Neuroeconomics at URI: The CBA Student Directed Hedge Fund with Big Data Informatics By Gordon H....

Neuroeconomics at URI: The CBA Student Directed Hedge Fund with

“Big Data” InformaticsBy

Gordon H. Dash, Jr.1 and Nina Kajiji2

1College of Business, University of Rhode Island2The NKD Group, Inc. and Computer Science and Statistics, University of Rhode Island.

www.GHDash.net [email protected] [email protected]

URI Neuroscience ColloquiumFebruary 25, 2011

http://www.ghdash.net/

http://www.ninakajiji.net/

mailto:[email protected]

mailto:[email protected]

Credits

• CBA - College of Business Administration• Hedge Fund – BUS 423-II, sec 02 “Student

Directed Investment Fund”• “Big Data” Informatics – URI Computer

Science Department is heading a drive for a new tract.

• RANN – Radial Basis function artificial neural network

URI-Neuroscience Colloquium 25-Feb-2013 – Dash and Kajiji 2

Dual Purpose

• To present the theory and application of a concentric RANN real-time automated trading (AT) algorithm and its ability to produce profitable trades.

• Using high frequency dimensions to represent low-frequency Fama-French-Carhart (FFC) firm fundamental variables, we estimate scale elasticity metrics to explain profitable trades produced by the AT algorithm. 3URI-Neuroscience Colloquium 25-Feb-2013 – Dash and Kajiji

AT System Development for Strategic Effects

• The AT algorithm is predicated on a four phase concentric strategic decision cycle that is capable of responding to various forecasts of future events (OODA):1. Observation (of markets)2. Orientation by neruoeconomic informatics (align

forecasts with reality)3. Decision on asset position (open / close / hold ?)4. Action (execute trade and store record structure)

4URI-Neuroscience Colloquium 25-Feb-2013 – Dash and Kajiji

Applied Problems:

• Image, Sound, and Pattern recognition• Financial Time Series Mapping• Decision making· Knowledge discovery · Context-Dependent Analysis· …and more…

Artificial Intellect:Who is stronger and why?

NEURO-INFORMATICS

- modern theory about principles and new mathematical models of information processing, which based on the biological prototypes and mechanisms of human brain activities

A Neural Network (AI) Primer


Concentric OODA


Justification• BIG DATA: “…high frequency trading firms can generate more than a million

trades in a single day … more than 50 percent of equity market volume. Stated another way: a firm that trades one million times per day may submit 90 million or more orders that are cancelled.” Mary L. Schapiro, Chairman, U.S. Securities and Exchange Commission, 07-Sep-2010.

• INFORMATICS: “The need for valid statistical tools is greater than ever; data sets are massive, often measuring hundreds of thousands of measurements for a single subject…With high-dimensional data, ... the correct specification of the parametric model an impossible challenge … The new generation of statisticians cannot be afraid to go against standard practice … The science of learning from data (i.e. statistics) is arguably…one in which we try to understand the very essence of human beings.” Mark van der Laan, Jiann-Ping Hsu, Sherri Rose, AMSTATNEWS, September 2010.


DataAcquisition

DataInformatics

Interpretation and

Decision Making

Signals&

parameters

Characteristics&

Estimations

Rules&

KnowledgeProductions

DataAcquisition

DataInformatics

Decision Making

“Big Data” Knowledge-Base

Adaptive Machine Learningvia Neural Network

An Intelligent Data Analysis Experiment


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Learning and AdaptationNN are capable to adapt themselves (the synapses connections between units) to special environmental conditions by changing their structure or strengths connections.

Non-Linear FunctionalityEvery new state of a neuron is a nonlinear function of the input pattern created by the firing nonlinear activity of the other neurons.

Robustness of AssociabilityNN states are characterized by high robustness or insensitivity to noisy and fuzzy input data owing to use of a highly redundant distributed structure.

Principles of Neurocomputing


Artificial Neural NetworksSingle Layer (e.g., the RBF)

Inputs

Output

An artificial neural network is composed of many artificial neurons that are linked together according to a specific network architecture. The objective of the neural network is to transform the inputs into meaningful outputs.


Neural Network Mathematics

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Learning with RBF Neural Networks

RBF neural network:

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An RBF neural network learns a nonlinear function.

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Bayesian Network Training

• Conventional training can be interpreted in statistical terms as variations on maximum likelihood estimation. The idea is to find a single set of weights for the network that maximizes the fit to the training data, perhaps modified by some sort of weight penalty to prevent overfitting.

• Ideal Bayesian training:– Before the start of data analysis obtain prior opinions about what the true relationship

might be expressed as a probability distribution over the network weights that define this relationship.

– After training the network collect revised opinions as a posterior distribution over network weights.

– Exact analytical methods for models as complex as neural networks are out of the question

• Practical Bayesian Training:– Find the weights that are most probable, using methods similar to conventional

training with regularization, and then approximate the distribution over weights using information available at this maximum.

– Approximation is preferred for computational efficiency instead of using a Monte Carlo method to sample from the distribution of the weights.


K4-RBF ANN (RANN) Extensions• The Kajiji (2001) extension to the traditional RANN

specification introduced multiple objectives within a Bayesian RANN framework.

• Efficient mapping. By adding a weight penalty or Tikhonov’s regularization parameter to the SSE optimization objective, the modified SSE is restated as the following cost function:

• Optimal Weight Decay. Additionally, Kajiji proposed a closed-form solution to the estimation of the weight parameter based on Hemmerle’s extensions to the traditional ridge-regression parameters and Crouse’s incorporation of priors:

• Under the Kajiji specification the function to be minimized is stated as:


K4 RANN Contributions• Excellent mapping capabilities of the K4-RANN

topology allows for better financial forecasts for a system exhibiting Brownian motion with drift and volatility – such as stock price movements.

• The algorithmic speed of the generalized RBF is greatly enhanced by the K4 enhancements making it suitable for HF valuation in N dimensional space.


Developing an Auto Trader using the K4-RANN


Trading System Evolution

• To assign stocks to wealth-building groups based on the historical trading performance of WINKS.

• To define the operational characteristics of the HF Trading system -- WINKS.

• To estimate the relative quasi-elasticity of firm-fundamental metrics to explain the production of WINKS trading profitability.

Automated Trading System (WINKS)

Mathematical Finance

Business Decision Theory

MCDA


Investor Trading Behavior

• Let (Ω, θ, P) be the measure space.• Let P(Ω) = 1. • Then the probability space is (Ω, θ, P) with a filtration of {Γt : t

є [0, ∞]}. This is an increasing sequence of σ-algebras of Γ that determines the relevant timing of information.

• That is, Γt is loosely viewed as the set of events whose outcomes are certain to be revealed to investors as true or

false by, or at, time t.


We assume the Investor’s probability space is a continuous-time stochastic process (Kajiji and Forman, 2013):

Model for Equity Trading Profits• Let Xt represent an individual stock’s market price at time t• We assume that the price process of X follows a geometric

Brownian motion with a constant drift and volatility.• Let θ represent a trading strategy.• Let θt (ω) be the quantity of each security held in each state ω

є Ω and at each time t. • We assume that the trading strategy can only make use of

available information at any time t. This prevents the possibility of unlimited gains through uncontrolled high-frequency trading or flash-crash trading – i.e. θ is adapted.

• We thus can define the total financial gain as:between any time s and r – (Ito’s stochastic integral).


Simple Buy and Hold Strategy (BH)

• Position is initiated after some stopping time T and closed at a later stopping time U.

• For a position size θt (ω), the trading strategy θ, is defined by θt = 1(T<t<U) θt (ω).

• By definition, the gain from simple BH is:


The N-Dimensional Trading Strategy

• Suppose we have n different securities with price process: X1, … Xn and a trading strategy of θ = (θ1, … θn ) then the total gain is:


The WINKS OOAD Algorithm


The WINKS Trading Model

• The high frequency model implemented in the automated trader is:

• yi = f(x1, x2) • Where:

• yi = Ln(1+ri) -- ri is the return on security i

• X1 = Lag(Ln(1 + rVXX))

• X2 = Lag(Ln(1 + rPLW))

• Note: – VXX = iPath S&P 500 VIX Short-Term Futures (ETN)– PLW = PowerShares 1-30 Laddered Treasury (ETF)


The database of 2,225 securities was established by random selection from the 8,000 tickers followed by Yahoo! Finance.

These five were chosen for demonstration as they have the some of the highest trading profit.

Trading Efficiency = (difference between BH and Trading Profit) / Ini. Investment) *100.

Note: All equities positions were created with an investment of $1000

Results: The BH Strategy v/s HF K4-RANN AT A Sample of Trading Profitability, June 01, 2009 to March 19, 2010


Trading Report Jul 1st, 2010


Summary Report: Page 1 Jul 1st, 2010


Summary Report: Page 2 Jul 1st, 2010


Trading History – Ticker = ADS Jul 1st, 2010


Trading Summary – Ticker = ADS Jul 1st, 2010


Do Firm Fundamentals Explain Profitable Trades?

• Goal: To use the K4 mapping efficiency to estimate non-parametric quasi-elasticity metrics of individual firm fundamental variables in the production of K4 trading profitability (see Dash and Kajiji, 2008 for univariate detail and Kajiji and Dash, 2013 for multivariate extensions).

• Which firm fundamental variables to use?– Fama & French (1993) found a three factor model efficiently modeled the excess

returns of individual firms.

– Subsequently, Carhart (1997) extended the FF model by including a fourth factor.

– We extrapolate from the low frequency principle of the Carhart four factor model by incorporating a real-time HF moving average:

• Vasicek’s Beta (Bayesian corrected Beta) Standard CAPM• Market Capitalization FFM added factor• Book to Last Trade Price FFM added factor• Percent change from 50 day Moving Average Carhart extension


K4- Estimation of Quasi-Scale Economies

• Establish historical period: 01-Jun-2009 through 19-Mar-2010, inclusive.• Create research sample (SAM):

– Obtain 20-minute price observations for 2,225 securities.– Eliminate all non-equity stocks, and stocks that do not have fundamental

information on Yahoo! -- sample size reduced to 1,765.– For efficient cross-sectional modeling we sample from within the full content

population. The data sampling is guided by the use of the target variable of the study – percent positive trades (PPT).

– 793 securities form the training set; 972 securities form the validation set.• For SAM, obtain stock fundamentals (source: Yahoo Finance)

– Vasicek’s Beta - created from reported Yahoo beta. (P1)

– Market Capitalization (P2)

– Book to Last Trade Price (P3)

– Percent change from 50 day Moving Average (P4)


ResultsNumber of Positive Trades by Security for SAM of 1,765 Securities

Notice that the %positive trades form a band between 30% and 70%33URI-Neuroscience Colloquium 25-Feb-2013 – Dash and Kajiji

The Production Model• Use K4 to estimate the double-log production theoretic model for positive

trades.• pi = f(P1, P2, P3, P4)

• Where:• pi = Ln(PPT)

• P1, P2, P3, P4 = Ln transformation of indicator variables as previously defined

• K4-RBF implemented with a softmax transfer function • K4 RBF weights are interpreted as quasi-production elasticity estimates• Sum to capture system returns to scale for profitable trading


A Sample of Alternative Modeling ResultsK4-RBF Analysis Using Softmax Transfer Function

Dependent Variable: Ln(% Positive Trades)Indicator Variables: Ln(Fundamental Variables)


Results: FFC Mapping of % Positive TradesActual and Predicted


Results: FFC Quasi-Elasticity MetricsComparative K4 RBF Weights from the Alternative Models

Dependent Variable: Ln(% Positive Trades)

• Model selected – Norm2• Except for the variable Market Capitalization, all other variables show an

inverse relationship to PPT. That is, as firm market capitalization increases so does the expected performance of the WINKS K4-AT.

• Interestingly any increase in Book Value to Price tends to lessen the probability that WINKS will trade the stock profitably.

• The WINKS K4-AT exhibits decreasing returns to scale of 0.484 units. This implies a decrease in PPT given a simultaneous and proportionate change in all indicator variables (factors of production).


Summary

• This research provides a synthesis of stochastic equity price behavior and the cognitive science of trading by implementation of the dual objective K4-RBF ANN as incorporated in WINKS.

– WINKS is an MCDA trading algorithm that integrates the AI properties of two unique, but coordinated, high-frequency RBF ANNs.

– Test results produced transaction cost adjusted trading profits that exceeded those generated by the simple buy-hold strategy.

• WINKS performance was modeled using a four-factor firm pricing model to estimate the system-wide returns to scale of PPT.

• The results suggest that the portfolio selection of stocks based on the estimated quasi-elasticity coefficients would greatly enhance trading profits. A test of this conclusion is left for future research.


Future Research

• Development of intelligent interfaces between “investor” and AT parameterization

• Use of psychology-based theories to explain human response to high frequency trade signals associated with capital market events

• Interrogation of reasoning under uncertainty or imprecision


References1. Dash Jr., G.H. and N. Kajiji, Operations Research Software. Vol. I and II. 1988, Homewood, Illinois: IRWIN.2. Dash Jr., Gordon H., and Kajiji, Nina. Engineering a Generalized Neural Network Mapping of Volatility Spillovers in European

Government Bond Markets, Handbook of Financial Engineering, Series: Springer Optimization and Its Applications, Vol. 18, Edited By: C. Zopounidis, M. Doumpos, and P. Pardalos, Springer, 2008

3. Kajiji, N., and Forman, J., Production of Efficient Wealth Maximization Using Neuroeconomic Behavioral Drivers and Continuous Automated Trading, Edited by: N. Thomaidis, and G. Dash, Recent Advances in Computational Finance, Nova Science Publishers, Inc., 2013.

4. Kajiji, Nina and Dash Jr., Gordon H. Computational Practice: Multivariate Parametric or Nonparametric Modeling of European Bond Volatility Spillover? Recent Advances in Computational Finance, Edited by: N. Thomaidis, and G. Dash. Nova Science Publishers, Inc., 2013.

2. Forman, J., Essentials of Trading: From the Basics to Building a Winning Strategy. Wiley Trading. 2006, Hoboken, New Jersey: John Wiley & Sons, Inc.

3. Brock, W., J. Lakonishok, and B. LeBaron, Simple Technical Trading Rules and the Stochastic Properties of Stock Returns. The Journal of Finance, 1992. 47(5): p. 1731-1764.

4. Refenes, A.-P.N., et al., eds. Neural Networks in Financial Engineering. 1996, World Scientific: Singapore.6. Kajiji, N., Adaptation of Alternative Closed Form Regularization Parameters with Prior Information to the Radial Basis

Function Neural Network for High Frequency Financial Time Series, in Applied Mathematics. 2001, University of Rhode Island: Kingston.

7. Broomhead, D.S. and D. Lowe, Multivariate Functional Interpolation and Adaptive Networks. Complex Systems, 1988. 2: p. 321-355.

9. Lohninger, H., Evaluation of Neural Networks Based on Radial Basis Functions and Their Application to the Prediction of Boiling Points from Structural Parameters. Journal of Chemical Information and Computer Sciences, 1993. 33: p. 736-744.

12. Tikhonov, A. and V. Arsenin, Solutions of Ill-Posed Problems. 1977, New York: Wiley.13. Hoerl, A.E. and R.W. Kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 1970. 12(3):

p. 55-67.14. Hemmerle, W.J., An Explicit Solution for Generalized Ridge Regression. Technometrics, 1975. 17(3): p. 309-314.15. Crouse, R.H., C. Jin, and R.C. Hanumara, Unbiased Ridge Estimation with Prior Information and Ridge Trace. Communication

in Statistics, 1995. 24(9): p. 2341-2354.


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Neuroeconomics at URI: The CBA Student Directed Hedge Fund with Big Data Informatics By Gordon H....

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