Sortino, Omega, Kappa: The Algebra of Financial Asymmetry

James Ming Chen
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James Ming Chen: Michigan State University

Chapter Chapter 6 in Postmodern Portfolio Theory, 2016, pp 79-105 from Palgrave Macmillan

Abstract: Abstract This chapter traces the development of entire families of downside risk measures from partial statistical moments. The Sortino, omega, and kappa ratios provide credible, workable single-factor measures of financial dispersion below mean return. At a minimum, specifying these ratios provides a useful contrast with conventional, two-tailed measures such as the Sharpe and Treynor ratios. Because it is based on downside semideviation, the square root of the lower partial second moment, the Sortino ratio is particularly easy to reconcile with the more traditional and more familiar tools of modern portfolio theory. Indeed, closer examination of the Sortino ratio reveals Pythagorean relationships between single-sided risk measures and their counterparts within the conventional capital asset pricing model (CAPM). These relationships allow single-sided measures of volatility to be evaluated with trigonometric tools.

Keywords: Risk Measure; Supra Note; Sharpe Ratio; Capital Asset Price Model; Downside Risk (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:pal:qpochp:978-1-137-54464-3_6

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DOI: 10.1057/978-1-137-54464-3_6

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