Contrary to the classic framework of passive strategies, if investors exploit return predictability through active strategies then there is a tension between the mean-variance frontiers that drive empirical work and the mean-variance preferences that are used in finance theory. We show that...

Financial Risk Forecasting is a complete introduction to practical quantitative risk management, with a focus on market risk. Derived from the authors teaching notes and years spent training practitioners in risk management techniques, it brings together the three key disciplines of finance,...

We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima...