Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model

TL;DR

This paper investigates the self-averaging property of minimal investment risk in mean-variance portfolio optimization, revealing that the typical risk converges to a predictable value and differs from traditional operations research results.

Contribution

It introduces a self-averaging analysis for minimal investment risk, providing a new perspective that aligns with numerical simulations but diverges from classical operations research outcomes.

Findings

Self-averaging property holds for minimal investment risk.

Results agree with numerical simulations.

Differences from traditional operations research approach.

Abstract

In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always result in the best rate of return on assets. Prior to making investment decisions, it is important to an investor to know the potential minimal investment risk (or the expected minimal investment risk) and to determine the strategy that will maximize the return on assets. We use the self-averaging property to analyze the potential minimal investment risk and the concentrated investment level for the strategy that gives the best rate of return. We compare the results from our method with the results obtained by the operations research approach and with those obtained by a numerical simulation using the optimal portfolio. The results of our method and the numerical simulation are in agreement, but they differ from that of the operations research approach.