The mean variance efficiency of the JSE all share index (ALSI) and it's implications for portfolio management.

Abstract

The use of proxies in the CAPM model to determine assets expected return has implications for portfolio management. An inefficient proxy can result in the lowering of beta estimates due to a weak regression relationship resulting in the misallocation of capital. For the CAPM equation to be satisfied would require that the proxy should at least have an alpha that centred on zero over a period of time. This would allow the linearity of the model to hold and we would advocate a passive portfolio strategy. If the proxy were mean variance inefficient would indicate that alpha values are present in asset returns that can allow us to rebalance portfolios using optimisation techniques. We test the hypothesis that alpha averages around zero using the market model by regressing Industrial and Gold index excess returns on the market premium. When tested from the SA investor perspective we find that the alpha of the ALSI regression is not zero for the Gold Index but centred on zero for the Industrial Index. The implications are that SA investors would get a fair return holding the ALSI index instead of trade in industrial shares. The result warrants a passive strategy. However, portfolio optimisation demonstrates that a higher return can be achieved by rebalancing the portfolio The regression using the Gold index produced a negative alpha implying that investors should actively sell Gold shares from their portfolios. The ALSI was not an adequate proxy of risk to the SA investor for gold shares. Overall the ALSI is inefficient since it has a nonlinear relationship to one sector of the lSE. Portfolio analysis and rebalancing is required to attain an optimal return. The Markowitz model recommends that all SA investment capital should be fully weighted in the Industrial index only. Introducing an international investment proxied by the Dow Jones significantly improved the returns to SA investors. This is evident in the improved Sharpe ratio achieved by the rand adjusted Dow Jones available to the SA investor. In the absence of exchange restrictions the model recommends that 87% of local investors assets should be moved abroad under the present investment conditions. When tested from the US investor's perspective using dollar returns the data estimates achieved from the regression analysis were: The alpha value of the Industrial index is non-zero and the Gold index alpha centres on zero. The results are a reversal of the Rand tests of the SA investor. Gold shares priced fairly in dollar terms as opposed to Industrial shares. Currency effects of Rand depreciation priced into the dollar return of Industrial shares led to their non-participation in the US investors' portfolio. Due to trade of gold in dollars, the gold shares were priced to provide a fair return to the dollar-adjusted ALSI as opposed to the rand denominated test. Overall, the ALSI was inefficient due to the Industrial sector pricing in dollars resulting in abnormal alpha values over time. Currency depreciation resulted in the distortion ofthe CAPM relationship between the INDI and ALSI. The US investor's domestic index, the Dow Jones was found to lie on the efficiency frontier for tests using the ALSI and the INDI. There was no reason to invest in SA, but if the US investor did chose to invest in SA shares then gold had the lowest beta and the lowest correlation to the Dow Jones. The beta values of the SA indices were all significant and the alpha values were negative when regressed against the Dow Jones. The implication of this would be to invest as much as possible in the international index portfolio as possible. Regression Statistics ALSIXS I:\DIXS GOLDIXS P-values ntercept a 1.18E-05 0.001992 1.51 E-OS DOWJONES 9.87E-15 1.32E-11 5.27E-05. Coefficients intercept a -0.09833 -0.07281 -0.15206 DOWJONES 1.082276 0.985812 0.831916. The Dow Jones introduces a significant diversification benefit to the SA investor's portfolio by increasing returns significantly per unit of risk. The Markowitz model recommends that 87% of SA investor's portfolio should be in the Dow Jones and 13% in the Industrial index. Due to independent pricing of the gold and industrial sectors, the former by international markets in dollars and the latter in rands in SA, a dichotomy is created in the local market. From an SA investor's point of view the CAPM would not capture the correct return of gold shares. It would overstate the expected return since beta of the SA market premium will not include dollar returns. The ALSI is an incorrect proxy for the SA investor analysing gold shares. The Gold sector is only correctly priced from the US investor's perspective once the ALSI is dollar adjusted. The industrial index can use CAPM analysis reliably with the ALSI as market proxy but higher returns are achievable through portfolio rebalancing. Active portfolio management is recommended. Nevertheless, this will not produce results significantly different to the CAPM once standard errors of the mean are accounted for. The results found currency depreciation of the Rand as a major factor contributing to the exodus of SA capital. The dollar had an expected mean return of 12,6% p.a. This substantially increased the rand adjusted Sharpe ratio of the international portfolio compared to its dollar return. The increased Sharpe ratio of the rand denominated international portfolio resulted in a substantial shift of the optimal portfolios weighting away from the domestic portfolio and towards the Dow Jones. International investors optimal portfolios were similarly impeded due to the depreciating currency.