Project Euler

Project Euler
A Quantitative Framework
on positive expectancy

2004 – 2011

Antonio Pamplona
http://pt.linkedin.com/in/pamplona

last updated on August 2011
Antonio 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.


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.


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 rethinks


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

Time


Two Building Blocks
• Algorithm

• Automated Execution Engine


Algorithm Principles

• Statistics

• Behavioural Finance

• Decision Theory

• Asset Price Drift

source: wikipedia.org


Automated Execution Engine

• Receives and interprets price information

• Generates trading decisions

• Manages order entry

• Monitors risk


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.


Statistical Analysis
Euler compared to its underlying, no leverage
(based on the German DAX Index)


Underlying Foundations,
Assumptions and Background


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 asset's 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 asset's non-diversifiable risk. The CAPM formula takes into account the asset's 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.


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 stock's 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).


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.


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 Economics


Project Euler


Project Euler

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