Johnson-Omega performance measure

The financial crisis culminating in the Lehman Brothers collapse in September 2008 was a revealing stress test for mathematical methods in finance. Due to disastrous breakdowns and experiences, managers returned to simplistic models such as minimum variance or equally weighted portfolios, despite the fact that these ignore certain important stylised facts of financial time series, eg, trends, asymmetry and tail fatness (DeMiguel, Garlappi & Uppal 2009). In addition, mean-variance restricted performance measures and methodologies still enjoy great popularity. For more than a decade, however, efforts have been made to include higher moments for portfolio construction. The multiple objective approach includes skewness and kurtosis in the optimisation and – similarly to conditional value-at-risk and expected tail loss – is sensitive to parameters, which need to be chosen arbitrarily (Davies, Kat&Lu 2009; Krokhmal, Palmquist & Uryasev 2002).

CLICK HERE TO VIEW THE PDF

The Omega measure intuitively accounts for the entire distribution (Keating & Shadwick 2002). Sharpe-Omega relates to the familiar Sharpe ratio by replacing the volatility with a put price, a widely accepted measure of risk in practice (Kazemi, Schneeweis & Gupta 2003. The Omega function allows assets to be ranked with respect to varying thresholds (Cascon, Keating & Shadwick 2004). Discrete empirical Omega optimisation, however, faces numerical challenges due to the insufficiency of the underlying empirical distribution and the fact that it implicitly accounts for ‘noise' in data and unstable moments (Kapsos et al 2011; Mauser, Saunders & Seco 2006).