Sponsor Dr KC Chang Tony Chen Ehsan Esmaeilzadeh Ali Jarvandi Ning Lin Ryan ONeil Spring 2010 Outline Background amp Problem Statement Project Scope Requirements Assumptions Approach ID: 561670
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Optimal Option Investment Strategy
Sponsor: Dr. K.C. ChangTony ChenEhsan EsmaeilzadehAli JarvandiNing LinRyan O’NeilSpring 2010Slide2
Outline
Background & Problem StatementProject ScopeRequirementsAssumptions
ApproachMethodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future WorkSlide3
Background
Investors can potentially earn huge profits by trading assetsMany investors trade on speculation and attempt to predict the marketOptions allow investors to trade with greater leverageSlide4
Definitions
Option Contract – A conditional futures contract to trade an asset at a given price and date. Option buyer gets right to exercise contract.Positions – Long (buyer) and short (seller) Expiration date –date underlying assets are tradedStrike price – Price the commodities are tradedPremium – Option priceSlide5
Definitions
Two general types: call (right to buy) and put (right to sell)American and EuropeanShort Strangle Strategy:Simultaneously selling a call and a put with the same expiration dateTypically call strike price > commodity price and put strike price is < commodity priceSlide6
Background – Short StrangleSlide7
Background – Strangle Payoffs
Call: Commodity price less than strike pricePut: Commodity price greater than strike priceSlide8
Background – Stop Loss
Stop Loss – Maximum amount seller is willing to lose. Executed by buying back the same optionSlide9
Volatility Smile
Volatility smile results from variation in implied volatility among options that vary only on premium value.Slide10
Previous Team This project is a continuation of Fall 2009 project
Estimated premiums using Black-Scholes modelEstimated return using strike prices, stop-loss, and days before expiration as inputSlide11
Problem StatementPrevious group used fixed implied volatility. Due to volatility smile, this results in inaccurate premiums.
Tradeoffs between profits and risk of ruin need to be balanced using a equity allocation and risk management methods.No easily accessible tools to quickly assess strangle strategy performance.Slide12
Optimal Option Investment Strategy Project Goals
To provide policy recommendations for the option sellers to balance profit and risk of loss using historical dataTo determine the optimal fraction for investment with associated risk of ruinTo develop a graphical user interface to provide useful information investors can act on.Slide13
Business CaseOur model and tools can aid fund managers to quickly assimilate information about the current options market conditions
We provide a software tool to display equity curves over a specified period of time. Our tool also shows payoffs from fractional investment allocations to match returns and risk of ruin to customer demandSlide14
Outline
Background & Problem StatementProject ScopeRequirements
AssumptionsApproach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future WorkSlide15
Project Scope
Range of data: 2004-2009 Underlying asset is S&P 500 future indexShort strangle strategies onlyCall strike prices +5 to +50 Put strike prices -5 to -50Stop loss from 5 to 45 and without limitMaximum acceptable volatility at 30, 40, 50 and without limitSlide16
Assumptions
Strategies missing more than 50% of data points (months) are ignoredOnly have closing price data so trade after marketOur trades do not affect the marketDo not simulate trading slippage (always a willing trade partner)Do not consider interest rate or inflation (time value of money)Slide17
Requirements [1 of 2]
Provide recommendations on investment strategiesrecommendations are based on expected return on investment and risk of ruinProvide a range of optimal strategies that trade off risk and return according to investors’ risk tolerancesSlide18
Requirements [2 of 2]
Develop a Graphical User Interface (GUI) to display results, statistics, and visual representation of selected strategies Take filtering criteria from users in the model interfacePlot the return (equity curve) for various fractional allocations of capitalSlide19
Approach
Research relevant papers and previous workParse and organize the historical data Develop the trading modelValidate model & analyze results Determine optimal strategiesDevelop graphical user interface Slide20
Outline
Background & Problem StatementProject ScopeRequirements
AssumptionsApproach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future WorkSlide21
Optimal Fraction AllocationFractional Investment: choosing investment size by fraction of equity Optimal f: fractional investment which brings the highest return
Relevant research: Kelly FormulaVince FormulaSlide22
Fractional Investment AlgorithmSlide23
Risk of RuinDefinition: Ruin is the state of losing a significant portion (often set at 50%) of your original equity
Futures Formula: Wherea = mean rate of return d = standard deviation of the rate z = how we define ruin. Here is 50%. Slide24
Methodology VerificationSlide25
Outline
Background & Problem StatementProject ScopeRequirements
AssumptionsApproach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future WorkSlide26
ModelingSlide27
Modeling
GUI ApplicationOptimization Model Days before expiration
Put & Call strike prices Stop loss Maximum volatility
Average return
Final TWR
Maximum Draw-Down
Optimal
Fraction
Risk of RuinSlide28
Outline
Background & Problem StatementProject ScopeRequirements
AssumptionsApproach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future WorkSlide29
Evaluation MetricsTerminal Wealth Relative (TWR) –
Average percent return – mean of monthly returnsMaximum drawdown – greatest negative difference between two dates over a time period Slide30
Days Before Expiration 2007-2009Slide31
Days Before Expiration – Individual YearsSlide32
Stop-Loss 2007-2009Slide33
Strike Prices 2007-2009
Day 44 Before ExpirationDay 42 Before ExpirationBetter strategies lie around call = +5 and put = -15Slide34
Volatility Index
Number of Strategies No Max. VixTotal Number Of Strategies = 34000 Max. Vix = 30Total number of Strategies = 33320Max.
Vix = 50Total number Of Strategies = 34000Slide35
Sensitivity AnalysisOptimal Strategy:
Call Price = +5Put Price = -15Stop-loss = 20Days before expiration = 42Fraction allocation = 100%Strategy Output:Final TWR = 711Risk of ruin = 0%Average monthly return = 16%Percent winning trades = 88%Maximum draw-down = 15%
Methodology:
Vary parameters of the optimal strategy one at a timeSlide36
Sensitivity AnalysisSlide37
Sensitivity AnalysisSlide38
Outline
Background & Problem StatementProject ScopeRequirements
AssumptionsApproach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future WorkSlide39
EvaluationDays 39-44 provide the highest returnStop-loss amounts of 15-25 were most common in the top strategies
Continuing to trade in high volatility market resulted in higher final returnSlide40
RecommendationsManageable higher stop-loss values should be chosen rather than low stop-loss values which can be difficult to implement in a volatile market.
Fractional investment allocation should also be less than 100% to avoid ruin because the market is constantly moving and therefore the future is still uncertain.Slide41
ConclusionIt would not be necessarily accurate to use our exact optimal strategies in the future since it may only remain optimal for a short period of time
A continuously weighted forecasting model with current data should be used to update optimal strategiesSlide42
Future WorkExpansion of scope to analyze more complex strategies to yield higher profits
Obtaining a more complete and suitable data set especially for earlier years to find better patterns for forecasting the futureAddition of adaptive logic so that optimal strategies are calculated using only a portion of dataSlide43
Questions