Abstract:

The purpose of this paper is to estimate Value-at-Risks (VaRs) for the S&P 500 stock market index for US and international investors. The S&P 500 is notoriously a major source of risk exposure for many financial institutions, corporations, and individuals. The results should serve as a reference for more elaborate computations, and should be applicable to any US security or portfolio of securities with minor modifications. The paper considers daily and monthly data for the S&P 500 and four foreign exchange rates, partitioned into sub-samples. Many levels of confidence are studied. Three models are assumed: historical, Gaussian, and mixture of Gaussians. It is found that the Gaussian assumption is not tenable because of significant negative skewness and significant kurtosis in the data. It is argued that the model of a mixture of Gaussians is the most adequate, and, not surprisingly, this model produces higher risk estimates. In addition, selected VaRs for international investors in the US stock market are provided, and the domestic and foreign risk exposures are determined.