Backtest Period
Markets Traded
Equities / Options
Maximum Drawdown
Period of Rebalancing
Daily
Return (Annual)
Sharpe Ratio
Standard Deviation (Annual)
Original paper
SSRN-id2495414.pdf838.0KB
Abstract
Ex-ante estimates of the volatility premium embedded in VIX futures, known as the VIX premium, fall or stay flat when ex-ante measures of risk rise. This is not an artifact of mismeasurement: 1) Ex-ante premiums reliably predict ex-post returns to VIX futures with a coefficient near one, and 2) Falling ex-ante premiums predict increasing ex-post market and investment risk, creating profitable trading opportunities. Falling hedging demand helps explain this behavior, as premiums and trader exposures tend to fall together when risk rises. These facts provide a puzzle for theories of why investors hedge volatility.
Keywords:Â VIX, volatility, variance risk premium
Trading rules
- Engage in trades using VIX futures, and employ the E-mini S&P 500 for hedging.
- When in contango and the daily roll > 0.10 points, sell the nearest VIX futures that still have over 10 business days until maturity.
- When in backwardation and the daily roll < -0.10 points, buy the nearest VIX futures that have more than 10 trading days left to maturity.
- Hold the position for a span of 5 business days and use corresponding E-mini S&P 500 positions to hedge against fluctuations in the spot VIX.
- Calculate daily roll as (front VIX futures price - VIX) / number of business days until settlement.
- Determine hedge ratios using regression analysis of VIX futures price changes and E-mini S&P 500 percentage changes.
Python code
Backtrader
import backtrader as bt
import numpy as np
from sklearn.linear_model import LinearRegression
class VIXFuturesStrategy(bt.Strategy):
def __init__(self):
self.vix = self.datas[0]
self.vix_futures = self.datas[1]
self.es = self.datas[2]
self.order = None
self.hold_days = 0
def next(self):
if self.order:
return
if self.hold_days > 0:
self.hold_days -= 1
return
days_to_maturity = self.vix_futures.days_to_maturity() # Implement this in your data feed
if days_to_maturity < 10:
return
daily_roll = (self.vix_futures[0] - self.vix[0]) / days_to_maturity
if daily_roll > 0.10:
position_size = self.broker.getvalue() * 0.9 / self.vix_futures # Adjust based on your risk management
self.sell(data=self.vix_futures, size=position_size)
hedge_ratio = self.calculate_hedge_ratio()
self.buy(data=self.es, size=position_size * hedge_ratio)
self.hold_days = 5
elif daily_roll < -0.10:
position_size = self.broker.getvalue() * 0.9 / self.vix_futures # Adjust based on your risk management
self.buy(data=self.vix_futures, size=position_size)
hedge_ratio = self.calculate_hedge_ratio()
self.sell(data=self.es, size=position_size * hedge_ratio)
self.hold_days = 5
def calculate_hedge_ratio(self):
vix_futures_returns = np.diff(np.log(self.vix_futures.get(size=252))) # 1-year lookback
es_returns = np.diff(np.log(self.es.get(size=252))) # 1-year lookback
lr = LinearRegression()
lr.fit(es_returns.reshape(-1, 1), vix_futures_returns)
return -lr.coef_[0]
def notify_order(self, order):
if order.status in [order.Submitted, order.Accepted]:
return
if order.status in [order.Completed]:
if order.isbuy():
self.log(f'BUY EXECUTED, {order.executed.price}')
elif order.issell():
self.log(f'SELL EXECUTED, {order.executed.price}')
elif order.status in [order.Canceled, order.Margin, order.Rejected]:
self.log('Order Canceled/Margin/Rejected')
self.order = None