Original paper
Abstract
Institutional investors subject to benchmarking, short-selling and leverage constraints have asymmetric effects on both low beta and low volatility anomalies documented by previous studies. Specifically, institutional investors prefer high-beta stocks to low-beta stocks to minimize the tracking error and utilize the embedded leverage of high beta stocks, leading to low-beta anomaly. They can act as the supply source of security lending to the short-sellers, mitigating the overpricing induced negative effect on expected returns from idiosyncratic volatility. Using size effect adjusted institutional ownership as a proxy for institutional limits to arbitrage, I confirm that mandated and financial constrained institutional investors contribute positively to the low beta anomaly but mitigate the low IVOL anomaly using sorting and Fama-MacBeth regressions. I distinguish the highly correlated low beta and low volatility anomalies and find a significantly positive risk premium for institutional holding. A strong January reversal effect of idiosyncratic volatility on expected return is also documented.
Trading rules
- Use the CRSP database for choosing stocks.
- Calculate a rolling 1-year beta for every stock relative to the MSCI US Equity Index.
- Organize stocks from lowest to highest based on their calculated beta values.
- Distribute stocks into either low beta or high beta portfolios.
- Assign weights to stocks according to their beta rankings.
- Adjust the portfolios on a monthly basis.
- Rescale both portfolios to have a beta of one at formation.
- Create a cost-neutral, beta-neutral Betting-Against-Beta strategy: take a long position in low-beta stocks and a short position in high-beta stocks.
- Explore basic tweaks (for instance, go long on the stocks in the lowest beta decile and short on those in the highest beta decile) to boost returns.
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.