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Portfolio Construction and Systematic Trading with Factor Entropy Pooling

R/Finance 2014. Portfolio Construction and Systematic Trading with Factor Entropy Pooling Meucci , Ardia , Colasante Presented by Marcello Colasante. STUDY IT: www.symmys.com (white papers and code)

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Portfolio Construction and Systematic Trading with Factor Entropy Pooling

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  1. R/Finance 2014 Portfolio Construction and Systematic Trading with Factor Entropy Pooling Meucci, Ardia, Colasante Presented by Marcello Colasante STUDY IT: www.symmys.com (white papers and code) DO IT: Advanced Risk and Portfolio Management® Bootcampwww.symmys.com/arpm-bootcamp

  2. Factor Entropy Pooling: purpose What is the optimal investment strategy if we believe that, qualitatively, higher price on earnings imply higher returns, but we do not know precisely? Inequalityviews of Sharpe-ratios

  3. Factor Entropy Pooling: purpose What is the set of expected returns andcovariances that are consistent with CAPM equilibrium and thus can be used effectively as a starting point of mean variance optimization? Equalityviewsconsistent with equilibrium

  4. Reference model • Set of risk drivers represented by probability density function is the number of risk drivers Approach • Non-parametric • Parametric

  5. Entropy pooling • Framework: • Prior distribution • Views • Posterior distribution Relative entropy (target function)

  6. Case study • Normal assumption: • Prior distribution • Viewson expectations and covariances • Posteriordistribution (analyticalsolution) Reletiveentropy (explicitform)

  7. Problem • General views are not addressed by analytical solution • Numerical approach iscomputationallyexpensive: • Large number of parameters • Constrained specification

  8. Solution • Covariance matrix of low-rank-diagonal type • Consistence with a systematic-idiosyncraticlinear factor model uncorrelated

  9. Numerical approach with general views is possible: • Small number of parameters ( ) • Unconstrained specification • Analytical expression of the gradient and the Hessian of the entropy • The high-dimensional inverses that appear in the gradient and in the Hessian are obtained analytically by means the binomial inverse theorem

  10. Viewson ranking • We back-test a standard reversal strategy processing ranking (inequality) trading signals: Step 1. Momentum/reversal indicator Step 2. Reorder the stocks in such a way that Step 3. Lower ranking gives rise to a lower Sharpe ratio is a buffer that induces stronger inequalities.

  11. Step 4. Standard approach Problem • Sharpe ratios never change through time • Volatilities are not updated Solution Step 4’. Compute the optimal parameters that satisfy the signal inequalities and are closest to the estimated covariances and expected returns

  12. Cumulative P&L generated by the reversal strategy back-test for various parametrizations. The plot reports the median (solid line), the 50% percentile range (dim shading) and the 90% percentile range (dimmer shading).

  13. Views on equilibrium Step 1. Target optimal portfolio Step 2. Equilibrium constraints Step 3. BL-equilibrium parameters Step 3’. Generalized FEP-equilibrium parameters

  14. Historical means and covariances (blue) for various pairs of stocks versus respective implied expected returns and covariances: Black-Litterman (black) and Factor Entropy Pooling (red).

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