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Risk Analysis of Stock Portfolios Using Value at Risk (VaR) with the Extreme Value Theory Approach (Case Study: Banking Sub-sector Stocks Period May 1, 2019 - May 31, 2025)
This document contains the R code syntax and computational workflow for an undergraduate thesis focusing on the risk analysis of a stock portfolio within the Indonesian banking sub-sector (BBCA, BBNI, BBRI, BMRI, and BRIS). This analysis specifically estimates market risk—rather than seeking an optimal portfolio—using the Extreme Value Theory (EVT) approach to capture fat-tail phenomena and extreme events in the capital market.
A crucial step in this computation is data transformation, where the log returns are multiplied by -1. This transformation is mandatory to invert the distribution direction so that the loss metric can be accurately modeled using extreme value theory.
Broadly, the workflow in this document encompasses:
Data Acquisition & Preparation: Retrieval of daily stock price data via Yahoo Finance (2019–2025) and calculation of log returns.
Loss Transformation & Weighting: Determination of individual asset weights and the transformation of portfolio returns into losses.
Extreme Value Identification: Data extraction using two EVT methods: Block Maxima and Peak Over Threshold (POT).
GEV & GPD Distributions: Fitting extreme data into the Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) models, followed by Anderson-Darling goodness-of-fit tests.
Value at Risk (VaR) Estimation: Calculation of VaR at a 95% confidence level for both models.
Backtesting: Validation of the VaR models' accuracy using the Likelihood Ratio test (Kupiec Test) to ensure the actual violation rate aligns with the expected target.
This document serves as a computational reference for students and quantitative practitioners looking to implement EVT-based VaR measurements using R packages such as quantmod, extRemes, evmix, and eva.