Copulas and Value-at-Risk: Risk Estimation of Portfolios
Authors
Jørgensen, Thea Lund ; Lauridsen, Charlotte Kargo ; Pedersen, Henriette Rønfeldt
Term
4. term
Education
Publication year
2022
Abstract
Dette speciale undersøger, hvordan én-dags Value-at-Risk (VaR)—et mål for den maksimale forventede tab med en given sandsynlighed—kan forudsiges for aktieporteføljer ved at kombinere ARMA-GARCH-modeller for de enkelte afkast med copulaer til at beskrive afhængigheder og Monte Carlo-simulation. Der opbygges to porteføljer med fem aktier, der repræsenterer global equity og emerging markets, baseret på daglige data fra 2010–2021, og out-of-sample forudsigelser vurderes for 2020–2021. En rullende Monte Carlo-procedure genererer VaR-prognoser, som evalueres med backtesting og statistiske tests. Resultaterne viser, at VaR-prognoserne er tilfredsstillende. VaR baseret på information fra Rådet for Afkastforventninger tenderer til at underestimere risiko for global equity og overestimere risiko for emerging markets sammenlignet med de modelbaserede estimater. Endelig viser de konstruerede porteføljer samme tendenser som de tilsvarende markedsindekser, hvilket tyder på, at de er repræsentative for deres markeder.
This thesis examines how to forecast one-day-ahead Value-at-Risk (VaR)—a measure of the maximum expected loss at a given probability—for equity portfolios by combining ARMA-GARCH models for individual returns with copulas to capture dependence and Monte Carlo simulation. Two five-stock portfolios are constructed to represent global equity and emerging markets, using daily data from 2010–2021 and evaluating out-of-sample forecasts for 2020–2021. A rolling Monte Carlo procedure generates VaR forecasts, which are assessed with backtesting and statistical tests. The results indicate that the VaR forecasts are satisfactory. VaR derived from the Council for Return Expectations tends to under-estimate risk for global equity and over-estimate risk for emerging markets relative to the model-based estimates. Finally, the constructed portfolios display trends similar to their corresponding market indices, suggesting they are representative of their asset classes.
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