Statistics on the CMT Exam
Statistical analysis carries 15% weight on CMT Level 1 and underpins quantitative methods on Level 2. Understanding these concepts is essential for risk management and volatility analysis.
For the complete exam overview, visit the CMT exam guide 2026.
Normal Distribution
The bell-shaped distribution is fundamental to understanding market returns:
- ~68% of data falls within ±1 standard deviation
- ~95% within ±2 standard deviations
- ~99.7% within ±3 standard deviations
Market returns approximate — but don't perfectly follow — the normal distribution. Fat tails (kurtosis) and skewness are important exam concepts.
Standard Deviation & Variance
- Variance = Σ(xᵢ − μ)² / N
- Standard deviation = √Variance
- Used in Bollinger Bands and volatility measures
Correlation & Covariance
- Correlation coefficient (r): Ranges from −1 to +1
- +1: Perfect positive correlation
- −1: Perfect negative correlation
- 0: No linear relationship
- Critical for intermarket analysis and portfolio management
Regression Analysis
- Linear regression identifies the trend line through data points
- R-squared measures how much variance is explained by the model
- Applications: trend channel construction, price prediction models
Key Exam Formulas
| Concept | Formula |
|---|---|
| Mean | μ = Σxᵢ / N |
| Variance | σ² = Σ(xᵢ − μ)² / N |
| Standard Deviation | σ = √σ² |
| Correlation | r = Cov(X,Y) / (σₓ × σᵧ) |
| Z-score | z = (x − μ) / σ |
Practice these calculations with our CMT practice tests and explore the full study guide.
Normal Distribution of Daily Returns
Most daily market returns cluster near zero — fat tails represent extreme events
Correlation Between Bond Yields and Stock Prices
Negative correlation indicates a risk-off rotation