Statistics on the CMT Exam
Statistical analysis belongs to the Advanced Techniques domain, which is 26% of CMT Level I and 40% of CMT Level II. 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