Double- and Single-Sided Risk Measures

Abstract

Traditional measures of volatility, variance, and beta assign equal weight to the upside and downside components of these measures of systematic risk. Such symmetry reflects neither actual market conditions nor investors’ behavioral reactions to abnormal financial events. Single-sided versions of all of these measures better reflect the state of markets and their likely interpretation by investors on either side of mean returns. As a bonus, single-sided volatility is related to the traditional double-sided volatility through the Pythagorean theorem. That relationship facilitates the application of trigonometry to mathematical finance.