A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions

摘要

A method of calculating the downside risk by fitting multivariate nonnormal distributions to financial data is proposed. Firstly, maximum likelihood method by using the random numbers of the Pearson distribution system are introduced. The rates of returns of the stock index are fitted to the multivariate nonnormal distributions by this method. Secondly, the cases of calculating the downside risk by the standard deviation, the percentile of historical simulation method and this method, are compared.