Effective Number of Scenarios in Fully Flexible Probabilities

When estimating risk from a window of historical observations, the confidence interval is inverse to the number of scenarios used, which is the length of the window. When estimating risk with exponential decay, where the relative weight of each scenario decreases with time, the confidence interval is inverse to the effective number of scenarios used, which is of the order of the half-life of the decay.Here we propose a methodology to count the number of scenarios used in the Fully Flexible Probabilities framework, where the relative weight of each scenario is arbitrary. This allows us to compute the confidence level in any risk numbers. We illustrate a case study, where we compute the effective number of scenarios and the confidence level in a set of portfolio risk statistics when the Fully Flexible Probabilities of the scenarios are defined as the Entropy Pooling mixture of an exponential decay and a pseudo-Gaussian conditional kernel that reflects the current level of the market.The code for the case study is available for download