Quantitative Finance

Beta in Finance: What It Is, How to Calculate It, and Why It Matters

Beta is one of the most important risk metrics in finance. Whether you’re evaluating a single stock, building a diversified portfolio, or studying for the CFA…

9 min readLevel: CoreCalculatorExcel modelVideo

Sharpe Ratio: Formula, Interpretation, and Examples

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

11 min readLevel: CoreCalculatorExcel modelVideo

Correlation vs Covariance in Finance: Key Differences

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

9 min readLevel: CoreCalculatorExcel modelVideo

Efficient Frontier: Portfolio Optimization Explained

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

13 min readLevel: CoreCalculatorVideo

Treynor Ratio: Formula, Interpretation, and Treynor vs Sharpe

The Treynor ratio measures risk-adjusted portfolio performance by dividing excess return by beta, making it the standard metric for evaluating well-diversified…

11 min readLevel: CoreCalculatorExcel modelVideo

Jensen’s Alpha: Definition, Formula, and Example

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…

10 min readLevel: CoreCalculatorExcel model

Maximum Drawdown: What It Is, How to Calculate It, and Why It Matters

Maximum drawdown measures the largest peak-to-trough percentage decline in a portfolio or investment before a new peak is established — the worst cumulative…

11 min readLevel: CoreCalculatorVideo

Monte Carlo Simulation in Finance: How It Works and Why It Matters

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

10 min readLevel: CoreCalculatorVideo

Descriptive Statistics: Central Tendency and Dispersion

Learn how to use descriptive statistics in finance including arithmetic mean, geometric mean, median, variance, standard deviation, and coefficient…

13 min readLevel: FoundationsCalculatorExcel modelVideo

Skewness and Kurtosis: Understanding Fat Tails in Return Distributions

Learn how skewness measures return asymmetry and kurtosis measures tail thickness. Understand why normal distribution assumptions can understate extreme event…

8 min readLevel: CoreCalculatorExcel modelVideo

Probability Distributions in Finance: Normal, Lognormal, Binomial, and Student’s t

Learn which probability distributions describe financial variables, how to read PDFs and CDFs, and when each assumption fails.

12 min readLevel: CoreCalculatorExcel modelVideo

Bayesian Updating in Finance: Revising Probabilities with New Evidence

Learn how to use Bayesian updating to revise probability estimates when new evidence arrives, with practical finance examples including credit risk signal…

8 min readLevel: CoreCalculatorExcel model

Central Limit Theorem and Sampling Distributions

The Central Limit Theorem explains why sample averages become normally distributed as sample size grows, enabling confidence intervals and hypothesis tests…

7 min readLevel: CoreCalculatorExcel model

Confidence Intervals: Statistical Estimation in Finance

Learn how confidence intervals quantify estimation uncertainty for means, proportions, and financial statistics.

9 min readLevel: CoreCalculatorExcel model

Hypothesis Testing in Finance: z-Tests, t-Tests, and p-Values

Learn how to apply hypothesis testing to evaluate investment performance, test portfolio strategies, and interpret statistical significance in finance.

11 min readLevel: Core

Type I and Type II Errors, Statistical Power, and p-Hacking

Every statistical test in finance carries the risk of two types of errors. A Type I error means acting on a signal that isn’t real — like hiring a manager…

9 min readLevel: CoreCalculatorExcel model

Simulation Methods: Historical, Bootstrap, and Monte Carlo

Compare historical simulation, bootstrap simulation, and Monte Carlo simulation methods in finance. Learn when to use each approach, their assumptions…

11 min readLevel: Core

Cholesky Decomposition for Correlated Asset Simulation

Learn how Cholesky decomposition converts independent random draws into correlated simulation inputs for multi-asset Monte Carlo analysis.

8 min readLevel: AdvancedCalculator

Vasicek Model: Mean-Reverting Interest Rates & Bond Pricing

The Vasicek model is the foundational framework for stochastic interest rate modeling. Learn the mean-reverting SDE, bond pricing formulas, yield curve…

12 min readLevel: CoreCalculatorExcel model

CIR Model: Square-Root Diffusion and Non-Negative Interest Rates

The Cox-Ingersoll-Ross (CIR) model uses square-root diffusion to ensure interest rates stay non-negative. Learn the CIR SDE, Feller condition, and bond pricing…

8 min readLevel: AdvancedCalculatorExcel model

Hull-White Model: Calibration to the Yield Curve

The Hull-White model extends Vasicek by adding a time-varying mean reversion level, enabling exact calibration to the initial term structure for interest rate…

8 min readLevel: Advanced

HJM Framework: Heath-Jarrow-Morton Forward Rate Modeling

The Heath-Jarrow-Morton (HJM) framework models the entire forward rate curve directly, with drift determined by volatility through the no-arbitrage condition.

9 min readLevel: Advanced

Value at Risk (VaR): Formula, Methods, and Examples From Financial Risk Management

Value at Risk (VaR) measures the loss threshold not expected to be exceeded at a given confidence level over a specified time horizon.

13 min readLevel: FoundationsCalculatorVideo

Expected Shortfall (CVaR): Formula, Calculation, and Examples From Financial Risk Management

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…

12 min readLevel: CoreCalculatorVideo

Historical Volatility: Parkinson, Garman-Klass & Rogers-Satchell

Learn efficient volatility estimation using OHLC data with Parkinson, Garman-Klass, and Rogers-Satchell estimators.

9 min readLevel: CoreCalculatorExcel model

Stochastic Volatility: Heston Model Explained From Options & Derivatives

Learn how the Heston stochastic volatility model treats variance as a random process, explains the volatility smile through correlation, and compares to GARCH…

13 min readLevel: Advanced