Knowledge Base
Quantitative Methods
Mathematical and statistical tools used to analyze financial data, evaluate investments, and support decision-making under uncertainty.
Sub-themes
Introduction to Big Data Techniques
Big data, machine learning, and fintech applications relevant to gathering and analyzing financial information.
Simple Linear Regression
Estimating and interpreting linear relationships between variables, including regression coefficients, ANOVA, and prediction intervals.
Parametric and Non-Parametric Tests of Independence
Correlation tests and contingency table analysis to determine whether variables are statistically independent.
Hypothesis Testing
Constructing and interpreting statistical tests, including significance levels, Type I and II errors, and test power.
Estimation and Inference
Sampling methods, the central limit theorem, and resampling techniques for estimating population parameters from financial data.
Simulation Methods
Monte Carlo and bootstrap resampling techniques for modeling uncertainty in investment outcomes, including the lognormal price model.
Portfolio Mathematics
Expected return, variance, and covariance of portfolio returns. Shortfall risk and the safety-first criterion for portfolio selection.
Probability Trees and Conditional Expectations
Bayesian updating, conditional expectations, and probability trees applied to multi-stage investment decisions.
Statistical Measures of Asset Returns
Measures of central tendency, dispersion, skewness, kurtosis, and correlation used to characterize the distribution of asset returns.
Time Value of Money in Finance
Present and future value calculations for fixed-income and equity instruments, including the cash flow additivity principle and implied forward rates.
Rates and Returns
How interest rates function as discount rates, required returns, and opportunity costs. Approaches to measuring and annualizing investment returns.