Risky Portfolio Efficient Frontier & Performance: Bayesian versus Frequentist

Abstract

The location of the Efficient Frontier in Expected Portfolio Return (Rp) / Portfolio Standard Deviation (Sp) space depends on what kind of summary estimates are utilized by the investor. By relying on Bayesian and Frequentist summary measures, in conjunction with a 5-stock portfolio of non-volatility free stocks, analysis in this paper proves that use of reliable Bayesian estimates (estimates that are not sensitive to prior distributions) (a) causes the locus of the Efficient Frontier to appear higher than, and to the right of, the one constructed on Frequentist geometric measures, and (b) generates improved measures of portfolio performance. Additionally, it is demonstrated that the decision of the investor to rely on simple (arithmetic or sample) summary measures describing non-volatility-free assets, would cause the Efficient Frontier to appear above the Bayesian, implying overoptimism. It is concluded that Bayesian estimates, that are not sensitive to mistaken prior distributions, take the investor closer to truer performance levels.