Quantitative Finance

Learn how Monte Carlo simulation generates probability distributions of portfolio outcomes for retirement planning, risk estimation, and scenario analysis.

Maximum drawdown measures the largest peak-to-trough percentage decline in a portfolio or investment before a new peak is established — the worst cumulative loss an investor would have experienced over a given period.

Expected Shortfall (CVaR) measures the average loss in the worst-case tail of a portfolio return distribution, answering the question VaR leaves open: how bad are losses when they exceed the threshold?

Value at Risk (VaR) measures the loss threshold not expected to be exceeded at a given confidence level over a specified time horizon. Learn parametric, historical, and Monte Carlo VaR methods with worked examples.

Learn how portfolio diversification reduces risk, the diversification ratio formula, and practical strategies for building a well-diversified portfolio.

Jensen’s Alpha measures a portfolio’s risk-adjusted performance by comparing its actual return to the return predicted by the CAPM, isolating the portion of return attributable to manager skill.

The Treynor ratio measures risk-adjusted portfolio performance by dividing excess return by beta, making it the standard metric for evaluating well-diversified portfolios on a systematic-risk basis.

Learn what the efficient frontier is, how Markowitz mean-variance optimization works, and how to identify optimal portfolios using the Capital Allocation Line.

Correlation and covariance quantify how two assets move relative to each other, forming the foundation of portfolio diversification and risk management.

The Capital Asset Pricing Model describes the relationship between systematic risk and expected return, providing a framework for pricing risky assets.

Standard deviation measures the dispersion of investment returns, quantifying how much a stock or portfolios performance varies over time.

The Sharpe ratio measures risk-adjusted return per unit of total volatility, making it the most widely used performance metric in finance.