Project Euler A Quantitative Framework on positive expectancy 2004 – 2011 Antonio Pamplona http://pt.linkedin.com/in/pamplona last updated on August 2011Antonio Pamplona proprietary information. All rights reserved.
IMPORTANT DISCLAIMER THIS DOCUMENT DOES NOT CONSTITUTE A SOLICITATION OF ANY KIND, INCLUDING BUT NOT LIMITED TO, MANAGE OR RAISE FUNDS FROM ANY INSTITUTION, COMPANY OR INDIVIDUAL OR A SOLICITATION TO ADVISE ON INVESTMENT STRATEGIES.Antonio Pamplona proprietary information. All rights reserved.
Principles • The advent of electronic markets and ubiquotous computer power created a whole new paradigm in financial markets, in which humans are being replaced by machines in most of the decision making • The central banks stance in fighting deflation coupled with stable economic growth has lead to strong positive drifts in those assets that track the economy, empirical analysis reveal. This has been the case for the last 60 years in European and North American markets • The increased liquidity and limited transaction costs in some asset classes enable quantitative strategies to efficiently trade in and out of positions on different time frames ranging from sub-second to daily • Behavioural aspects in price formation creates ineficiencies that can be turned into positive expectancy strategies on a consistent basis • The market prices neither follow a normal distribution nor are random.Antonio Pamplona proprietary information. All rights reserved.
Approach • Looks for highly liquid trading vehicles • Analyzes structured and non-structured data • Creates new processes to address inefficiencies • Automates or semi-automates the processes • Evaluates and rethinksAntonio Pamplona proprietary information. All rights reserved.
An Example – German DAX Index Note: The DAX is a cross-industry index that is comprised of 30 different companies that are among the most respectable and profitable in the country. The index is actively managed in order to represent the whole economy effectively. Its performance is said to trail (loosely) the country’s economic development. However it is subject to major biases and deviations from fair price due to behavioural aspects of the investment decision making. Based on empirical evidence, it is commonly accepted that the long term real return of an index such as the DAX is circa of 5% per annum. Comparison of Euler vs a Stock Index passive strategy (simulation for illustration purposes) Price Highlights • Captures most of the index upside Euler • Subject to limited downside • Reshapes the risk to reward equation Stock Index TimeAntonio Pamplona proprietary information. All rights reserved.
Two Building Blocks • Algorithm • Automated Execution EngineAntonio Pamplona proprietary information. All rights reserved.
Algorithm Principles • Statistics • Behavioural Finance • Decision Theory • Asset Price Drift source: wikipedia.orgAntonio Pamplona proprietary information. All rights reserved.
Automated Execution Engine • Receives and interprets price information • Generates trading decisions • Manages order entry • Monitors riskAntonio Pamplona proprietary information. All rights reserved.
Performance Historical (1) Expected (2) From To Rate of Return per Annum (3) (5) 176.74% 80.00% 120.00% Standard Deviation 52.90% 20.00% 50.00% Drawdown Maximum (4) 29.35% 20.00% 40.00% Drawdown Period (in calendar days) 44 20 50 Sharpe Ratio 3.34 2.00 4.00 Calmar Ratio 6.02 2.00 5.00 Correlation(5) -0.34 -0.40 0.40 (1) Based on data records from 2007 to 2010. (2) Expectation for future returns is more modest due to scalability, volatility and liquidity related problems. (3) The rate of return is based on a leverage mechanism that leads to compounding. (4) The maximum percentage loss incurred from the equity peak to its lowest value. (5) Weekly analysis between Euler and its underlying asset, in this case the German DAX Index.Antonio Pamplona proprietary information. All rights reserved.
Statistical Analysis Euler compared to its underlying, no leverage (based on the German DAX Index)Antonio Pamplona proprietary information. All rights reserved.
Underlying Foundations, Assumptions and BackgroundAntonio Pamplona proprietary information. All rights reserved.
Mainstream Finance Foundations • fficient Market Hypothesis asserts that financial markets are "information efficient", or that prices E on traded assets, e.g., stocks, bonds, or property, already reflect all known information and therefore are unbiased in the sense that they reflect the collective beliefs of all investors about future prospects • odern Portfolio Theory proposes how rational investors will use diversification to optimize their M portfolios, and how a risky asset should be priced. MPT models an assets return as a random variable, and models a portfolio as a weighted combination of assets; the return of a portfolio is thus the weighted combination of the assets returns • apital Asset Pricing Model is used in finance to determine a theoretically appropriate required C rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that assets non-diversifiable risk. The CAPM formula takes into account the assets sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β), as well as the expected return of the market and the expected return of a theoretical risk-free asset.Antonio Pamplona proprietary information. All rights reserved.
Browniam Motion and Bachelier • Random Walk is a mathematical formalization of a trajectory that consists of taking successive steps in random directions. The results of random walk analysis have been applied to computer science, physics, ecology, economics and a number of other fields as a fundamental model for random processes in time • It is used as a stock market theory that states that the past movement or direction of the price of a stock or overall market cannot be used to predict its future movement. In short, random walk says that stocks take a random and unpredictable path. The chance of a stocks future price going up is the same as it going down • Louis Bachelier was the first person to model a Brownian motion, which was part of his PhD thesis The Theory of Speculation (published 1900).Antonio Pamplona proprietary information. All rights reserved.
Complex Economics Approach to Markets Behaviour • Power Laws describe the distribution of occurences in a wide variety of phenomena, including natural, and economic sciences • Markets are Complex Adaptive Systems caractherized by punctuated equilibrium, oscillations and power laws • Gaussian, random walks almost never have fluctuations greater than five standard deviation, yet in real economic data, such as stock market crashes, five standard deviation events and even greater ones, do in fact occur • Financial market prices show a Fractal Geometry – not only there is a structure in financial data but also the structures appear in multiple timescales • Markets are an Ecosystem of Expectations. The complex interaction of the market participants, their changing strategies and new information from their environment causes patterns and trading opportunities to constantly appear and disappear over time • Prices show a Temporal Structure, that is, prices are formed by the interaction between market particiapants having bias and momentum in them.Antonio Pamplona proprietary information. All rights reserved.
Project Euler Foundations Mainstream Finance Alternative Finance Capital Asset Pricing Model Temporal Structure Complex Adaptive Systems Modern Portfolio Theory Ecosystems of Expectations Efficient Market Hypothesis Power Laws Browniam Motion and Chaos Theory and Random Walk Theory Fractal Geometry Classical Physics Quantum Physics Behavioural Economics Classical Economics Complex EconomicsAntonio Pamplona proprietary information. All rights reserved.
Project EulerAntonio Pamplona proprietary information. All rights reserved.