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Sortino, Omega, Kappa: The Algebra of Financial Asymmetry

In: Postmodern Portfolio Theory

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  • James Ming Chen

    (Michigan State University)

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.

Suggested Citation

  • James Ming Chen, 2016. "Sortino, Omega, Kappa: The Algebra of Financial Asymmetry," Quantitative Perspectives on Behavioral Economics and Finance, in: Postmodern Portfolio Theory, chapter 0, pages 79-105, Palgrave Macmillan.
    • Handle: RePEc:pal:qpochp:978-1-137-54464-3_6
    DOI: 10.1057/978-1-137-54464-3_6
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