Perfect foresight portfolios on the Johannesburg stock exchange

Abstract

The main aim of this study was to determine the effect of unanticipated information, or noise, on the returns of cap-weighted portfolios in various segments of the JSE for the period 1995 to 2014.

According to Fuller, Han and Tung (2012), all investors in a segment would gain maximum alpha from a portfolio weighted by ex post market capitalisation – in other words, a ‘perfect foresight’ (PF) portfolio. The PF portfolio is a buy-and-hold portfolio of all shares in a particular segment with weights at the beginning of the return period set to be proportional to the market capitalisation of the shares at the end of the return period. The excess return of the PF portfolio over the benchmark portfolio therefore is an estimate of the effect of unanticipated information on the return of the benchmark portfolio. It provides an estimate of the maximum annual amount of available alpha to all investors involved in that segment in a given year. In this study, the returns of PF portfolios were compared with the All Share, Large Cap, Mid Cap and Small Cap segments of the JSE.

Intuitively, information to guide decisions on portfolio weighting would be more valuable and deliver more profit when the cross-sectional standard deviation of share returns is high. Therefore a secondary aim was to investigate the correlation between cross-sectional standard deviation and PF excess return. It was found that a strong positive correlation (more than 90%) existed between cross-sectional standard deviation and PF excess return in all segments.

In ascending order of annual PF excess return and average cross-sectional standard deviation the results for the segments were: Large Cap (8% and 29%), All Share (9% and 32%), Mid Cap (13% and 36%) and Small Cap (17% and 43%).