Original paper

SSRN-id2548050.pdf598.7KB

Abstract

The shape of the VIX term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. A single principal component, Slope, summarizes nearly all this information, predicting the excess returns of S&P 500 variance swaps, VIX futures, and S&P 500 straddles for all maturities and to the exclusion of the rest of the term structure. Slope's predictability is incremental to other proxies for the conditional variance risk premia, is economically significant, and can only partially be explained by variations in observable risk measures.

Keywords: VIX, variance risk, term structure, expectations hypothesis, variance swaps, VIX futures, straddles

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

Risk Premia and the VIX Term Structure

Original paper

Abstract

Trading rules

Python code

Backtrader