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Abstract
Although the equity investment horizon required to optimise the probability of realising specific returns is of significant interest to investors, little research has been published globally in this regard. In this paper we, for the first time, use reverse statistics to derive probability distributions of the times required to achieve specific levels of returns on the JSE. Specifically, we consider the total returns of the All Share Index (ALSI) for the period 1995 to 2012. We show that for matched pair target returns ranging from ±2% to ±8%, the maximum probability of the negative return on a timeline lies to the left of the maximum probability of the equivalent positive return. This gain-loss asymmetry is similar to that previously found for developed markets (e.g. for the Dow Jones Index), but opposite to that found for indices in Eastern Europe. Given that previous researchers ascribed this difference to a developed vs. emerging market dichotomy, this may indicate that the JSE more closely resembles developed than emerging equity markets. In addition, our probability distributions for the times required to achieve both specific positive and negative total returns should assist investors on the JSE to better plan their investment strategies.
Notes
1 See, for example, CitationStrugnell, Gilbert & Kruger (2011) and CitationVan Rensburg & Robertson (2003)
2 See for example, CitationVan Rensburg (1999), CitationVan Rensburg & Robertson (2003), and CitationAuret & Sinclaire (2006)
3 See for example, CitationJensen (1999)
4 See CitationSimonsen et al., 2002; CitationJensen et al., 2003A; CitationJensen et al., 2003B; CitationDonangelo, Jensen & Simonsen, 2006; CitationJohansen et al., 2006, CitationSimonsen et al., 2007, CitationSiven & Lins, 2009, and CitationBalogh, Simonsen, Nagy & Néda, 2010.
5 In addition to these studies, inverse statistics have also been applied to the intraday trading of the Deutsche Mark against the US dollar (see CitationJensen, Johansen, Petroni & Simonsen, 2004), and in an attempt to formulate a mathematical law to explain the inverse statistial behaviour of 40 equity indices across the world (CitationZhou & Yuan, 2005). The latter study is the only inverse statistical study to date which have included the JSE.
6 The researchers do this in order to remove the upward drift or trend in the index.
7 This argument is of course more relevant for equity markets with a relatively high dividend yield, such as the JSE.