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QMA 102: Probability & Statistics for Finance
Course Code QMA 102
Course Name Probability & Statistics for Finance
Department Mathematics
Semester Offered Even (usually Term 2)
Tuition Hours 30 hours
Course Level Foundational to Intermediate
Pre-requisite QMA 101: Mathematics for Finance
Co-requisite FTM 102: Investment Theory & Portfolio Management, TFS 102: Data Analysis & Financial Modeling
Course Objective Finance is not about certainty. It is about making decisions when you are almost always wrong in small ways and occasionally very wrong in big ways.

This course builds the mental machinery to reason under uncertainty. You will learn probability not as abstract math, but as a way to think about markets, risk, and decisions. Distributions stop being textbook curves and start becoming models of returns, losses, and extreme events.

By the end of this course, you should be able to look at any financial claim, backtest result, or investment pitch and ask one simple question: what is the probability that this is just noise?
Course Philosophy This course emphasizes
  • Thinking in distributions, not single numbers
  • Understanding uncertainty before trying to optimize it
  • Skepticism over blind trust in data
We do not train statisticians. We train decision-makers who can see through randomness, question conclusions, and avoid expensive mistakes.
Course Learning Outcomes Upon successful completion of this course, students will be able to:
  • Model uncertainty using probability distributions relevant to financial data.
  • Compute and interpret expected value, variance, and covariance in portfolio contexts.
  • Understand correlations and their limitations, especially during market stress.
  • Perform hypothesis testing and construct confidence intervals for financial decisions.
  • Critically evaluate financial claims, backtests, and investment strategies using statistical reasoning.
  • Connect statistical thinking directly to portfolio decisions in the capstone fund.
Course Author Sagar Udasi
MSc Statistics and Data Science with Computational Finance from The University of Edinburgh.
Contact: sagar.l.udasi@gmail.com
Course Organiser TBD
No. Lecture Title Concepts Covered Lecture Objective
01 Why Markets Feel Random (And Why They Aren’t) Deterministic vs stochastic systems, randomness in markets Build intuition that markets are not predictable point-wise but can be modeled probabilistically. Sets the foundation for all investing decisions.
02 The Only Language Uncertainty Speaks Probability basics, sample space, events Learn how to formally describe uncertainty so it can be measured and reasoned about.
03 Expected Value Is All You Need (Until It Isn’t) Expectation, weighted averages, decision making Understand how investors think in expected outcomes and why this alone can be dangerously misleading.
04 Risk Is Not What You Think It Is Variance, standard deviation, downside risk Move beyond "volatility = risk" and understand what risk actually means in portfolios.
05 The Shape of Returns Matters Distributions: Normal, Lognormal, Fat tails Understand how real market returns differ from textbook assumptions and why tail risk dominates outcomes.
06 When Rare Events Run the World Black swans, tail events, kurtosis Learn why extreme events dominate long-term performance and how to think about them.
07 Correlation: The Most Dangerous Number in Finance Covariance, correlation Understand how assets move together and why correlations break exactly when you need them most.
08 Diversification: Free Lunch or Expensive Illusion? Portfolio variance, diversification math Connect correlation and variance to real portfolio construction decisions in the capstone.
09 Data Is Lying to You (Most of the Time) Sampling, bias, overfitting Learn to question datasets and avoid false conclusions in financial modeling.
10 How to Test an Investment Idea Without Fooling Yourself Hypothesis testing basics, null hypothesis Build the ability to validate or reject investment strategies statistically.
11 Statistical Significance vs Real Money Significance p-values, Type I & II errors Understand why statistically significant results may still lose money in real markets.
12 Confidence Intervals: How Wrong Could You Be? Confidence intervals, estimation Quantify uncertainty in predictions and portfolio outcomes.
13 Backtests That Look Brilliant (And Why They Fail) Overfitting, data snooping bias Learn to spot fragile strategies before deploying them in the capstone portfolio.
14 Regression: Finding Signal in Noise Simple regression, relationships in data Build basic predictive intuition and understand limitations of linear models.
15 When Models Break: Regime Changes Non-stationarity, structural breaks Understand why past data stops working and how markets evolve.
16 Building a Statistical Lens for Investing Integrating concepts into decision-making Connect probability, statistics, and investment thinking directly to portfolio decisions.
17 Case Study: A Fund That Blew Up Real-world failure analysis Analyze statistical mistakes that led to real financial losses.
18 Case Study: A Strategy That Actually Worked Robust strategies, risk-adjusted returns Understand what statistically sound investing looks like in practice.
19 Applying Statistics to Your Capstone Portfolio Portfolio analysis, risk metrics Directly apply course concepts to live investment decisions.
20 Final Synthesis: Thinking Like a Probabilistic Investor Integrated decision framework Develop a mental model for making decisions under uncertainty across all financial contexts.
Component Weightage
Problem Sets (3 total) 30%
Capstone Integration Assignment (Portfolio Analysis) 30%
Final Examination (Applied + Conceptual) 40%
Type Resource Provider
Lecture Statistics and Probability (Khan Academy) Khan Academy
Lecture Introduction to Probability MIT OpenCourseWare
Reading The Signal and the Noise Nate Silver