On Biased Correlation Estimation

TL;DR

This paper addresses the issue of underestimating correlation coefficients in financial risk management by formalizing existing methods, analyzing their underestimation probabilities, and proposing a new consistent estimator with controllable underestimation risk.

Contribution

It introduces a novel correlation estimator with a fixed underestimation probability and proves its statistical consistency, improving risk estimation reliability.

Findings

Existing methods vary in underestimation probability

The new estimator maintains a constant underestimation probability

The proposed estimator is statistically consistent

Abstract

In general, underestimation of risk is something which should be avoided as far as possible. Especially in financial asset management, equity risk is typically characterized by the measure of portfolio variance, or indirectly by quantities which are derived from it. Since there is a linear dependency of the variance and the empirical correlation between asset classes, one is compelled to control or to avoid the possibility of underestimating correlation coefficients. In the present approach, we formalize common practice and classify these approaches by computing their probability of underestimation. In addition, we introduce a new estimator which is characterized by having the advantage of a constant and controllable probability of underestimation. We prove that the new estimator is statistically consistent.