Kakenov, Assanali2024-05-032024-05-032024-04-19Kakenov, A. (2024). Calculations of value at risk for the portfolio of 5 s&p 500 stocks using 5-dimensional copula functions. Nazarbayev University School of Sciences and Humanitieshttp://nur.nu.edu.kz/handle/123456789/7615The purpose of this project is to compare copula estimations of Value at Risk (VaR) for a portfolio of 5 S&P 500 stocks to historical, normal distribution, and Monte Carlo methods employing dependence measures and ARIMA-GARCH time series models. This study will provide interpretations of financial data between 2019-2024 in a scope of 5 equations: Gaussian, Clayton, t-Copula, Gumbel, and Frank copulas. Correlations between closing prices of the largest 30 S&P 500 companies by market capitalization were calculated, and the portfolio was constructed by selecting 5 stocks with the least average correlation. The Markowitz portfolio optimization model was utilized to estimate the weights of the assets in the portfolio. Log returns, skewness, kurtosis, Shapiro-Wilk, and ADF were measured to describe stationarity and normality of the data. Data autocorrelation was assessed using ACF and PACF for volatility before ARIMA-GARCH modeling. All methodology was followed by appropriate hypothesis tests. Finally, 5-dimensional copulas were used for the VaR estimations for different confidence intervals. While AIC and BIC showed that t-copula was the best fit, the Clayton copula passed the goodness-of-fit test with the largest p-value. Subsequently, the Clayton copula generated VaR estimations closest to the historical data. The method used in this study can be extended for more than five assets without theoretical obstacles.enAttribution-NonCommercial-ShareAlike 3.0 United StatesType of access: Open AccessVaRportfolio5-dimensional copulaMarkowitzdependencetime seriesARIMA-GARCHmarginal distributionCapstone Project