Abstract
This paper presents a methodology for calculating the Value at Risk (VaR) of portfolios of financial assets using a multivariate ARCH model. A slight modification of the factor-ARCH model proposed by Engle, Ng, and Rothschild (1990) is used to calculate VaR of portfolios of Danish zero-coupon bonds. The proposed method combines the ARCH model with a factor model. The factors are constructed as orthogonal portfolios of the bonds (denoted factor representing portfolios) using principial components analysis. The returns of the factor representing portfolios are assumed to be described by the univariate GARCH(1,1) model. From the findings of the factor representing portfolios, the model for the returns of the individual zero-coupon bonds is determined. Models with one and two factors are estimated, and the two-factor model is shown to outperform the one-factor model. Hence, the VaR is estimated solely in the two-factor setting for a number of zero-coupon bond portfolios, and these VaR quantities are compared to actual losses. The calculated VaR amounts are also compared to the RiskMetrics estimates. At the 1% VaR it is not conclusive whether the factor-ARCH approach or RiskMetrics is most effective in estimating VaR for the analyzed data. However, for the 5% VaR RiskMetrics is preferred to the factor-ARCH model.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.