If a portfolio manager who cannot count finds a four-leaf clover, is he still lucky?

Abstract

This paper examines a poignant but essentially generic problem that plagues the world of financial analysis—the extent to which visual or analytical interpretation of relationships between accumulating (and therefore auto-correlated or serially dependent) series—are demonstrably fallacious by means of standard statistical techniques that assume stationarity. The problem, despite being age-old, continues to be ignored by an appreciable proportion of tertiary educated financial professionals the world over, and is imputed to contribute, in no small part, to broad market inefficiency. The problem persists from high-frequency pairs- trading strategies in hedge funds through to top-down macro-economic inferences by institutional strategists. We examine the mechanism for the error in accessible non-mathematical prose, and demonstrate by way of several common examples how easily well-used inferences fall foul of the requisite statistical rigour and correct interpretation. We further note that there is a well developed, although less frequently utilised, suite of econometric tools, termed cointegration, that considers relationships between two or more non-stationary price series. Cointegration techniques are cast at the unit of the non-stationary price series, rather than the unit of the stationary differences.