Modeling Tail Risk in Portfolio Management with Extreme Value Theory

In the world of finance, managing and mitigating risk is a crucial aspect of portfolio management. One particular type of risk that investors need to be aware of is tail risk, which refers to the risk of extreme market movements that occur beyond what is considered normal. These extreme events, such as market crashes or sudden price drops, can have a significant impact on investment portfolios.

In this tutorial, we will explore how to model tail risk in portfolio management using Extreme Value Theory (EVT). EVT is a statistical approach that focuses on modeling the extreme events in a dataset. By understanding the tail behavior of asset returns, we can better assess the risk associated with our investment portfolios and take appropriate measures to mitigate it.

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Table of Contents

1. Introduction to Tail Risk
2. Understanding Extreme Value Theory (EVT)
3. Data Collection and Preparation
4. Calculating Asset Returns
5. Analyzing the Tail Behavior of Asset Returns
6. Fitting the Generalized Extreme Value (GEV) Distribution
7. Estimating Value at Risk (VaR)
8. Backtesting VaR Estimates