Algorithmic Trading Strategies

Algorithmic Trading: An Introduction

• Algorithmic trading utilizes computer programs to execute trades based on a defined algorithm, which may involve timing, price, quantity, or mathematical models.
• It is known by various names including Algo Trading, Automated Trading, Black-Box Trading, Systematic Trading, and Quantitative Trading.
• Buy-side firms like mutual funds, pension funds, hedge funds, insurance companies, and sovereign wealth funds use algorithmic trading.
• Sell-side firms, including market makers and proprietary trading desks, also employ algorithmic trading.
• Algorithmic trading is applicable wherever clear rules or instructions are available.
• Benefits: reduced transaction costs, improved order execution, access to more markets, backtesting & optimization, and reduced emotional biases.

Types of Algorithmic Trading Strategies

• Trend Following Strategies: use moving averages, breakout techniques, and mean reversion.
• Arbitrage Strategies: include triangular arbitrage, statistical arbitrage, and index arbitrage.
• Execution Algorithms (Market Making): volume-weighted average price (VWAP), time-weighted average price (TWAP), and implementation shortfall are used.
• Machine Learning Algorithms: employ supervised learning, unsupervised learning, and reinforcement learning.

High-Frequency Trading (HFT)

• High-Frequency Trading (HFT) is a subset of algorithmic trading.
• It is characterized by extremely short time horizons, high turnover rates, high order-to-trade ratios, and co-location.
• HFT firms compete on speed through cutting-edge technology and advanced infrastructure.

Pitfalls of Algorithmic Trading

• Model Risks, Technical Risks, Data Risks, Regulatory Risks, and Market Risks are involved and must be managed.

Algorithmic Trading: Summary

• Algorithmic trading is used by both buy-side and sell-side firms, as well as individual investors.
• The field is constantly evolving with new strategies and technologies.
• **

Algorithmic Trading: Strategy Development

• The algorithmic trading strategy development process has multiple stages including idea generation, data collection, backtesting, paper trading, and live trading.
• Idea Generation occurs though Brainstorming, Research Papers, and Market Analysis
• Data Collection: involves Tick Data, Fundamental Data, and Alternative Data from sources like Bloomberg, Refinitiv, and Web Scraping.

Backtesting

• Backtesting utilizes historical data for realistic simulation and performance evaluation.

Paper Trading

• Paper Trading takes place in a Live Market, with Simulated Capital to allow for Further Evaluation.

Evaluating Strategy Performance

• Key Metrics include: Returns, Sharpe Ratio, Maximum Drawdown, Win Rate, Profit Factor, and Transaction Costs.
• Sharpe Ratio: calculated as $\frac{R_p - R_f}{\sigma_p}$ where $R_p$ = Portfolio Return, $R_f$ = Risk-Free Rate, and $\sigma_p$ = Portfolio Standard Deviation.

Common Pitfalls in Strategy Development

• Overfitting, Data Mining Bias, Survivorship Bias, Look-Ahead Bias, Ignoring Transaction Costs, and Neglecting Risk Management are all common pitfalls.

Algorithmic Trading Strategy Development: Summary

• Algorithmic trading strategy development is an iterative process requiring continuous monitoring and adjustment.

Tensiones

Tensiones Normales

Tensión

• Tensión ($\sigma$) is calculated as $\sigma = \dfrac{F}{A}$, where F is force applied and A is the area.

Deformación

• Deformación ($\epsilon$) is calculated as $\epsilon = \dfrac{\Delta L}{L_0}$, where $\Delta L$ is change in length and $L_0$ is original length.

Ley de Hooke

• Hooke's Law: $\sigma = E\epsilon$, where E is the modulus of elasticity or Young's modulus.

Tensiones Cortantes

Tensión Cortante

• Tensión Cortante ($\tau$) is calculated as $\tau = \dfrac{V}{A}$, where V is the shear force and A is the area.

Deformación Cortante

• Deformación Cortante ($\gamma$) is calculated as $\gamma = \dfrac{\Delta x}{h} = tan \theta$, where $\Delta x$ is displacement, h is height, and $\theta$ is the angle of deformation.

Ley de Hooke para Cortante

• Hooke's Law for Shear: $\tau = G\gamma$, where G is the shear modulus or modulus of rigidity.

Relación entre E, G y ν

• The relationship between E, G, and $\nu$ is given by $G = \dfrac{E}{2(1+\nu)}$, where $\nu$ is Poisson's ratio.

Coeficiente de Poisson

• Poisson's ratio ($\nu$) is calculated as $\nu = -\dfrac{\epsilon_{lateral}}{\epsilon_{axial}}$, where $\epsilon_{lateral}$ is lateral strain and $\epsilon_{axial}$ is axial strain.

Notas

• Normal stress ($\sigma$) relates to forces perpendicular to the area.
• Shear stress ($\tau$) relates to forces parallel to the area.
• Hooke's Law is valid only in the elastic region of the material.

Estadística Descriptiva

Introducción

• Estadística descriptiva involves collecting, organizing, summarizing, and presenting data, with the primary goal of describing a dataset's main characteristics without inferring or generalizing to a larger population.

Tipos de variables

• Variables are categorized into qualitative (categorical) and quantitative (numerical) types.
• Qualitative Variables: Nominales (no inherent order) and Ordinales (inherent order).
• Quantitative Variables: Discretas (integer values) and Continuas (any value within a range).

Medidas de Tendencia Central

• Measurements represent a typical center or value of a dataset.

Media Aritmética

• Media Aritmética (average): $\bar{x} = \frac{\sum_{i=1}^{n}x_i}{n}$, where $\bar{x}$ is the mean, $x_i$ are individual values, and $n$ is the number of values.

Mediana

• Mediana: The value in the center of an ordered dataset; if even amount of values, the average of the two central values.

Moda

• Moda: the most frequently occurring value in a dataset; unimodal, bimodal, or multimodal can occur.

Medidas de Dispersión

• Measurements indicate data dispersion around the central tendency measurement.

Rango

• Rango (range): $Rango = x_{max} - x_{min}$

Varianza

• Varianza (variance) measures average data dispersion around the mean.

• Sampling variance: $s^2 = \frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}$

• Population variance: $\sigma^2 = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N}$

• Where: $s^2$ is sampling variance, $\sigma^2$ is population variance, $x_i$ are individual values , $\bar{x}$ is the sample mean, $\mu$ is the population mean, $n$ is sampling size, and $N$ is population size.

Desviación Estándar

• Desviación Estándar: the square root of the variance.
• Sampling deviation: $\qquad s = \sqrt{s^2}$
• Population deviation: $\qquad \sigma = \sqrt{\sigma^2}$

Coeficiente de Variación

• Coeficiente de Variación: $CV = \frac{s}{\bar{x}} * 100$% which is useful for comparing variability between datasets of various units or scales.