Ardia, David

2014, Meucci, Attilio, Ardia, David, Colasante, Marcello

The Entropy Pooling approach is a versatile theoretical framework to process market views and generalized stress-tests into an optimal "posterior" market distribution, which is then used for risk management and portfolio management. Entropy Pooling can be implemented non-parametrically or parametrically. The non-parametric implementation with historical scenarios is more suitable for risk management applications. Here introduce the parametric implementation of Entropy Pooling under a factor structure, which we name Factor Entropy Pooling. The factor structure reduces the dimension of the problem and linearizes the parameter space, allowing for fast computation of the posterior market distribution. We apply Factor Entropy Pooling to two portfolio construction problems. First, we use the Factor Entropy Pooling to construct the "implied returns", i.e. a market distribution consistent with a target optimal portfolio, such as maximum diversification/risk parity, or the CAPM equilibrium. Our approach improves on the implied returns a-la-Black-Litterman, and the ensuing distribution can be used as the starting point for further portfolio construction. Second, we use Factor Entropy Pooling to construct and backtest quantitative systematic trading strategies based on ranking views, or "portfolios from sorts". Unlike standard approaches, Factor Entropy Pooling closely ties to the actual empirical data.