Structured Monte Carlo. Estimated value at risk in a stock portfolio in Colombia

Abstract

This research explores various methods to estimate Value at Risk for a portfolio of high and medium liquidity Colombian stocks. It concludes that, according to the characteristics of these assets, Full Montecarlo is more robust than other parametric methods –particularly the Normal method-, and the historical simulation. However, to avoid model risk, it requires a correct specification of the stochastic process followed by each of the risk factors. Given the evidence of fat tails on the return series, volatility models such as GARCH, EGARCH, PARCH and APARCH are used for this purpose. After that, we compare the one-step ahead VaR forecast given by these models with the one obtained by parametric methods. It is found that Garch models predict VaR better since they capture the fat tails characteristic of these series. Once the stochastic process for each asset is properly identified, the Full Montecarlo is applied to estimate VaR.