1. The Volatility Premium Puzzle
Eric Falkenstein
Jan
The Volatility Premium Puzzle

2. 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

3. Vol Risk Premium Internationally

4. 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

5. 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)?

6. 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

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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%

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

15. 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

16. 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

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

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

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

20. 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%

21. 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

22. 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

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

24. 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….