Portfolio Mathematics – Module 5 – Quantitative Methods – CFA® Level I 2026
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0:00 Introduction to Portfolio Mathematics (CFA Level 1)
Overview of expected return, variance, covariance, and correlation
Importance for portfolio management and risk assessment
0:32 Expected Return & Weighted Averages
Basics of expected value
Role of asset weights in a portfolio
1:50 Variance, Covariance & Risk
Variance as a measure of return dispersion
Covariance (positive vs. negative vs. zero)
Diversification benefits from lower covariance
3:31 Correlation & Portfolio Implications
Standardized measure of linear relationships (range: -1 to +1)
Perfect positive vs. perfect negative correlation
Diversification strategies and correlation effects
4:53 Forecasting Correlation via Joint Probability
Understanding joint distributions for multi-asset returns
Example with Tech Corp & Health Inc. (joint probabilities)
Calculating expected returns & covariance from scenarios
6:32 Independence & Uncorrelated Variables
Independent vs. uncorrelated (key differences)
Multiplication rule for independent variables (joint probability = product)
Portfolio implications of independence
7:55 Uncorrelated Random Variables & Expected Value
Assumption of normal distribution in portfolio returns
9:00 Mean-Variance Analysis & The Normal Distribution
Balancing expected return vs. risk
Portfolio optimization & risk-return tradeoffs
Application in real-world portfolio construction
10:01 Safety-First Rule & Sharpe Ratio
Minimizing probability of returns dropping below a certain threshold
Comparing portfolios by the Sharpe Ratio (excess return / standard deviation)
11:30 Risk Management Tools: Value at Risk (VaR) & Stress Testing
VaR as a worst-case loss measure at a given confidence level
Stress testing and scenario analysis for extreme market conditions
How these methods complement mean-variance approaches
14:00 Conclusion & CFA Exam Study Tips
Recap of expected return, variance, covariance, correlation, and risk tools
Importance of practice with end-of-chapter questions
Final encouragement for mastering portfolio management concepts