Evaluating portfolio Value-at-Risk using semi-parametric GARCH models

Abstract

In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. Finally, we examine the economic value of the multivariate GARCH models by determining optimal portfolios based on maximizing expected returns subject to a VaR constraint, over a period of 500 consecutive days. Again, the superiority and robustness of the semi-parametric model is confirmed.

The Impact of Catastrophes on Insurer Stock Volatility

“…ρ obtained from CC GARCH model (ρ t+1 from DCC GARCH model). The calculation of the portfolio VaR follows Rombouts and Verbeek (2009). Models are fitted over [ t −499, t ].…”

“…40 40 Considering that we are interested in the 1‐day VaR , we follow the literature (Rombouts and Verbeek, 2009) and assume that the conditional 1‐day‐ahead forecast of the return of i equals zero. …”

“…41 41 Rombouts and Verbeek (2009) discuss the calculation of VaR using multivariate GARCH models. Investigating the appropriateness of the assumption of bivariate normality, they find that this assumption works particularly well for the 5 percent‐portfolio VaR . …”

Portfolio Value at Risk Estimate for Crude Oil Markets: A Multivariate Wavelet Denoising Approach

“…Only until recently some limited attempts emerged to investigate the MGARCH based VaR estimates, i.e., Rombouts and Verbeek [46], Ku and Wang [47], Huang et al [48].…”

Portfolio Risk of Chinese Stock Market Measured by VaR Method

“…How to accurately measure the market risk and better operate the market are commonly concerned by the investors and securities institutions. The economy and finance of China are growing rapidly, so it is necessary to research the stock price index of Chinese stock market while making considerable progresses in securities market, especially the stock market [1][2][3][4][5][6][7].…”