Sponsor: Dr. K.C. Chang
Tony Chen
Ehsan Esmaeilzadeh
Ali Jarvandi
Ning Lin
Ryan O’Neil
Spring 2010
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Background & Problem Statement
Project Scope
Requirements
Assumptions
Approach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future Work
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Investors can potentially earn huge profits by
trading assets
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Many investors trade on speculation and
attempt to predict the market
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Options allow investors to trade with greater
leverage
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
traded
 Strike price – Price the commodities are traded
 Premium – Option price
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Two general types: call (right to buy) and put
(right to sell)
American and European
Short Strangle Strategy:
 Simultaneously selling a call and a put with the
same expiration date
 Typically call strike price > commodity price and
put strike price is < commodity price
SP500 Index, Strangle Put=1100, call=1120
1125
1120
1115
Asset Price
1110
Close
1105
call strike
put strike
1100
1095
1090
1085
11/13/2009
11/18/2009
11/23/2009
11/28/2009
12/3/2009
Date
12/8/2009
12/13/2009
12/18/2009
12/23/2009
 Call: Commodity price less than strike price
 Put: Commodity price greater than strike price
Payoffs Put=1100, call=1120
100
90
80
Payoff
70
60
50
40
30
20
10
0
1080
1090
1100
1110
1120
1130
Asset Price at Expiration
1140
1150
1160
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Stop Loss – Maximum amount seller is willing to
lose. Executed by buying back the same option
Premium Prices for Put=1100, stop loss=5
45
40
35
Premium Prices
30
25
put premium
20
put stop loss
15
10
5
0
11/13/2009
11/18/2009
11/23/2009
11/28/2009
12/3/2009
Date
12/8/2009
12/13/2009
12/18/2009
12/23/2009
Implied Volatility of Call Options on 12/31/09 Expiring on 1/2010
Implied Volatility
0.33
0.28
0.23
0.18
0.13
975
1025
1075
1125
1175
1225
Strike Price
Volatility smile results from variation in implied volatility
among options that vary only on premium value.
1275
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This project is a continuation of Fall 2009
project
 Estimated premiums using Black-Scholes model
 Estimated return using strike prices, stop-loss,
and days before expiration as input
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Previous group used fixed implied volatility. Due to
volatility smile, this results in inaccurate premiums.
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Tradeoffs between profits and risk of ruin need to be
balanced using a equity allocation and risk
management methods.
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No easily accessible tools to quickly assess strangle
strategy performance.
 To provide policy recommendations for the option
sellers to balance profit and risk of loss using
historical data
 To determine the optimal fraction for investment
with associated risk of ruin
 To develop a graphical user interface to provide
useful information investors can act on.
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Our model and tools can aid fund managers to
quickly assimilate information about the current
options market conditions
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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 demand
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Background & Problem Statement
Project Scope
Requirements
Assumptions
Approach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future Work
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Range of data: 2004-2009
Underlying asset is S&P 500 future index
Short strangle strategies only
Call strike prices +5 to +50
Put strike prices -5 to -50
Stop loss from 5 to 45 and without limit
Maximum acceptable volatility at 30, 40, 50
and without limit
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Strategies missing more than 50% of data points
(months) are ignored
Only have closing price data so trade after market
Our trades do not affect the market
Do not simulate trading slippage (always a willing
trade partner)
Do not consider interest rate or inflation (time value
of money)
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Provide recommendations on investment
strategies
 recommendations are based on expected return
on investment and risk of ruin
 Provide a range of optimal strategies that trade
off risk and return according to investors’ risk
tolerances
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Develop a Graphical User Interface (GUI) to
display results, statistics, and visual
representation of selected strategies
 Take filtering criteria from users in the model
interface
 Plot the return (equity curve) for various fractional
allocations of capital
Research relevant papers and previous
work
 Parse and organize the historical data
 Develop the trading model
 Validate model & analyze results
 Determine optimal strategies
 Develop graphical user interface
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Background & Problem Statement
Project Scope
Requirements
Assumptions
Approach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future Work
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Fractional Investment: choosing investment
size by fraction of equity
Optimal f: fractional investment which brings
the highest return
Relevant research:
 Kelly Formula
 Vince Formula
Initialization
Evaluate all
strategies and
fractions
Decide the investment
amount
Decide the number of
contracts
Calculate the investment
amount for next trade
Select the best TWR
and the
corresponding
fraction in the array
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Definition: Ruin is the state of losing a significant
portion (often set at 50%) of your original equity
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Futures Formula:
Where
▪ a = mean rate of return
▪ d = standard deviation of the rate
▪ z = how we define ruin. Here is 50%.
TWR of 20th trade and the corresponding risks of ruin
1.1
0.6
1.08
0.5
TWR
0.4
1.04
0.3
1.02
0.2
1
0.1
0.98
0.96
0
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Fraction
1
Risk of Ruin
1.06
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Background & Problem Statement
Project Scope
Requirements
Assumptions
Approach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future Work
Optimization
Model
• Days before
expiration
• Put & Call strike prices
• Stop loss
• Maximum volatility
• Average return
• Final TWR
• Maximum Draw-Down
• Optimal Fraction
• Risk of Ruin
GUI Application
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Background & Problem Statement
Project Scope
Requirements
Assumptions
Approach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future Work
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Terminal Wealth Relative (TWR) –
𝐹𝑖𝑛𝑎𝑙 𝐴𝑐𝑐𝑜𝑢𝑛𝑡
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐴𝑐𝑐𝑜𝑢𝑛𝑡
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Average percent return – mean of monthly
returns
Maximum drawdown – greatest negative
difference between two dates over a time
period
80
70
Average final TWR
60
50
40
30
20
10
0
60
59
58
57
56
53
52
51
50
49
46
45
44
43
42
39
38
37
36
35
32
Days Before expiration
31
30
29
28
25
24
23
22
21
18
17
16
15
Average Final TWR
2008
Average Final TWR
2009
9
9
8
8
8
7
7
7
6
6
6
5
4
Average Final TWR
9
Average Final TWR
Average Final TWR
Average Final TWR
2007
5
4
5
4
3
3
3
2
2
2
1
1
1
0
0
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
Days Before Expiration
0
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
Days Before Expiration
60 58 56 52 50 464442 38 36 32 30 282422 18 16
Days Before Expiration
Stop-Loss 10
250
Average Final TWR
Average Final TWR
250
200
150
100
50
0
200
150
100
50
0
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
Days Before Expiration
Days Before Expiration
Stop-Loss 30
250
Average Final TWR
Average Final TWR
250
Stop-Loss 20
200
150
100
50
0
Stop-Loss 40
200
150
100
50
0
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
Days Before Expiration
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
Days Before Expiration
Day 44 Before Expiration
Day 42 Before Expiration
Better strategies lie around call = +5 and put = -15
25000
25000
20000
20000
20000
15000
15000
15000
10000
10000
10000
5000
5000
5000
0
0
0
Number of Strategies
25000
Max. Vix = 30
Max. Vix = 50
No Max. Vix
Total number
of Strategies = 33320
Total number
Of Strategies = 34000
Total Number
Of Strategies = 34000
 Methodology:
▪ Vary parameters of the optimal strategy one at a time
 Optimal Strategy:
▪
▪
▪
▪
▪
Call Price = +5
Put Price = -15
Stop-loss = 20
Days before expiration = 42
Fraction allocation = 100%
 Strategy Output:
▪
▪
▪
▪
▪
Final TWR = 711
Risk of ruin = 0%
Average monthly return = 16%
Percent winning trades = 88%
Maximum draw-down = 15%
Stop-Loss
800
800
700
700
600
600
500
500
Final TWR
Final TWR
Days Before Expiration
400
300
400
300
200
200
100
100
0
0
60 58 56 52 50 46 44 42 38 36 32 30 28 24 22 18 16
Days Before Expiration
5
10
15
20
25
30
Stop Loss
35
40
45
None
Sensitivity Analysis by Put Strike
800
800
700
700
600
600
500
500
Final TWR
Final TWR
Sensitivity Analysis by Call Strike
400
300
400
300
200
200
100
100
0
0
5
10
15
20
25
30
35
Call Strike Price
40
45
50
-5
-10
-15
-20
-25
-30
-35
Put Strike Price
-40
-45
-50
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Background & Problem Statement
Project Scope
Requirements
Assumptions
Approach
Methodology
Modeling
Analysis
Evaluation & Recommendations
Conclusion & Future Work
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Days 39-44 provide the highest return
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Stop-loss amounts of 15-25 were most
common in the top strategies
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Continuing to trade in high volatility market
resulted in higher final return
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Manageable higher stop-loss values should be
chosen rather than low stop-loss values which can
be difficult to implement in a volatile market.
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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.
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It 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
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A continuously weighted forecasting model with
current data should be used to update optimal
strategies
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Expansion of scope to analyze more complex
strategies to yield higher profits
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Obtaining a more complete and suitable data set
especially for earlier years to find better patterns for
forecasting the future
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Addition of adaptive logic so that optimal strategies
are calculated using only a portion of data