Constrained Kelly Portfolios Under Alpha-Stable Laws

Abstract

Weekly, quarterly and yearly risk measures are crucial for risk reporting according to Basel III and Solvency II. For the respective data frequencies, the authors show in a simulation and back-test study that available data series are not sufficient in order to estimate Value at Risk and Expected Shortfall sufficiently, given confidence levels of 99.9% and 99.99%. Accordingly, this paper presents a semi-parametric estimation method, re-scaling data from high- to low-frequency which allows to obtain significantly more data points for the estimation of the respective risk measures. The presented methodology in the α-stable framework, which is able to mimic multi-fractal behavior in asset returns, provides tail events which never occurred in the original low-frequency data set.

Keywords: High-Frequency, Multi-Fractal, Stable Distribution, Re-Scaling, Risk Management, Value at Risk, Quantile Distribution

JEL Classification: C14, C22, C46, C53, G32