CALCULATIONS OF VALUE AT RISK FOR THE PORTFOLIO OF 5 S&P 500 STOCKS USING 5-DIMENSIONAL COPULA FUNCTIONS
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Date
2024-04-19
Authors
Kakenov, Assanali
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Sciences and Humanities
Abstract
The 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.
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Keywords
Type of access: Open Access, VaR, portfolio, 5-dimensional copula, Markowitz, dependence, time series, ARIMA-GARCH, marginal distribution
Citation
Kakenov, 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 Humanities