Regression Analysis and Quantitative Trading Strategies. χtrading Butterfly Spread Strategy

Transcription

1 Regression Analysis and Quantitative Trading Strategies χtrading Butterfly Spread Strategy Michael Beven June 3, 2016 University of Chicago Financial Mathematics 1 / 25

2 Overview 1 Strategy 2 Construction 3 Backtesting 4 Risk Management 2 / 25

3 Strategy Butterfly Strategy Exploits fluctuations in the implied volatility of options Buys (sells) a call and put at-the-money to the nearest strike (levels of 5) Sells (buys) a call and put B units above and below the nearest at-the-money strike respectively Butterfly is re-evaluated daily Spread is hedge-able using delta 3 / 25

4 Strategy Butterfly Strategy Outer options (wings) reduce capital requirements Robust strategy with controllable results Applicable to several options markets Backtest suggests annualized returns of 14.7% Backtest suggests Sharpe ratio of 0.09 Backtest suggests Sortino ratio of / 25

5 Strategy Investment Universe and Securities Potential underlying assets: all exchange traded securities with options Requires liquid options with multiple strikes Four options (two at-the-money and two wings), and The underlying for an optional delta hedge Can be long or short the butterfly 5 / 25

6 Payoff Strategy Investment Universe and Securities A payoff illustration: 15 Butterfly Strategy ATM Call K=15 Wing Call K=20 ATM Put K=15 Wing Put K=10 Overall Underlying 6 / 25

7 Strategy Competitive Edge Employs exponentially weighted moving averages (EWMA) for analyzing implied volatility Flexibility adjustable days used for EWMA Ability to exploit multiple markets Adds alpha to an already diversified portfolio Low cost structure Wing options trade on the opposite side to at-the-money options Does not require view on market direction 7 / 25

8 Model Construction This strategy takes advantage of the changing implied volatility level: 1 Obtain daily implied volatilities of options Entire strip of strikes Accurate minimization techniques 2 Track implied volatility (at-the-money and near strikes) against EWMA Search for large deviations between EWMA and implied volatility 3 Buy or sell the butterfly spread appropriately Captures returns from increasing and decreasing volatility 8 / 25

9 Empirical Exploration Options can only exist at certain strikes when far from maturity. The S&P 500 E-mini June 2016 contracts are assessed: Call and Put Prices at , S&P 500 E-mini June Calls Puts Price ESM6P_1800 ESM6P_1900 ESM6P_2000 ESM6P_2100 ESM6P_2200 ESM6P_2300 Strike 9 / 25

10 Empirical Exploration Missing prices can be interpolated for backtesting purposes: Call and Put Prices (Interpolated) at , S&P 500 E-mini June Calls Puts Price ESM6P_1800 ESM6P_1900 ESM6P_2000 ESM6P_2100 ESM6P_2200 ESM6P_2300 Strike 10 / 25

11 Empirical Exploration Most important is the change in level of implied volatility (Sinclair, 2008). Calls and puts have slightly different implied volatilities: Call and Put Implied Volatilities at , S&P 500 E-mini June Calls Puts 0.18 Volatility ESM6P_1800 ESM6P_1900 ESM6P_2000 ESM6P_2100 ESM6P_2200 ESM6P_2300 Strike 11 / 25

12 Empirical Exploration Average index level: 2006, standard deviation of index level: S&P 500 E-mini Futures Index Level Jul 2015 Aug 2015 Sep 2015 Oct 2015 Nov 2015 Dec 2015 Jan 2016 Date Feb 2016 Mar 2016 Apr 2016 May / 25

13 Empirical Exploration A shorter history for EWMA increases agility; a longer history increases stability: EWMA Predicted vs. Actual Implied Volatility Actual Implied Volatility EWMA Predicted Implied Volatility 0.22 Volatility Jul 2015 Aug 2015 Sep 2015 Oct 2015 Nov 2015 Dec 2015 Jan 2016 Date Feb 2016 Mar 2016 Apr 2016 May / 25

14 Empirical Exploration Choosing thresholds to buy/sell the butterfly is quantiles based: Quantiles of EWMA Predicted Minus Actual Implied Volatility Difference Quantile 14 / 25

15 Empirical Exploration EWMA predictions are higher on average compared to realized implied volatility. The difference is also negatively skewed: Histogram of EWMA Predicted Minus Actual Implied Volatility Frequency Difference 15 / 25

16 Empirical Exploration Butterfly wingspan: 20, EWMA history: 10 days, buy/sell thresholds are ±0.3 standard deviations from the mean. 185 trades are made: 5 Cumulative Profit 4 3 Daily Profit Jul 2015 Aug 2015 Sep 2015 Oct 2015 Nov 2015 Dec 2015 Jan 2016 Date Feb 2016 Mar 2016 Apr 2016 May / 25

17 Implications of Empirical Exploration Strategy performs best when closer to maturity (within 6 months) Call and put implied volatilities are averaged around the at-the-money strike for an overall level Maximum cost of the spread is half the wingspan (arbitrage arguments) Capital set at 3 times the above is cost 17 / 25

18 Implications of Empirical Exploration Capital set at $30 yields a profit over 13.3%: 15 Cumulative Returns 10 Percentage Return Jul 2015 Aug 2015 Sep 2015 Oct 2015 Nov 2015 Dec 2015 Jan 2016 Date Feb 2016 Mar 2016 Apr 2016 May / 25

19 Implementation Positions are reviewed at the beginning of each day Position sizes are scaled to the desired level of investment Refrain from delta hedging for symmetrical volatility trading Set buying and selling thresholds based on the empirical difference between EWMA predicted and realized implied volatilities 19 / 25

20 Investment Process Mechanism of strategy diversifies well in a factor-based portfolio Can apply the butterfly strategy across different asset classes Candidate assets are selected through a rigorous process Chosen assets are reassessed for each option expiration 20 / 25

21 Backtesting Results June May 2016 Fees and costs are to be incorporated Strategy focuses on liquid assets Long and short butterfly positions Consistent performance over time 21 / 25

22 Backtesting Return and Risk Cumulative return: 13.3% Annualized cumulative return: 14.7% Annualized standard deviation of returns: 11.7% Sharpe ratio: 0.09 Sortino ratio: 0.18 Maximum drawdown: 7.5% 22 / 25

23 Risk Management Portfolio Structure Possible diversified portfolio of butterfly spreads Aim for diversification benefits in markets with different foundations of volatility Diversification across different option expiration dates 23 / 25

24 Risk Management Process Frequent revision of positions Wings of butterfly are stops Monitor returns versus capital outlay 24 / 25

25 About the Manager Michael Beven graduated as a National Merit Scholar from the Australian National University in 2012 with a Bachelor of Actuarial Studies and a Bachelor of Finance (Majors in Quantitative and Corporate Finance). He is currently completing a Master of Science in Financial Mathematics at the University of Chicago. Prior to starting at the University of Chicago, Michael was an Actuarial Analyst in Sydney at Quantium, a data analytics focused actuarial consultancy. He has also interned at Macquarie Group and Westpac Institutional Bank in quantitative risk analytics. Michael is deeply interested in electronic trading and sees Chicago as a great place to progress his career. 25 / 25