Risk Measures

Read these first

1. 01Correlation Breakdown in Crises

   The diversification you counted on when you built the portfolio is measured in calm markets, and calm-market correlations are not the correlations that show up when everything actually goes wrong at once.

2. 02Historical Simulation VaR

   Instead of assuming a shape for tomorrow's losses, replay the last few hundred real market days through today's positions, sort the results, and read off the loss you exceed only rarely. Simple, popular, and quietly full of assumptions.

3. 03Mapping Positions to Risk Factors

   A trading book holds thousands of different instruments, but their risk comes from a few dozen shared drivers. Mapping is the translation step that rewrites every position as a set of sensitivities to those drivers, so the whole book can be aggregated and measured.

4. 04VaR Backtesting and the Kupiec Test

   A VaR model makes a promise you can check: losses should breach the number on 1% of days and no more. Backtesting counts the breaches, and Kupiec's test decides whether the gap between promised and observed is ordinary bad luck or a broken model.

5. 05Euler Allocation of Portfolio Risk

   A precise way to answer "how much of the portfolio's total risk does this one position actually cause," using a mathematical property that guarantees the pieces add up exactly to the whole.

6. 06Extreme Value Theory for Tail Risk

   A statistical theory for the worst days specifically, built from the idea that the shape of extremes doesn't have to match the shape of the everyday, and that you can estimate a 1-in-1000-day loss from a lot fewer than 1000 bad days.

Then the rest

1. 07Drawdown Duration and Time Under Water
2. 08EWMA Volatility and RiskMetrics
3. 09Lower Partial Moments
4. 10Semideviation and Downside Risk
5. 11The Diversification Ratio
6. 12The Square-Root-of-Time Rule
7. 13Variance-Covariance VaR
8. 14Aggregating Risk Across Books and Desks
9. 15Backtesting Expected Shortfall
10. 16Component VaR
11. 17Conditional Drawdown at Risk
12. 18Cornish-Fisher VaR
13. 19Coskewness and Cokurtosis
14. 20CoVaR and Marginal Expected Shortfall
15. 21Delta-Gamma VaR for Option Books
16. 22Distortion Risk Measures
17. 23Evaluating Volatility Forecasts
18. 24Filtered Historical Simulation
19. 25Incremental VaR
20. 26Liquidity-Adjusted VaR
21. 27Monte Carlo VaR
22. 28Peaks Over Threshold and the Generalised Pareto Distribution
23. 29Spectral Risk Measures
24. 30Tail Dependence Coefficients
25. 31The Hill Estimator and the Tail Index