ABSTRACT
Gt) where Gt = [ 2ii,t ] is the forecast variance covariance matrix of vector Gt. The vector Gt is not observable. We suppose the dependence structure of Gaussian variables Gi,t is "inherited" from the dependence structure of truncated values of stable variables where the truncation values for zi,t are sufficiently large in order to value the effect of outliers. Thus, we can introduce and control the dependence among different returns with the first component of portfolio z,(1)p,t . In fact variance and covariance matrix is given by the following rules:
ii,t 1/t 2 + (1 ) z2i,t l (50) 2 ij,t/t 1 =
As it follows from the above discussion, all the multivariate models introduced here can be empirically tested. A first performance analysis can be found in Ortobelli, Huber, Höchstötter and Rachev (2002). While a comparison among different multivariate portfolio selection models can be found in Ortobelli, Huber, Rachev and Schwartz (2002). An empirical analysis and a comparison among the Rachev Schwartz and Khindanova model and calssical conditional models for VaR calculation was recently proposed by Consiglio, Massabò, Ortobelli (2001). Clearly, the above models can be extended and generalized considering continuous time processes or relaxing the implicit assumptions of a perfect financial market. Recently, these assumptions are weakened in different aspects. There are papers which consider problems with constrains on the strategies (see Cvitanic and Karatzas (1992), He and Pearson (1991)). While other papers consider problems of taxes and transaction costs, (see, among others, Davis and Norman (1990), Morton and Pliska (1995), Korn (1998), Cadenillas and Pliska (1999)). However, a more general theoretical and empirical analysis with further discussions, extensions and comparisons of the above models does not enter in the objective of this paper and it will be the subject of future research.
