Original paper
Abstract
The 'low-beta' or 'low-volatility anomaly' is one of the most researched in the field of 'alternative beta'. Despite strong published evidence going back to the 1970s that high beta/volatility stocks underperform relative to expectations generated by the Capital Asset Pricing Model (CAPM), the anomaly still persists. The explanations given for this are all behavioural; that investor biases lead to overpricing of high volatility stocks. This paper shows that investor biases cannot be the explanation for the anomaly. Instead, it is proposed that the anomaly stems from a destruction of shareholder value. The strong implication is that the more market leverage a firm has, the more shareholder value is destroyed. Although the prevailing view for a long time has been that adding debt is good for shareholders, making balance sheets more 'efficient', there is in fact a considerable volume of evidence that the opposite is true; evidence which has been incorrectly interpreted for many years. Some possible mechanisms for this shareholder-value destruction are proposed.
Keywords:Â Low-Beta, Low-Volatility, Factor Investing
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.