Introduction to Quantitative Trading

Introduction to Quantitative Trading

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Quantitative Trading Overview

Quantitative trading involves creating a statistical edge and executing it to generate risk-adjusted returns. It consists of two core components:

• Model: Generates the statistical edge, often using machine learning techniques.
• Strategy: Executes the model’s predictions in the market.

Execution quality is as important as the model itself; poor execution can eliminate any edge.

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Models in Quantitative Trading

Types of Models

• Regression models: Predict real-valued outputs such as future price, price delta, or returns. Returns are unitless, allowing cross-asset comparison.
• Classification models: Predict categories (e.g., price up/down) with associated probabilities.

Features and Model Complexity

• Features are inputs to models. Univariate models (using a single feature) are preferred for simplicity and robustness to avoid overfitting.
• Simpler models (e.g., linear regression) are favored over complex ones (e.g., neural networks) due to the risk of overfitting and better interpretability, following the principle of Occam’s Razor.
• Models typically use time series inputs, predicting future values based on past values (lags). The simplest case uses the last known value as a feature (AR1 model).

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Core Skills for Quantitative Trading

• Econometrics: Foundation for time series analysis, including concepts like autocorrelation, non-stationarity, and co-integration.
• Machine Learning: Scalable and flexible, with no strong assumptions, ideal for large or high-frequency data.
• Programming: Essential for latency-sensitive execution and building reliable, scalable systems.
• Mathematics: Key areas include linear algebra, multivariable calculus, probability, and statistics.

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Statistical Edge & Performance Metrics

• Expected Value (EV): The average net profit and loss (P&L) per trade after costs. Focus on EV rather than win rate.

Example: A high win rate does not guarantee profitability if losses are large. Even a small positive EV (1-2 cents) compounded over many trades can lead to strong returns.

• Risk-Adjusted Returns: Measured by the Sharpe Ratio, calculated as expected returns minus the risk-free rate divided by the standard deviation of returns.

  • For intraday strategies, the risk-free rate is often ignored due to short holding periods.
  • A higher Sharpe ratio indicates a smoother equity curve and safer leverage usage.

• Returns Calculation:

  • Simple returns are asymmetric (e.g., +20% up, -6.6% down).
  • Log returns are symmetric and time-additive, making them preferable for modeling.

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Market Microstructure & Order Book Fundamentals

• Order Book: Displays supply (asks) and demand (bids) at various price levels.
• Spread: The difference between the best bid and ask prices; wider spreads occur in less liquid markets and represent a hidden cost for liquidity takers.
• Mid Price: The average of the best bid and ask prices; preferred over the last trade price to avoid bid-ask bounce noise.
• Market Orders: Remove liquidity (taking), filled at the best opposite side price, and can cause slippage if order size exceeds available quantity.
• Limit Orders: Add liquidity (making), earn rebates or lower fees, but may not always fill.

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Quantitative Trading Strategies

Two Broad Types

1. Market Making

   • Adds liquidity via limit orders.
   • Profits from capturing the spread.
   • Key parameters:
     • Spread: Profit margin.
     • Bias/Skew: Adjusts bid/ask to increase fill probability aligned with model predictions.
   • Trade-off between spread size (profit vs. fill likelihood) and adverse selection risk.

2. Market Taking

   • Removes liquidity via market orders.
   • Pays higher fees, better suited for longer time horizons.
   • Key decisions:
     • Timing: When to trade.
       • Time-based: Trades executed at fixed intervals (e.g., hourly, daily).
       • Predicate-based: Trades triggered only when model predictions cross thresholds (e.g., predicted return > 0.01).
     • Sizing: How much to trade.
       • Constant: Fixed trade size regardless of prediction strength.
       • Piecewise linear: Scale trade size linearly with prediction strength, bounded by a maximum size (e.g., using a hard tangent function).
       • Nonlinear: Smooth scaling using functions like tanh, allowing finer sensitivity to prediction strength.

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Modeling Trading Behaviors with Linear Regression (AR1 Model)

• Mean Reversion: Negative weight in the linear model; price tends to revert to the mean.
• Momentum: Positive weight; price tends to continue in the same direction.
• The linear regression model has two parameters (weight and bias), offering:
  • High interpretability.
  • Good generalization.
  • Very fast computation (3-5 CPU cycles per prediction).

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Parameter Optimization Methods

• Closed Form Solution (Ordinary Least Squares):

  • Provides an exact analytical solution.
  • Efficient for small datasets but not scalable to large or high-frequency data.

• Gradient Descent:

  • Iterative approach improving parameters stepwise.
  • Suitable for large datasets.
  • Learning rate controls step size; choice of loss function is flexible and critical.
  • Can handle non-convex loss functions with local minima.

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Risk Management & Leverage

• Strategies with low Sharpe ratios limit leverage due to the risk of large drawdowns.
• High Sharpe ratio strategies enable safer leverage and more stable returns.
• Conservative trade sizing is important to avoid blowups.

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Explicit Recommendations & Cautions

• Focus on expected value rather than win rate.
• Prefer log returns over simple returns for modeling.
• Start with simple univariate models before exploring complex ones.
• Backtest any stop-loss or take-profit rules to ensure they improve expected value.
• Use constant trade sizing as a baseline before exploring scaling methods.
• Be cautious with leverage, especially with low Sharpe ratio strategies.
• Aggressively bias quotes in market making to increase fill rates if the edge is small.
• Avoid overfitting by limiting model complexity.
• Reliability and scalability of execution systems are as important as raw speed.
• Backtest all strategy parameters thoroughly.
• Understand trade-offs in spread size and fill probability in market making.

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Assets, Instruments, and Sectors Mentioned

• No specific tickers or companies mentioned.
• Instruments include:
  • Stocks (implied).
  • Order book data.
  • Limit orders (market making).
  • Market orders (market taking).
  • Time series data (price, returns).
  • High-frequency data (order book ticks).

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Methodology / Framework Summary

1. Modeling: Build a predictive model (linear regression AR1) using time series features (last value).
2. Optimization: Use closed form or gradient descent to find model parameters.
3. Edge Quantification: Calculate expected value (EV) and Sharpe ratio.
4. Strategy Execution: Convert model predictions into trades via:
   • Market making (limit orders with spread and bias).
   • Market taking (market orders with timing and sizing).
5. Trade Sizing: Choose constant, piecewise linear, or nonlinear sizing based on prediction strength.
6. Backtesting: Validate all assumptions, parameters, and filters.
7. Risk Management: Monitor Sharpe ratio, control leverage, and manage drawdowns.

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Disclosures / Disclaimer

• The video is educational and introductory.
• No explicit financial advice is given.
• Emphasizes backtesting before applying any strategy or parameter.
• Real-world complexities like market impact and latency optimization are acknowledged but out of scope.

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Presenter / Source

• Single presenter (unnamed in subtitles).
• Presents as an experienced quant trader/educator sharing foundational knowledge on quantitative trading.

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End of Summary