Using equations that arise in quantum mechanics, this paper describes a way to more accurately and efficiently represent non-Gaussian return distributions than the standard method of invoking skewness and kurtosis. Then, it provides a new single intuitive number, defined here as the “crash...

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...

The inherent assumption with most Monte Carlo techniques is that one may ignore autocorrelations, but doing so compromises the quality of the prediction from the data. Simulations that do not take account of autocorrelation will not properly model reality, as there is significant autocorrelation...

In order to take advantage of the “one true free lunch” in investing, namely the increase in compound return due to the reduction of volatility by regular re-balancing among uncorrelated assets, it is necessary to first establish what those uncorrelated asset classes are. In practice, many...

A previous paper (“The Probability Frontier or, Covariance Crunch: A New Paradigm for Mean-Variance Optimization”) introduced the concept of a Directional Covariance matrix, which reduces market returns to pure directionality (+1 or -1), treating the magnitudes as noise. This is intended to...