Adjusted Evaluation Measures for Asymmetrically Important Data

Abstract

In this paper we introduce adjustments for standard evaluation measures appropriate for the analysis of data with asymmetrical importance. In risk analysis, it is understood that the returns of an asset do not all provide the same amount of information. This asymmetry of information is crucial for choosing the most appropriate model and evaluating its forecasting ability. In risk analysis, measures like value at risk (VaR) and expected shortfall (ES) concentrate on the left tail of the distribution of returns so that failures in fitting a model on the right tail are not important. Therefore, when we estimate the VaR of an asset, the days of violations are more important than the days of non-violations. The proposed adjustments take into consideration the asymmetry in importance and are filling the gap in the theory of evaluation of percentiles measures. The measures are divided into fixed partition, based on prior information or the goal of forecasting, and non fixed partition, based on the time proximity of the model failure. The performance of the proposed measures is illustrated with the use of a stock from the industrial metals and minerals index of the American Stock Exchange (NYSE MKT), as well as a warrant, from the Athens Exchange (ATHEX).