An energy-based measure for long-run horizon risk quantification

Abstract

Capital requirements for financial institutions are based on the accurate quantification of the inherent risk. To this end, time is the important parameter for all the well-established risk measures, whereas risk managers make no explicit distinction between the information captured by patterns of different frequency content. Accordingly, the original full-time-resolution series of returns is considered, regardless of the selected trading horizon. To address this issue, we propose a novel risk quantification method exploiting the time-evolving energy distribution of returns, which is expressed by the sum of squared magnitudes of a set of transform coefficients. Specifically, a wavelet-based time-scale decomposition is applied first on the returns series to extract the energy contribution of the wavelet coefficients at multiple frequencies. Then, the statistics of an optimal subset of frequencies are linearly combined to estimate the overall risk at a given trading horizon. Most importantly, our proposed energy-based method can be coupled with the commonly used quantile-based risk measures to enhance their performance. The experimental results reveal an increased robustness of our method at efficiently controlling under- or over-estimated risk values, especially for long-run horizons.