The Probability Frontier or, Covariance Crunch : A New Paradigm for Mean-Variance Optimization

Three innovative concepts are combined here to create a new and unique framework for optimizing a portfolio of investments or bets. These inventions are:1) The Probability Frontier, a generalization of the Markowitz Efficient Frontier;2) The Positive Probability Estimate, which estimates the chance of a market to move up in the coming period, regardless of the magnitude of the move; and3) The Directional Covariance, which measures the tendency of markets to move together, regardless of the size of the moves.Looking at both market moves and their covariances in terms of pure directionality, treating their magnitudes as “noise” on the premise (demonstrated decisively in this paper) that direction is more robustly predictable, dramatically improves the optimized system performance. Indeed, if our estimates can't even get market directions right, what's the point of quibbling over tenths of a percentage point? Don't shrink that covariance matrix; crush it!