Original paper
Abstract
Berkshire Hathaway has realized a Sharpe ratio of 0.79 with significant alpha to traditional risk factors. However, the alpha becomes insignificant when controlling for exposures to Betting-Against-Beta and Quality-Minus-Junk factors. Further, we estimate that Buffett’s leverage is about 1.7-to-1 on average. Therefore, Buffett’s returns appear to be neither luck nor magic, but, rather, reward for leveraging cheap, safe, quality stocks. Decomposing Berkshires’ portfolio into ownership in publicly traded stocks versus wholly-owned private companies, we find that the former performs the best, suggesting that Buffett’s returns are more due to stock selection than to his effect on management.
Keywords: investments, market efficiency, leverage, quality, value, betting against beta
Trading rules
- Use the CRSP database to choose stocks.
- Calculate each stock's rolling 1-year beta against the MSCI US Equity Index.
- Sort stocks from lowest to highest based on their determined beta.
- Categorize stocks into either low or high beta portfolios.
- Assign weights to stocks based on their beta rankings.
- Adjust portfolios on a monthly basis.
- 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.