to_msci_index_csv')
etf_list = ['path_to_etf1_csv', 'path_to_etf2_csv', 'path_to_etf3_csv', ...]
cerebro.adddata(msci_index_data)
for etf_data_path in etf_list:
etf_data = bt.feeds.YahooFinanceCSVData(dataname=etf_data_path)
cerebro.adddata(etf_data)
cerebro.addstrategy(BettingAgainstBeta)
cerebro.broker.setcash(100000.0)
cerebro.broker.setcommission(commission=0.001) # Set broker commission
print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue())
cerebro.run()
print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue())Note: Make sure to replace the ‘path_to_msci_index_csv’, ‘path_to_etf1_csv’, ‘path_to_etf2_csv’, ‘path_to_etf3_csv’, … with the actual file paths for the MSCI US Equity Index and country ETFs historical data.