Entropy Pooling with Discrete Weights in a Time-Dependent Setting

Long term investors typically base their allocation decisions on a combination of expert knowledge and forecasting models. The forecasting models combine historical data with forward-looking market assumptions to produce a multivariate density forecast for the relevant asset classes. The investor’s allocation decisions, however, can be sensitive to small adjustments in these density forecasts. In this paper, we present a framework for adjusting density forecasts and, in particular, the forecast’s correlation structure. For this, we use the computational approach to Meucci’s entropy pooling method. When the density forecast is represented by sample points, the computational approach adjusts the density forecast by assigning weights to the sample points. This paper contributes to the literature in two ways. First, we show how to apply the computational approach in a time-dependent setting with sample paths, called scenarios, instead of sample points. Second, to ease the method’s use in practice, we present a heuristic that forces the resulting weights to be discrete. With this, the adjusted density forecast can be represented by a finite number of equally weighted scenarios.