Original paper
Abstract
Traditional risk factor models indicate that hedge funds capture pre-fee alphas of 6% to 10% per annum over the period from 1996 to 2012. At the same time, the hedge fund return series is not reliably distinguishable from the returns of mechanical S&P 500 put-writing strategies. We show that the high excess returns to hedge funds and put-writing are consistent with an equilibrium in which a small subset of investors specialize in bearing downside market risks. Required rates of return in such an equilibrium can dramatically exceed those suggested by traditional models, affecting inference about the attractiveness of these investments.
Keywords:Â hedge funds, downside risk, replication, performance evaluation, risk management, endowment model
Trading rules
- Construct a portfolio that incorporates a monthly short position in an out-of-the-money S&P 500 put option.
- Strike price distance Z: 1.0x monthly S&P 500 Index standard deviation.
- Apply a consistent 2.0x leverage for the portfolio.
- Allocate any remaining funds to the risk-free interest rate.
- On a monthly schedule, adjust the portfolio and write put options.
Python code
Backtrader
import backtrader as bt
import mathimport numpy as np
class PutOptionWritingStrategy(bt.Strategy):
params = (
('leverage', 2.0),
('strike_price_distance_multiplier', 1.0)
)
def __init__(self):
self.put_option = None
self.sp500 = self.datas[0]
def next(self):
# Calculate the standard deviation of the S&P 500 Index for the last month
monthly_std = np.std(self.sp500.get(size=21))
# Calculate the strike price for the put option
strike_price = self.sp500[0] - (self.params.strike_price_distance_multiplier * monthly_std)
# Calculate the option premium
option_premium = max(self.sp500[0] - strike_price, 0)
# Calculate the required capital to short the put option
capital_required = option_premium * self.params.leverage
# Calculate the capital to invest in the risk-free rate
free_capital = self.broker.get_cash() - capital_required
# Invest free capital in risk-free rate
self.buy(data=self.datas[1], size=free_capital)
# Short the put option
self.sell(data=self.put_option, size=self.params.leverage, exectype=bt.Order.Put, strike=strike_price)
if __name__ == '__main__':
cerebro = bt.Cerebro()
# Add the S&P 500 Index and risk-free rate data feeds
cerebro.adddata(bt.feeds.YahooFinanceData(dataname='^GSPC', fromdate='2000-01-01', todate='2021-09-30'))
cerebro.adddata(bt.feeds.FRED(dataname='DTB3', fromdate='2000-01-01', todate='2021-09-30'))
# Add the put option data feed
cerebro.adddata(bt.feeds.GenericCSVData(dataname='put_option_data.csv', dtformat=('%Y-%m-%d')))
cerebro.addstrategy(PutOptionWritingStrategy)
cerebro.broker.setcash(100000.0)
cerebro.run()
cerebro.plot()Please note that you’ll need to provide a CSV file named ‘put_option_data.csv’ with the put option data. This code assumes that the file has a column named ‘Close’ for the option price and a ‘Date’ column with the format YYYY-MM-DD. Adjust the code as needed based on your data source.