In general, the properties of the conditional distribution of multiple period returns do not follow easily from the one-period data generating process. This renders computation of Value-at-Risk and Expected Shortfall for multiple period returns a non-trivial task. In this paper we consider some...

In this note it is argued that the estimation error in Value-at-Risk predictors gives rise to underestimation of portfolio risk. We propose a simple correction and find in an empirical illustration that it is economically relevant.

The paper studies the forecasting of a future size distribution of plants. As a model we use an open Markov chain model for macro data. Estimation is by reparametrization instead of by inequality restrictions using single equation least squares. The estimator is studied in a small Monte Carlo...