Portfolio Theory and Security Investment Risk Analysis Using Coefficient of Variation: An Alternative to Mean-Variance Analysis

TL;DR

This paper introduces coefficient of variation (CV) as a direct risk measure in portfolio theory, demonstrating its correlation with stock performance and showing it outperforms traditional volatility measures in risk assessment and return maximization.

Contribution

It provides the first proof that CV is a direct risk measure and presents a new method to generate stock CV based on return, offering an alternative to mean-variance analysis.

Findings

Stock CV correlates strongly with price performance.

Low CV stocks show approximately exponential growth.

Minimizing CV leads to higher returns than minimizing volatility.

Abstract

We provided proof here that coefficient of variation (CV) is a direct measure of risk using an equation that has been derived here for the first time. We also presented a method to generate a stock CV based on return that strongly correlates with stock price performance. Consequently, we found that the price growths of stocks with low but positive CV are approximately exponential which explains our finding here that the total return of US domestic stocks within $0 \le CV \le 1$ between Dec 2008 to Dec 2018 averaged at around 475% and outperformed the average total return of stocks within $CV > 1$ and $CV > 4$ by 144% and 2000%, respectively. From these observations, we posit that minimizing portfolio CV does not only minimize risk but also maximizes return. Minimizing risk by minimizing the standard deviation of return (volatility) as espoused by the Modern Portfolio Theory only resulted in a meager average total return of 15%, and the low-risk (low volatility) portfolio outperformed the high-risk portfolio by only 25%. These observations suggest that CV is a more reliable measure of risk than volatility.