Isolating the Systematic Component of a Single Stock’s (or Portfolio’s) Standard Deviation

Abstract

This paper revisits the roots of modern portfolio theory and the recognition that a stock’s (or a stock portfolio’s) risk can be decomposed into a systematic component and an unsystematic component, and, further, that only the former should contribute to expected return. However, instead of isolating the systematic component of risk by recasting the risk in terms of a stock’s beta coefficient, I choose to decompose the standard deviation, or variance if one prefers the original risk measure, directly into its systematic and unsystematic components allowing one to focus on systematic risk and yet remain in the mean/standard deviation (or mean/variance) space. When the standard deviation of return is decomposed into its systematic and unsystematic components, an “adjusted CML” can be derived and it is easily shown that this adjusted CML is equivalent to Sharpe’s SML. This alternative way of looking at systematic and unsystematic risk offers easily accessible insights into the very nature of risk. This has a number of interesting implications including, but not limited to, reducing the computational complexities in calculating the relevant portion of a portfolio’s volatility, facilitating sophisticated dispersion trades, estimating risk-adjusted returns, and improving risk-adjusted performance measurement. This paper is, in part, pedagogical and, in part, an introduction to an alternative way of measuring systematic and unsystematic risk.systematic risk, unsystematic risk, capital asset pricing model, dispersion trading, risk adjusted performance measurement