Peter Beven Northumbria University. * For inviting me from here: (3 Celsius)
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Transcript of phoenixanalysis.files.wordpress.com · Title: Regression Analysis and Quantitative Trading...
Regression Analysis and QuantitativeTrading Strategies
χTrading
Butterfly Spread Strategy
Michael Beven
June 3, 2016
University of Chicago | Financial Mathematics
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Overview
1 Strategy
2 Construction
3 Backtesting
4 Risk Management
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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 nearestat-the-money strike respectively
Butterfly is re-evaluated daily
Spread is hedge-able using delta
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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 0.18
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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
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Strategy
Investment Universe and SecuritiesA payoff illustration:
0 5 10 15 20 25 30Underlying
-15
-10
-5
0
5
10
15
Pay
off
Butterfly Strategy
ATM Call K=15Wing Call K=20ATM Put K=15Wing Put K=10Overall
Figure:
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Strategy
Competitive Edge
Employs exponentially weighted moving averages (EWMA) for analyzingimplied volatility
Flexibility – adjustable days used for EWMA
Ability to exploit multiple markets
Adds alpha to an already diversified portfolio
Low cost structureWing options trade on the opposite side to at-the-money options
Does not require view on market direction
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Construction
Model ConstructionThis strategy takes advantage of the changing implied volatility level:
1 Obtain daily implied volatilities of optionsEntire strip of strikesAccurate minimization techniques
2 Track implied volatility (at-the-money and near strikes) against EWMASearch for large deviations between EWMA and implied volatility
3 Buy or sell the butterfly spread appropriatelyCaptures returns from increasing and decreasing volatility
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Construction
Empirical ExplorationOptions can only exist at certain strikes when far from maturity. TheS&P 500 E-mini June 2016 contracts are assessed:
ESM6P_1800 ESM6P_1900 ESM6P_2000 ESM6P_2100 ESM6P_2200 ESM6P_2300Strike
0
50
100
150
200
250
300
350
Pri
ce
Call and Put Prices at 2015-06-25, S&P 500 E-mini June 2016
CallsPuts
Figure:9 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationMissing prices can be interpolated for backtesting purposes:
ESM6P_1800 ESM6P_1900 ESM6P_2000 ESM6P_2100 ESM6P_2200 ESM6P_2300Strike
0
50
100
150
200
250
300
350
Pri
ce
Call and Put Prices (Interpolated) at 2015-06-25, S&P 500 E-mini June 2016
CallsPuts
Figure:10 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationMost important is the change in level of implied volatility (Sinclair,2008). Calls and puts have slightly different implied volatilities:
ESM6P_1800 ESM6P_1900 ESM6P_2000 ESM6P_2100 ESM6P_2200 ESM6P_2300Strike
0.12
0.14
0.16
0.18
0.20
Vola
tilit
y
Call and Put Implied Volatilities at 2015-06-25, S&P 500 E-mini June 2016
CallsPuts
Figure:11 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationAverage index level: 2006, standard deviation of index level: 73.75
Jul 2015
Aug 2015
Sep 2015
Oct 2015
Nov 2015
Dec 2015
Jan 2016
Feb 2016
Mar 2016
Apr 2016
May 2016
Date
1800
1850
1900
1950
2000
2050
2100
2150
Index L
evel
S&P 500 E-mini Futures
Figure:12 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationA shorter history for EWMA increases agility; a longer historyincreases stability:
Jul 2015
Aug 2015
Sep 2015
Oct 2015
Nov 2015
Dec 2015
Jan 2016
Feb 2016
Mar 2016
Apr 2016
May 2016
Date
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
Vola
tilit
y
EWMA Predicted vs. Actual Implied Volatility
Actual Implied VolatilityEWMA Predicted Implied Volatility
Figure:13 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationChoosing thresholds to buy/sell the butterfly is quantiles based:
0.0 0.2 0.4 0.6 0.8 1.0Quantile
0.025
0.020
0.015
0.010
0.005
0.000
0.005
0.010
0.015
Diffe
rence
Quantiles of EWMA Predicted Minus Actual Implied Volatility
Figure:14 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationEWMA predictions are higher on average compared to realized impliedvolatility. The difference is also negatively skewed:
0.025 0.020 0.015 0.010 0.005 0.000 0.005 0.010 0.015Difference
0
2
4
6
8
10
12
14
16
Frequency
Histogram of EWMA Predicted Minus Actual Implied Volatility
Figure:15 / 25
χTrading – Butterfly Spread Strategy
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Construction
Empirical ExplorationButterfly wingspan: 20, EWMA history: 10 days, buy/sell thresholdsare ±0.3 standard deviations from the mean. 185 trades are made:
Jul 2015
Aug 2015
Sep 2015
Oct 2015
Nov 2015
Dec 2015
Jan 2016
Feb 2016
Mar 2016
Apr 2016
May 2016
Date
2
1
0
1
2
3
4
5
Daily
Pro
fit
Cumulative Profit
Figure:16 / 25
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Construction
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-moneystrike for an overall level
Maximum cost of the spread is half the wingspan (arbitrage arguments)
Capital set at 3 times the above is cost
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Construction
Implications of Empirical ExplorationCapital set at $30 yields a profit over 13.3%:
Jul 2015
Aug 2015
Sep 2015
Oct 2015
Nov 2015
Dec 2015
Jan 2016
Feb 2016
Mar 2016
Apr 2016
May 2016
Date
10
5
0
5
10
15
Perc
enta
ge R
etu
rn
Cumulative Returns
Figure:18 / 25
χTrading – Butterfly Spread Strategy
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Construction
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 differencebetween EWMA predicted and realized implied volatilities
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Construction
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
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Backtesting
Results
June 2015 - May 2016
Fees and costs are to be incorporated
Strategy focuses on liquid assets
Long and short butterfly positions
Consistent performance over time
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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%
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Risk Management
Portfolio Structure
Possible diversified portfolio of butterfly spreads
Aim for diversification benefits in markets with different foundations ofvolatility
Diversification across different option expiration dates
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Risk Management
Process
Frequent revision of positions
Wings of butterfly are stops
Monitor returns versus capital outlay
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About the Manager
Michael Beven graduated as a National Merit Scholar from theAustralian National University in 2012 with a Bachelor of ActuarialStudies and a Bachelor of Finance (Majors in Quantitative andCorporate Finance). He is currently completing a Master of Science inFinancial Mathematics at the University of Chicago. Prior to startingat the University of Chicago, Michael was an Actuarial Analyst inSydney at Quantium, a data analytics focused actuarial consultancy. Hehas also interned at Macquarie Group and Westpac Institutional Bankin quantitative risk analytics. Michael is deeply interested in electronictrading and sees Chicago as a great place to progress his career.
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