### Probability-weighted return is the optimal method to construct a portfolio

Alpha Theory recently ran a Monte Carlo simulation comparing the Alpha Theory position sizing technique to a myriad of common position sizing methodologies including Kelly Criterion (Optimal F), Up / Down Ratio, Equal Weighting (and by proxy 14 Markowitz Mean-Variance Modern Portfolio Theory systems). Alpha Theory measured success by measuring the amount of Portfolio Expected Return added per 1% of portfolio exposure. Alpha Theory beat the closest methodology, Kelly Criterion, by 18%, Up / Down Ratio by 52%, Equal Weighting by 48%.

Two studies of Markowitz Mean-Variance systems show that mean-variance maximization does not beat Equal Weighting (DeMiguel et al (2006) / Jobson-Korkie).

Kelly Criterion is the superior method for generating the maximum long-term geometric expected return when the whole portfolio can be wagered on a single investment. However, portfolios are comprised of multiple investments and thus Kelly Criterion under bets good expected returns because it trying to protect against complete loss of capital and over bets poor expected returns with very high probability of success. Because portfolio investing has inherent capital protectors by limiting position size maximums, Kelly Criterion breaks down.

To see a brief slide and list of variables please go to: http://www.alphatheory.com/pdf/MonteCarloSimulationSlide.pdf.