Quantitative Trading Foundations

Quantitative trading uses mathematical models and statistical analysis to identify trading opportunities.

What is Quantitative Trading?

Definition

• Data-driven decision making
• Statistical edge validation
• Systematic approach
• Removes emotional bias

Statistical Concepts

Probability and Expected Value

• Every trade is a probability
• Expected Value = Sum of (Outcome x Probability)
• Positive EV = profitable over time
• Individual outcomes are random

Standard Deviation

• Measures volatility/dispersion
• 68% within 1 SD, 95% within 2 SD
• Used for position sizing
• Risk quantification

Correlation and Covariance

• How variables move together
• Portfolio risk depends on correlation
• Diversification benefits
• Regime changes alter correlations

Backtesting Properly

Avoiding Curve Fitting

• Out-of-sample testing required
• Simple rules over complex
• Large sample sizes (500+ trades)
• Test across market regimes

Walk-Forward Analysis

• Optimize on period 1
• Test on period 2
• Re-optimize, test on period 3
• Most realistic performance estimate

Key Metrics

• Sharpe Ratio (risk-adjusted return)
• Maximum Drawdown
• Calmar Ratio (return/max DD)
• Win Rate and Profit Factor

Building a Trading Model

Step 1: Hypothesis

• What market behavior are you exploiting?
• Why does this edge exist?
• Is it likely to persist?

Step 2: Define Rules

• Clear entry/exit criteria
• No discretion
• Can be programmed

Step 3: Backtest

• Historical data testing
• Multiple timeframes
• Various market conditions

Step 4: Validate

• Out-of-sample testing
• Paper trading
• Small live testing

Step 5: Deploy and Monitor

• Full implementation
• Ongoing performance tracking
• Regime monitoring