Probability Trees and Conditional Expectations – Module 4 – Quant. M. – CFA® Level I 2026
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0:00 Introduction to Probability Trees & Conditional Expectations
Why these topics are crucial for CFA Level 1 and real-world risk management
Overview of session goals and structure
0:24 Expected Value, Variance & Standard Deviation Basics
Definition of expected value (EV) as a probability-weighted average
Variance as a measure of outcome dispersion
Standard deviation (sqrt of variance) for easier interpretation
1:55 Probability Trees: A Visual Approach
Mapping out scenarios and probabilities step by step
How probability trees organize multi-stage decision-making in finance
2:54 Conditional Expectations & Variance
Definition of conditional expectation (E[X|S])
Conditional variance and its role in assessing scenario-specific risk
Total probability rule for combining scenario outcomes
4:42 Real-World Example: EPS Scenarios & Probability Tree
Interest rate scenarios (declining vs. stable) and their probabilities
Sub-branches for earnings outcomes under each scenario
Calculating final outcome probabilities
6:00 Conditional Expectation in EPS Analysis
Determining expected EPS under declining and stable interest rates
Combining conditional expectations via total probability
Overall expected EPS = $2.39
7:50 Why Probability Trees & Conditional Logic Matter
Practical applications in corporate earnings predictions & investment decisions
Clarifying uncertainties and refining risk assessments
8:40 Bayes’ Formula: Updating Probabilities
Definition and importance of Bayes’ Theorem in finance
Adjusting (posterior) probabilities when new information arrives
9:03 Bayes’ Example: Tech Company Earnings & Expansion
Prior probabilities (45%, 30%, 25%) for EPS outcomes
Conditional probabilities of expansion based on EPS performance
Calculating posterior probability (EPS beat) given expansion news (82.3%)
12:57 Diffuse Priors & Posterior Probability in Finance
Assigning equal probabilities when lacking prior knowledge
Refining forecasts with new data for better decision-making
14:00 Conclusion & CFA Exam Study Tips
Recap of probability tree logic, conditional expectations, and Bayes’ updates
Emphasis on practice for risk management and financial decision-making
Final words of encouragement for CFA candidates