On risk prediction

This thesis comprises four papers concerning risk prediction. Paper [I] suggests a nonlinear and multivariate time series model framework that enables the study of simultaneity in returns and in volatilities, as well as asymmetric effects arising from shocks. Using daily data 2000-2006 for the Baltic state stock exchanges and that of Moscow we nd recursive structures with Riga directly depending in returns on Tallinn and Vilnius, and Tallinn on Vilnius. For volatilities both Riga and Vilnius depend on Tallinn. In addition, we find evidence of asymmetric effects of shocks arising in Moscow and in the Baltic states on both returns and volatilities. Paper [II] argues that the estimation error in Value at Risk predictors gives rise to underestimation of portfolio risk. A simple correction is proposed and in an empirical illustration it is found to be economically relevant. Paper [III] studies some approximation approaches to computing the Value at Risk and the Expected Shortfall for multiple period asset returns. Based on the result of a simulation experiment we conclude that among the approaches studied the one based on assuming a skewed t distribution for the multiple period returns and that based on simulations were the best. We also found that the uncertainty due to the estimation error can be quite accurately estimated employing the delta method. In an empirical illustration we computed five day Value at Risk’s for the S&P 500 index. The approaches performed about equally well. Paper [IV] argues that the practise used in the valuation of the portfolio is important for the calculation of the Value at Risk. In particular, when liquidating a large portfolio the seller may not face horizontal demand curves. We propose a partially new approach for incorporating this fact in the Value at Risk and in an empirical illustration we compare it to a competing approach. We find substantial differences.