Fat-tailed ETL Optimal Portfolios
Mean-variance optimization, first proposed by Harry Markowitz in 1952, is popularly referred to as modern portfolio theory. Markowitz suggested that portfolio selection be made with respect to two criteria: the expected portfolio return and the variance of the portfolio return with the latter used as a proxy for risk. Portfolios are selected from an efficient frontier generated by either maximizing the expected return of the portfolio, while keeping the return variance to a certain level, or by minimizing the return variance for a given expected return. A drawback in mean-variance optimization is that variance is used as a proxy for risk.
Taking full advantage of the informative power of ETL, a mean-ETL framework significantly enhances optimization by adopting ETL as a coherent downside risk measure instead of variance and by incorporating a realistic multivariate model in the optimization problem. This mean-ETL framework produces scenarios through Monte Carlo simulation based on models that accurately fit fat-tailed distributions.
Cognity can optimize portfolios using multivariate t-distributions and through patent-pending stable-Paretion distribution methods. Cognity also offers the ability maximize risk-adjusted return using the STARR performance measure. In most cases, mean-ETL portfolio optimization yields superior risk-adjusted returns relative to conventional mean-variance portfolios at equivalent ETL risks.