The Volatility Premium Puzzle Eric Falkenstein Jan 3 2017 The Volatility Premium Puzzle

S&P500, Straddle, Variance Swap returns 1986-2016 Monthly data on Straddles, SP500, Variance Swaps S&P500 Sell Straddle Short VarSwap AnnRet 10.6% 2.56 2.80 AnnStdev 15.1% 3.18 3.46 Sharpe 0.70 0.81 Beta -0.02 0.48

Vol Risk Premium Internationally

How to Trade Selling gamma Not trivial to implement in real time Variance swaps Options (eg, straddles) Futures & ETFs on implied vol Not trivial to implement in real time

What is the essence of the volatility premium? Bias in expected volatility (implied volatility)? Autocorrelation in SPY? Time varying autocorrelation in SPY? Fat tails (jumps)? Skew? Option Term (1 week vs. 1 year)?

Straddle Replicate Straddle by momentum trading At-the-money long put and call is long straddle If actual volatility > implied volatility long straddle makes positive profit

Straddle: Black-Scholes S=Stock Price T=Option maturity (trading days to expiry)/252 =implied volatility N() =Normal cdf of standard normal c=Call=max(ST – K,0) at t=T p=Put=max(K – ST,0) at t=T

Straddle: Option Risk Neutral Valuation Assumption about stock motion Assume expected return of the stock is the risk free rate Easy to prove with binomial model Discount at risk-free rate, assume expected stock return is the risk- free rate

Straddle: Option Gamma and Theta Daily pnl=gamma pnl + theta pnl + vega pnl + …. Theta is negative of gamma: you pay for gamma

Straddle Term and Profitability 2010+ Weekly Monthly AnnRet 9.21 7.21 AnnStdev 6.73 6.33 Sharpe 1.37 1.14 2006+ Ann 8.90 0.42 8.20 9.81 1.09 0.04

Variance Swap A bet an actual vs. expected variance Notional set to 100,000/(2*) to be constant 1 ‘vega’ Use Variance Swap implieds, VIX, not atm implied vol

VIX Implied 30-day volatility from Variance Swap (not atm implied) Uses option prices on range of options on S&P500 Weighted blend Square root of par variance swap rate for 30-day term Payoff to variance swap: Notional*(realized variance – strike) Annualized Data on VIX started in 1986 Futures on VIX started in 2006 ETF on VIX futures—VXX—started in 2009

VIX: VXX ETF vs. VIX Futures Use Adjusted futures prices Adjusted for ‘roll’ from one contract to next as expiry approaches VXX targets 30-day futures Data from Feb 2009-Dec 2016 VXX Futures AnnRet 87.5% 84.6% AnnStdev 62.8% 66.9%

VIX: Volatility Curve Generally in Contango But not always, especially when vol is very high (eg, October 2008)

VIX: 1 Month ATM Implied < VIX VIX is a function of several option, not just at the money Volatility generally higher for puts: skew in implied volatilities at-the-money implieds

Comparing Volatility Strategies Strategies normalized to have same volatilities SPY Straddle VarianceSwap VXX AnnRet 1.74 3.92 2.45 1.59 AnnStdev 3.61 3.59 3.63 3.58 Ratio 0.48 1.09 0.68 0.44 Beta 1.00 0.07 0.63 0.78

Expected Vol and SPX changes Strong negative correlation Strongest in short run

Actual Vol and SPX Extreme moves correlated with actual vol Correlation strongest in short run

Monthly, Annual vs. SPX Short Variance Swap Short Straddle Short VXX

Daily AutoCorrelation SPX returns Negative autocorrelation at high frequency 1986+ 2006+ Daily Monthly Annual stdev 18.4% 15.3% 17.5% skew -1.18 -0.62 -0.06 kurtosis 27.28 2.87 0.07 VIX^2 VIX 30-day iVol 12-month iVol 4.93% 20.05% 17.78% 19.92% 1D Actual Var 1D Actual Vol 1M Actual Vol 12M Actual Vol 4.10% 20.24% 14.80% 17.60% Daily AutoCorrelation 1926+ 1994+ 2003+ 1-day 6.87% -3.93% -8.23% 2-day -0.44% -6.21% -8.28% 3-day 1.44% -6.38% -7.36% 4-day 1.06% -9.17% -10.27% 5-day 0.30% -10.71% -11.39%

Trading costs SPY: 0.01 bid-ask for $216 stock 10-day atm option 0.01 on 0.45 option 1 year atm option 0.16 on $14.00 option

Daily data available to students Fed Funds, 10yrBond, Utility Index, VIX and SPX daily to 1986 1986- 10 day, 1month and 12 month SPY at-the-money implied volatility 2006- Weekly SPY option data 2010- Current Transaction cost estimates

Documents JPMorgan white paper on Variance Swaps CBOE on VIX Nomura on the Volatility Risk Premium

Project Derive optimal strategy ratio based on an assumption about a deeper pattern Show—empirically and theoretically—how deep pattern drives volatility premium Argue in what way it complements or substitutes for equity risk premium What is optimal? Not as obvious as you would think. Max Sharpe Ratio Max Information Ratio Best complement to S&P500 Other….