Quantitative Methods

Quantitative Methods is the mathematical backbone of the finance curriculum and a prerequisite for nearly every other study session. The tools developed here — from present value calculations to regression analysis — reappear constantly in Equity Investments, Fixed Income, Derivatives, and portfolio management. For DeFi practitioners, these same techniques power yield calculations, risk models, and on-chain analytics.

Topics

• Rates and Returns — Interest rate decomposition, holding period returns, MWRR vs TWRR, and annualized/continuously compounded returns.
• Time Value of Money in Finance — PV/FV of single sums and annuities, bond and equity valuation via DCF, cash flow additivity and no-arbitrage.
• Statistical Measures of Asset Returns — Central tendency, dispersion, skewness, kurtosis, and correlation for investment analysis.
• Probability Trees and Conditional Expectations — Expected value, variance, probability trees, conditional expectations, and Bayes’ theorem.
• Portfolio Mathematics — Portfolio return and risk, covariance and correlation via joint probability, Roy’s Safety-First criterion.
• Simulation Methods — Normal vs lognormal distributions, Monte Carlo simulation, and bootstrap resampling.
• Estimation and Inference — Sampling methods, the Central Limit Theorem, standard error, and resampling techniques.
• Hypothesis Testing — Test construction, Type I/II errors, power, and parametric vs nonparametric tests.
• Parametric and Non-Parametric Tests of Independence — Pearson and Spearman correlation tests, chi-square tests of independence.
• Simple Linear Regression — Least squares estimation, R-squared, ANOVA, prediction intervals, and functional forms.
• Introduction to Big Data Techniques — Fintech data, AI/ML fundamentals, and applications to investment management.