Investigating the conditional correlations of style portfolios on the JSE

Abstract

ABSTRACT Negative market shocks can drive the standard deviation of the broader market several iterations away from its mean. During these periods, international research, mainly originating from the stock markets of the United States, has documented an increase in correlation between actively managed portfolios and the broader market index. This research found that the conditional correlation between the actively managed portfolio and the market increased more on the left-tail than the right-tail as standard deviations increased on either side. The correlations are conditional in the sense that the sample points used to calculate the correlation are only measured from the daily trading days when the portfolio and the market exhibit the same standard deviation move in the same direction. The correlation profile then measures the conditional correlation between the portfolio and the market across the standard deviation spectrum. It is a noteworthy cause to investigate portfolio conditional correlation as this will help document the reaction of the portfolio to the market for varying degrees of standard deviation moves. The reactions of each style portfolio to the market will be compared against each other. By reviewing correlation of the various style portfolios at the same standard deviation levels will help determine which portfolios are more robust under the advances and declines of the market. It is useful for portfolio design to consider whether the portfolio has a diminishing ability to withstand a market shock in times of an extreme market move caused by heightened volatility. An undesirable portfolio will have a left tail that has an increasing positive relationship between correlation and standard deviation – the bigger the market shock the more the portfolio begins to resemble the market. Equally concerning is a portfolio with a right-tail with declining correlation as standard deviation is increased - for market advances the portfolio does not closely track the market, with below satisfactory correlation. The benefit of this knowledge will have a far reaching impact on portfolio design. This study adopts style portfolios derived from stocks listed on the JSE as a proxy for actively managed portfolios. Shares are sorted into style portfolios according to size, price-to-earnings ratio, dividend yield and volume traded. Each style factor metric is ranked in ascending order and a median split allows for v the formation of sub-portfolios. To measure correlation symmetry in a tangible manner, piecewise linear regression and GARCH-M models are both considered. GARCH models can be sensitive to reduced data sets and when possible need to be fitted to a sample which incorporates an expansive data set. Hence the GARCH-M was fitted to the left and right-tails, as two complete samples, whereby the piecewise linear regression was used on the samples derived at the individual exceedance levels. The models were compared and both conclude evidence of correlation asymmetry amongst sub-portfolios. The findings concur with other international studies on conditional correlations. Over the 10-year study period, the positive tail of the high-volume sub-portfolio has the highest average correlation and tracks the market the closest for advances. For the negative tail the lowest average correlation on the downside is for the low-PE portfolio and tracks the market the least for declines.