The Kappa Ratio generalises the Sortino Ratio by using higher-order lower partial moments — it captures tail risk beyond just variance, making it suitable for non-normal return distributions.
Kappa (n) = (Portfolio Return − MAR) ÷ LPMₙ^(1/n), where LPMₙ is the nth-order Lower Partial Moment (the average of absolute losses below MAR raised to the nth power). When n=1: Kappa 1 = Omega−1 (related to Omega Ratio). When n=2: Kappa 2 = Sortino Ratio. When n=3: Kappa 3 penalises extreme losses more heavily. Higher-order Kappa ratios are increasingly sensitive to tail events, making them particularly useful for evaluating funds with fat-tailed return distributions.
Kappa Ratio is the family of risk measures that the Sortino Ratio belongs to. Sortino uses squared downside deviations (n=2). Kappa 3 cubes the deviations — making it much more sensitive to extreme tail losses. Think of it as a progressively strict judge of fund quality: Kappa 2 (Sortino) cares about typical downside volatility; Kappa 3 is also deeply troubled by rare catastrophic events.
Sortino Ratio = Kappa 2 — uses squared lower partial moments.
Kappa 3 — uses cubed lower partial moments: extreme losses matter much more.
Higher Kappa order = more sensitive to fat tails and extreme events.
Relevant for sophisticated risk analysis of hedge funds and structured products.