Foundations of Quantitative Risk Management in Trading

Risk management in quantitative trading is not about avoiding losses — it is about understanding their distribution and ensuring that no single event or sequence of events can remove you from the game. Many traders learn position sizing rules as formulas without understanding the statistical reasoning behind them, which means they apply the rules correctly in familiar situations and completely abandon them in unfamiliar ones. This course builds the conceptual foundation that makes risk rules stick. By the end of this course you will be able to explain what Value at Risk (VaR) measures and what it does not measure, describe the assumptions behind mean-variance portfolio optimization and where those assumptions break down, calculate and interpret the Sharpe ratio in context, understand drawdown metrics and why maximum drawdown is a lagging rather than predictive indicator, and explain the logic behind position sizing approaches including fixed fractional and Kelly criterion methods. What you will learn: - Probability distributions of returns: why the normal distribution underestimates tail risk in real markets - Value at Risk: parametric, historical simulation, and Monte Carlo methods — and the limitations of each - Expected Shortfall (CVaR): why it is preferred over VaR for risk reporting and what it actually measures - Mean-variance optimization: efficient frontier construction, correlation inputs, and sensitivity to estimation error - Sharpe ratio, Sortino ratio, and Calmar ratio: what each rewards and which market environments each suits - Drawdown analysis: maximum drawdown, average drawdown, recovery period, and what these reveal about a strategy's risk profile - Position sizing fundamentals: fixed fractional sizing and the mathematical logic of the Kelly criterion - Risk limits and exposure management: gross exposure, net exposure, and sector concentration constraints The course is structured as a progression of conceptual readings, each building a component of the overall risk framework. Worked examples use simplified numerical scenarios to illustrate abstract concepts. Self-assessment exercises ask you to reason through risk metrics for hypothetical strategy outcomes before seeing the calculations. This course is designed for individuals new to quantitative trading who want to understand risk management rigorously, as well as for discretionary traders transitioning to a more systematic approach. No prior background in statistics or quantitative finance is required — core concepts are introduced from scratch. This course is informational and educational and does not constitute financial or investment advice. All trading involves risk of loss.