Portfolio Inversion : Finding Market State Probabilities From Optimal Portfolios

Abstract: In this project, we aim to find a method for obtainingthe factors in a bull/bear market factor model for asset returnand variance, given an optimal portfolio. The proposed methodwas derived using the Karush-Kuhn-Tucker (KKT) conditionsfor optimal solutions to the convex Markowitz portfolio selectionproblem. For synthetic data where all necessary parameters wereknown exactly, the method could give bounds on the factors. Theexact values of the factors were obtained when short selling wasallowed, and in some instances when short selling was forbidden.The method was evaluated on real-world data with varyingresults, possibly due to estimation errors and invalid assumptionsabout the model of the investor.I. INTRODUC