Entropy Pooling in Quant analytics—> Portfolio Optimization?
I confess I am charmed by the speed and elegance of the entropy-pooling approach. In Meucci’s paper “Fully Flexible Views – Theory and Practice” paper it states in the Introduction: “The output [of entropy pooling] is a distribution, which we call “posterior”, that incorporates all inputs and can be used for risk management and portfolio optimization.” Exactly how does one perform asset allocation based on the updated probabilities for the various joint-scenarios? For example — suppose one has J = 50,000 joint scenarios. Entropy pooling furnishes revised probabilities corresponding to these scenarios. How does construct an optimal portfolio (i.e. max some utility function choosing security weights) given these J discrete scenarios? Does one optimize a single probability weighted average utility function (consisting of 50,000 components!)? Or does one use a re-sampling approach (i.e. optimize each joint-scenario) and probability weight each of the J-weight vectors?
You can use those probabilities to create (effectively) a weighted average mean or weighted average covariance matrix. Then do optimization on those, rather than the whole thing. My recommendation is to take a look at some of the code he provides in the examples. Sometimes things are easier to understand from the perspective of code.
More generally, the benefit of a scenario approach is that it is much better for calculating Expected Shortfall, which is critical for accounting for tail risk of your portfolio.
I have gone thru “Entropy Pooling – Theory & Practice”, “Fully Flexible Extreme Views”, “Flexible Probabilities”, “Robust Bayesian Allocation”, etc. including the Matlab code. There is no case where an optimal allocation is identified based on a numerical or monte carlo (as opposed to analytical) joint distribution. I’ll take another gander but if something comes to mind, please let me know. BTW, I’ve enjoyed your other contributions on this site. Keep it up and thanks for the suggestion!
Go in the Entropy Pooling one, check RankingInformatiom\EffcientFrontier.m or ButterflyTrading\LongShortMeanCVaRFrontier.m, both basically do what you’re trying to understand.
First I admit that I did not study in detail paper and code of the EP approach.
However, if you have scenarios and probabilities a natural choice is to perform asset allocation in a linear programming framework. See “Portfolio Construction and Risk Budgeting“ (B. Scherer) the chapter on Scenario Optimization
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