Control Finance ACC 2010
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Transcript of Control Finance ACC 2010
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Control Systems Methods in Finance:Modeling and Optimal Trading
James A. PrimbsManagement Science and Engineering
Stanford University
ACC 2010
Baltimore, MD
June 30, 2010
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Introduction
Outline
Future Outlook
Modeling Market Dynamics
Optimal Trading in Financial Market
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Important Early Developments in Quantitative Finance
1964: William Sharpe publishes the Capital Asset Pricing Model. (Lintner,
Mossin, and Treynor independently discover the same theory).
1955: Harry Markowitz develops mean-variance portfolio optimization in a
single period framework in his PhD thesis from University of Chicago.Quantitative finance is born.
1969+: Samuelson (69) and especially Merton (69,71,73) publish dynamic
portfolio optimization work using control theory and dynamic programming.
1973: Black and Scholes (with input from Merton) publish the seminal paper
on option pricing theory that shows that dynamic strategies can be used to
create options. Option pricing theory takes off and quantitative finance is
here to stay.
http://en.wikipedia.org/wiki/File:Robert_C._Merton.jpghttp://www.bing.com/reference/search?q=paul%20samuelson&FORM=K1RE1http://upload.wikimedia.org/wikipedia/en/5/5a/Markowitz_1.jpghttp://en.wikipedia.org/wiki/File:William_sharpe_2007.jpg -
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Introduction
Outline
Future Outlook
Modeling Market Dynamics
Optimal Trading in Financial Markets
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Control Problems in Finance
What can we control?
We control what we hold inour portfolio and this
determines our wealth
dynamics.
Most of the standard financial engineering problems can
be cast in a stochastic optimal control framework.
)( rSdtdSurWdtdW
How many shares do you want?
SdZSdtdS
rBdtdB
Example:
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Control Problems in Finance
Most of the standard financial engineering problems can
be cast in a stochastic optimal control framework.
)( rSdtdSurWdtdW
SdZSdtdS
rBdtdB
Example:
Stochastic
System
Dynamics
Things can quickly get more complicated:
Transaction CostsMargin Constraints
Liquidity Constraints
Market Impact
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Control Problems in Finance
What is the objective?
Portfolio Optimization: Maximize the utility of wealth.
))](([max TWUEu
Who uses this: Assets Management Firms, Hedge Funds, Investment
Advisors. All of us! (Think about your retirement account!)
Most of the standard financial engineering problems can
be cast in a stochastic optimal control framework.
1. Grow Wealth
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Control Problems in Finance
What is the objective?
Dynamic Hedging: Minimize the difference between wealth and a
payoff at a specified time T.
2))((min payoffTWE
u
Who uses this: Investment Banks (Option Pricing, Risk Management),
Hedge Funds (Statistical Arbitrage).
Most of the standard financial engineering problems can
be cast in a stochastic optimal control framework.
2. Replicate a payoff
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Control Problems in Finance
What is the objective?
Index Tracking: Minimize the tracking error between your wealth and
a pre-specified index such as the S&P 500.
0
2))()((min dttItWeE
t
u
Who uses this: Asset Management Firms (variations such as beat a
benchmark index), ETFs.
Most of the standard financial engineering problems can
be cast in a stochastic optimal control framework.
3. Track an index
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What are the challenges and
opportunities for control engineers?
Bottom line: Do what we already do, just tailor it to
financial engineering applications.
Create practical, engineering oriented solutions to real
financial engineering problems.
Handle transaction costs and constraints
Efficient algorithms for large problems sizes.
Examples:
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Introduction
Outline
Future Outlook
Modeling Market Dynamics
Optimal Trading in Financial Market
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Financial Market Dynamics
Price dynamics results from the interaction of manytraders using a variety of strategies and objectives.
Lots offeedback loops! To understand such a system, one
must understand feedback. That is what we know best
Market
Financial
Institutions
Funds
Individuals
Government
Regulation
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Motivating Example 187 Stock Market Crash
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
1
1/19/1987
12/1/1987
1
2/10/1987
1
2/21/1987
Returns
Returns
0
500
1000
1500
2000
2500
3000
8/27/1987
9/4/1987
10/1/1987
10/9/1987
11/12/1987
11/20/1987
12/17/1987
12/28/1987
Stock Prices
DJI
The Dow Jones Industrial Average Drops over 500 points (more than 22%) in
a single day!
There is no apparent fundamental reason for the crash. What happened?
The finger is pointed at feedback effects from so called portfolio insurance
ideas. (See the Brady Commission Presidential Report.)
Crash!
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Motivating Example 2Stock Pinning
Stocks on options with high open interest can become pinned to the strike
price at expiration. Why does this happen?One explanation: Feedback effects from Black-Scholes option pricing theory
based dynamic hedging strategies are responsible.
See Avellaneda and Lipkin (03), Primbs and Rathinam (09).
Strike PriceStock Path
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Motivating Example 3August 2007 Hedge Fund Unwinding
See What Happened to the Quants in August 2007? by Khandani and Lo (07).
The price impact of the unwind causes other hedge funds to de-leverage
which exacerbates losses.
Top quant hedge funds lose big: Renaissance loses 8.7% in first 10 days of
August. Highbridge drops 18%. Tykhe is down 20%.
Note: Nothing unusual in overall market during that time. Losses were narrowly
confined to model driven long/short market neutral strategies. Could a control
systems/feedbacks analysis explain and even have predicted this?
What happened: The rapid unwinding of one or more quantitative market
neutral portfolios ripples through the entire quant hedge fund industry.
Long Short
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Feedback Phenomena
Lots of interesting feedback phenomena occurring in the
market!
Control and systems perspective can help to understand,
explain, and perhaps even predict and mitigate
phenomena.
1. Volatility Clustering
2. Heavy Tail Distributions
3. Volatility Smile and Smirks
4. 1000 point drop in 2010.
5. Etc
Theres more!
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Introduction
Outline
Future Outlook
Modeling Market Dynamics
Optimal Trading in Financial Market
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Looking to the Future
Control and systems engineering can become a major tool
for the design, optimal management, and understanding of
financial systems.
Lots of interesting problems that have not been explored
from the control perspective.
We have the tools to address real problems whose impact
is felt on a global scale. An exciting opportunity!