Introduction to Machine Learning

What is Machine Learning?

• Machine learning provides computers the ability to learn without explicit programming.
• A computer program learns from experience E, improving its performance (P) on a task (T) with more experience.

Types of Machine Learning

• Supervised Learning: Training data with labels to map inputs to outputs.
  • Regression: Predicts a continuous output (e.g., stock prices).
  • Classification: Predicts a categorical output (e.g., spam emails).
• Unsupervised Learning: Training data without labels, aiming to find patterns.
  • Clustering: Groups similar data points (e.g., customer segmentation).
  • Dimensionality Reduction: Reduces the number of variables (e.g., feature extraction).
• Reinforcement Learning: An agent learns decisions in an environment to maximize rewards, like training a robot to walk.

Short History of Machine Learning

• 1950s: Arthur Samuel’s checkers program; Frank Rosenblatt’s perceptron.
• 1960s: Widrow and Hoff’s Adaline and Madaline; pattern recognition research.
• 1970s: Expert systems; symbolic learning.
• 1980s: Backpropagation; connectionism.
• 1990s: Data mining; statistical learning.
• 2000s: Support vector machines; kernel methods.
• 2010s: Deep learning; big data.

Example Applications

• Machine learning is applicable to spam filtering, fraud detection, image recognition, natural language processing, medical diagnosis, and financial modeling.

Goals of Machine Learning

• The goals are prediction, knowledge discovery, and decision making.

Algorithmic Trading

• An algorithmic trading system is a computer program with a specific trading strategy that may automatically submit trades.
• Terminology also includes automated trading, black-box trading and systematic trading.

Order Execution

• Order execution algorithms minimize market impact and improve execution prices by breaking up large orders into smaller pieces over time.
• Brokers may offer this service.

Motivation for Algorithmic Trading

• Reasons include reduced transaction costs, improved speed, simultaneous trading, reduced errors/market impact, anonymity and the ability to backtest strategies.

Algorithmic Trading Strategies

• Types inclide execution algorithms, market-making algorithms, statistical arbitrage, and trend following.

Execution Algorithms

• Execution algorithms minimize market impact and transaction costs by splitting large orders (parent orders) into smaller ones (child orders) submitted over time.

Types of Execution Algorithms

• Volume-Weighted Average Price (VWAP): Executes at the VWAP observed between the order's start and end.
• Time-Weighted Average Price (TWAP): Executes at the TWAP observed between start and end.
• Percentage of Volume (POV): Participates at a defined rate of market trading volume. For example, algorithm executes 10% of market volume.
• Implementation Shortfall: Minimizes the difference between the actual execution price and the hypothetical instantaneous execution price.

Market-Making Algorithms

• These may manage the inventory of a market maker, adjusting bid/ask prices to changing conditions, while profiting from the bid-ask spread.

Statistical Arbitrage

• Statistical arbitrage profits from temporary deviations from statistical relationships, requiring sophisticated math and stats.

Trend Following

• Trend-following identifies and profits from price trends based on technical analysis like moving averages which perform well in trending, but poorly in choppy, markets.

Example: Moving Average Crossover System

• Buy signal: a short-term (e.g., 50-day) moving average crosses above a longer-term (e.g., 200-day) moving average.
• Sell signal: the short-term moving average crosses below the longer-term moving average.

Backtesting

• Algorithmic trading strategies require thorough backtesting, which optimizes parameters and identifies flaws by simulating past performance using historical data.

Drawbacks of Backtesting

• The past may not accurately predict the future
• Data-mining bias can impact the integrity

Data-Mining Bias

• Many different variants of trading rules may find parameters that worked historically but lack future predictive power

Algorithmic Trading and Market Quality

• Possible improvements may include increased liquidity and reduced transaction costs.
• Can contribute to market instability, especially during times of stress (e.g., the "Flash Crash" of May 6, 2010).

Problems Caused by Algorithmic Trading

• Adverse selection risk, increased risk of "fat finger" errors, and possible market manipulation.

Adverse Selection Risk

• It arises when traders exploit better information than others in the space

"Fat Finger" Errors

• Large losses may result from algorithmic systems, which are vulnerable to incorrect trades.

Market Manipulation

• Algorithms can be utilized to manipulate prices (e.g., "quote stuffing" floods market with orders then cancels to create confusion).

Regulation of Algorithmic Trading

• Regulatory scrutiny is increasing due to potential instability and manipulation.
• Algorithmic traders may need to register and be subject to oversight.
• In the U.S., firms must register as broker-dealers or investment advisers, subject to SEC/FINRA oversight and SEC Rule 15c3-5 require risk management controls in place to prevent erroneous orders.

Autoregressive (AR) Model Equation

• Equation: $y_t = c + \phi_1 y_{t-1} + \phi_2 y_{t-2} +... + \phi_p y_{t-p} + \epsilon_t$
  • $y_t$ is the value at time t
  • c is a constant
  • $\phi_i$ are parameters
  • $\epsilon_t$ is white noise

Autoregressive (AR) Model

• The AR model uses p past values to predict future values in a time series.

Moving Average (MA) Model Equation

• Equation: $y_t = \mu + \theta_1 \epsilon_{t-1} + \theta_2 \epsilon_{t-2} +... + \theta_q \epsilon_{t-q} + \epsilon_t$
  • $y_t$ is the value at time t
  • $\mu$ is the mean of the time series
  • $\theta_i$ are parameters
  • $\epsilon_t$ is white noise

Moving Average (MA) Model

• The MA model uses q past errors (residuals) to predict future values.

ARMA Model Equation

• Combines AR and MA models. An ARMA(p, q) model has p autoregressive terms and q moving average terms.
• Equation: $y_t = c + \phi_1 y_{t-1} + \phi_2 y_{t-2} +... + \phi_p y_{t-p} + \theta_1 \epsilon_{t-1} + \theta_2 \epsilon_{t-2} +... + \theta_q \epsilon_{t-q} + \epsilon_t$
  • $y_t$ is the value at time t
  • c is a constant
  • $\phi_i$ are AR parameters
  • $\theta_i$ are MA parameters
  • $\epsilon_t$ is white noise

Autoregressive Moving Average (ARMA) Model

• The ARMA model combines past values and past errors.

Model Selection

• Use ACF/PACF plots to determine the order (p, q) and AIC/BIC to compare different models.

Stationarity

• For ARMA models stationarity is assumed and data may require differencing if it's not originally stationary.