Optimal Portfolio Management in Highly Volatile Markets

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In this book, we consider the static problem of portfolio selection in highly volatile markets. From the point of view of risk forecasting, we focus on expected tail loss (ETL) and the more general family of spectral risk measures when the underlying distribution is heavy-tailed. From an optimization perspective, we concentrate on objectives of reward-risk ratio type and how the optimization problem can be simplified depending on the properties of the risk and the reward measures. Finally, we explore the impact of a risk forecasting model, that is a combination of a distributional assumption of asset returns and a risk measure, on the optimal solution. We investigate the variability of the optimal solution and the rate of convergence to the true solution when the probabilistic model is the sub-Gaussian distribution and the multivariate t-distribution and the risk measure is the ETL. The book would be useful for finance professionals and academics working in the area of portfolio construction and risk measurement. The core of this book is based on the 2005 doctoral dissertation at University of Karlsruhe of one of the authors, Stoyan Stoyanov.