The Measurement, Decomposition And Application Of Portfolio Risk Under The General Distributions

In the real-time investment decisions, managers not only need to know the total risk of the portfolio, but also want to know the structure of the risk and every asset's marginal risk. The information above can be got by decomposing the portfolio risk.In this paper, the measurement of portfolio VaR & ES were intensively studied under the historical and analytical methods. Furthermore, the corresponding methods to estimate marginal risk and the applications were proposed. Considering that financial return was always nonnormally distributed and the heteroscedasticity, the linear portfolio's risk can be evaluated by modeling its historical return with EGARCH-GED model. Based on the statistical meaning of marginal risk formulas, two new methods were proposed to estimate marginal VaR and ES when the portfolio risk were estimated by using historical and EGARCH-GED methods: linear local weighted average and piecewise-linear curve-fitting. In view of financial data's fat-tail and high kurtosis, Delta-Normal was extended to Delta-Elliptical. Furthermore, Delta-Elliptical mixture models were proposed to capture the multifactor. source of residual part. Both the portfolio VaR & ES and the marginal VaR & ES formulas were deducted on the assumptions of Delta-Elliptical and Delta-Elliptical mixture respectively. Assets' correlation matrix was estimated by EWMA and diagonal model respectively. The data example testified that: Delta-Elliptical and Delta-Elliptical mixture models fit the actual data better than Delta-Normal; the methods of linear local weighted average and piecewise-linear curve-fitting decompose portfolio risk very well, and the latter's accuracy is higher than the existing; when portfolio contains a number of assets, the diagonal model displays a higher computational efficiency and promises to be highly accurate.