Peaks-Over-Threshold EVT for VaR, Expected Shortfall, and Position Sizing

Summary

The article explains why historical VaR, normal-based volatility measures, and resampling can understate rare losses: each is constrained by assumptions or observations that may not represent the far tail. It presents the Peaks-Over-Threshold method, which models losses beyond a chosen threshold with a Generalized Pareto Distribution (GPD). Maximum likelihood estimates the GPD shape and scale parameters, which are then used to calculate Value at Risk and Expected Shortfall at selected confidence levels.

The author implements the approach in MQL5 as a reusable model, an on-chart crash gauge, and an Expert Advisor that adjusts exposure using the estimated tail risk. It requires a minimum number of threshold exceedances before treating a fit as usable and notes that Expected Shortfall is undefined when the fitted shape parameter reaches one. A Strategy Tester comparison reports lower maximum drawdown with the same trades, but this is a single backtest rather than evidence of general performance. EVT estimates depend on threshold choice, tail data, and fit quality, and they measure loss magnitude rather than predict crash timing or market direction.

Key ideas

• Peaks-Over-Threshold models losses above a threshold rather than fitting the entire return distribution.
• The Generalized Pareto Distribution describes the excess losses using shape and scale parameters.
• The fitted tail supports estimates of Value at Risk and Expected Shortfall beyond observed sample losses.
• The implementation withholds usable risk estimates when there are too few exceedances or the fit fails.
• The Expert Advisor uses tail-risk estimates to adjust position exposure rather than forecast direction.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.