In this study we investigate the common firm-specific factors associated with shares that experience extreme monthly performance on the Johannesburg Securities Exchange.



The Optimal Portfolio Leverage Ratio provides the level of leverage to use to attain the highest expected long-term terminal value of an investment and is calculated independently of investors’ indifference curves. This article applies a discrete multi-period compounding framework to both discrete and continuous cross-sectional pay-off distributions. In both cases, an Optimal Portfolio Leverage Ratio is derived from first principles and in the case of the latter, a multi-asset solution is also presented. The primary implications for equilibrium asset pricing are considered and a multi-period analogue to the CAPM is derived. This version of the CAPM is to be tested as a joint hypothesis with a specified Optimal Growth Portfolio.

Journal of Asset Management advance online publication, 3 December 2015; doi:10.1057/jam.2015.36

Keywords: multi-period portfolio construction; Kelly rule; optimal portfolio leverage ratio; growth optimal asset pricing


Abstract: Recent investigations of the Sharpe (1964), Lintner (1965), Mossin (1966), and Black (1972) Capital Asset Pricing Model (CAPM) have identified numerous inconsistencies with the model’s predictions. A number of variables have displayed evidence of the ability to explain the cross-sectional variation in share returns beyond that explained by beta. This study sets out to ascertain the identity of these firm-specific characteristics over the period June 1994–May 2004 for members of the Australian Stock Exchange (ASX) All Ordinaries stock index. A data set including 207 firm-specific attributes is created for stocks in the sample and, with over 4.85 million observations, this is the largest set yet assembled for a study on the ASX. Using the Fama and Macbeth (1973) cross-sectional regression approach, attributes are tested for the ability to explain the cross-sectional variation in ASX share returns beyond that explained by the CAPM and a principal components-derived APT model. Similar significant characteristics are found when unadjusted and both sets of risk-adjusted returns are examined. The set of significant characteristics derived from the unadjusted returns test is then simplified using correlation analysis and an agglomerative hierarchical clustering algorithm, resulting in a list of 27 variables that are not highly correlated with each other. The existence of anomalies found in prior Australian literature (size, price-per-share, M/B, cashflow-to-price, and short- to medium-term momentum) is confirmed. As these previously documented anomalies only comprise five of the final simplified list of 27 significant characteristics, this paper identifies 22 previously undocumented Australian anomalies. The 27 significant style characteristics are then used to construct a multifactor model that comprises a set of factors that are simultaneously statistically significant when cross-sectionally regressed on share returns. A five-factor characteristic-based model for the ASX is empirically derived, which comprises (1) prior 12-month return, (2) book-to-market value, (3) two-year percentage change in dividends paid, (4) cashflow-to-price, and (5) two-year percentage change in market-to-book value as explanatory variables.

Abstract: This paper investigates whether the analysts‟ consensus recommendations from South African brokerage houses were of value to investors over the period from March 2000 to April 2003. If an investor strictly follows analysts‟ consensus recommendations of shares listed on the JSE, only the buy recommendations result in a significant alpha, estimated under a two-factor APT model of 0.99% over a one-month holding period. The hold and sell recommendations produce insignificant results under all performance measures. The implication for the potential investors in the stock exchange is not to base their investment decisions solely on the level of analysts‟ consensus recommendations. Several investment strategies designed to take advantage of changes in or recurrences of analysts‟ consensus recommendations are investigated and they show considerably more promise. If an investor acts on the recurrences (reiterations of a firm‟s recommendation over two successive months) of hold and buy recommendations, positive two factor APT alphas of 2.47% and 3.74% respectively are earned over a three-month holding period. A high positive APT alpha is earned by holding shares for three months that reappear as a buy recommendation after previously being dropped from coverage. Shares that have reappeared as a sell recommendation earn a significant market-adjusted return of –14.58% for a one-month holding period. Both of the latter findings are based on small sample sizes. Surprisingly, the recurrences of sell recommendations yield significantly positive abnormal returns over a three-month holding period. Shares for which a sell recommendation is discontinued, earn a significant positive alpha of 13.57% for a one-month holding period. Also, shares that are covered for the first time by analysts and appear as a buy recommendation yield a significant market-adjusted return over a two-month holding period of –8.05%. However, it should be noted that the above findings are also based on a very small sample. It is found that an investor generally earns significantly higher returns by acting on downgrades instead of strictly following the level of South African stock-broking firms‟ analysts‟ consensus buy, hold and sell recommendations. Over a two-month holding period, shares with a change from a hold to a sell recommendation achieve an abnormal return of –10.72%. In addition, shares with a change from a buy to a hold recommendation also earn negative market-adjusted and abnormal returns over one and two-month holding periods.

Abstract: The investigation of the accuracy of security analysts’; earnings forecasts of firms listed on the JSE demonstrates that analysts display a pattern of increasing accuracy as the announcement date approaches. A declining trend in the level of error, using both the average absolute percentage error and Theil‟s inequality coefficient methods, is observed. A 1-month forecast horizon displays a 7,95% of average absolute percentage error and 0,07 Theil‟s inequality coefficient, while a 6-month horizon results in 16,66% average absolute percentage error and 0.1 Theil’s inequality coefficient. The 12-month horizon depicts a 23,62% of average absolute percentage error and 0,17 Theil’s inequality coefficient. This result is consistent with findings of prior international research.

Abstract: This study extends the analysis of Daniel and Titman (1997) and Daniel, Titman and Wei (2001) to the Johannesburg Securities Exchange (JSE) and reconsiders the theoretical interpretation of this branch of research. The empirical results, which are also presented graphically, are consistent with the interpretation that the asset pricing relationship on the JSE is better specified using attribute values rather than factor loadings. The theoretical reconsideration points out that this finding is insufficient to distinguish between a risk-based and non-risk-based explanation of the cross-section of returns as has been ‘debated’ in previous research. More precisely, it performs the task of identifying the form of the more appropriate form of asset pricing model specification.

Abstract: Using a technique similar to Fama and French (1992), simulated portfolios are constructed in each month from July 1990 to June 2000 by ranking stocks on their market capitalisation, price-to-earnings rations and betas. The selection of these factors is based on a prior exploratory study (van Rensburg and Robertson, 2003). It is found that the size and price-to-earnings effects are not proxies for the underlying influence of beta. Using two way sorts it is found that these effects also operate independently of each other. A mild negative relation is found between beta and the cross section of returns! The results of this study present a strong challenge to covariance based models of asset pricing on the JSE.

Abstract: Given the reclassification of the Johannesburg Stock Exchange (JSE) sector indices that occurred in March 2000, this paper updates the factor analytic procedure conducted by van Rensburg and Slaney (1997). It is found that the new Financial-Industrial (CI21) and Resources (CI11) indices may be used as observable proxies for the first two principal components extracted from the covariance matrix of JSE returns. Consequently, it is suggested that these indices replace the Industrial and All-Gold index in future applications of the two factor arbitrage pricing theory (APT) model. Prior research is extended by considering the implications of the dichotomy in the return generating processes underlying JSE financial-industrial and resource stocks for the estimation of security betas. It is mathematically demonstrated that this dichotomy implies that the cross-sectional correlation matrix of the market model’s residual errors is not diagonal. As a result, conventionally conducted market model regressions are characterised by the problem of omitted variable bias and downwardly biased t statistics. A remedial procedure is proposed, which may serve as a general correction for omitted variable bias in ordinary least squares regression analysis when using panel data. Finally, it is pointed out that the All-Share Index, conventionally employed as the market proxy in South African beta estimation, is not mean-variance efficient given the opportunity for offshore investment. This implies that the capital asset pricing model, as conventionally specified by South African academics does not hold on the JSE.

Abstract: This study investigates whether style characteristics exhibit different properties across the major JSE industry sectors. Using monthly data on a broad sample of non-thinly traded JSE shares over the period July 1990 to June 2000, it is observed that a large proportion of financial ratios exhibit right skewness that is related to a lower bound of zero on their values. Financial ratios that incorporate levels of debt are markedly higher in the financial sector. It is argued that, as deposit-taking institutions, the market interprets leverage differently for these companies. Stock returns are regressed cross-sectionally on lagged style characteristics in each month using a dummy variable to indicate sector membership. The results show that, to varying degrees, small size and several interrelated measures of „value‟ exhibit a positive relationship with equity returns within all industry sectors. However, the value effects tend to be stronger in the financial and industrial sectors than in the resource sector. In contrast to the other sectors, financial stock returns are positively rewarded for high debt-to-equity ratios. Notwithstanding the above, it is concluded that, a size and price-earnings style-based model of expected returns is broadly representative of the entire JSE Securities Exchange.

Abstract: While it is evident that market concentration on the JSE is largely responsible for much of the inefficiencies of existing equity benchmarks, liquidity also plays an increasingly important role in the determination of fund holdings as the fund’s size increases. Funds wishing to reduce concentration in their benchmark portfolios by spreading their holdings more equitably will find themselves hampered in their efforts by the need to keep holdings at levels which enable smooth entry into and exit from less liquid shares. This imposes a cap on the weights that can be attributed to shares at the tail end of the index and forces an increase in holdings in the more liquid shares at the top of the index. Given that most of these liquid, large cap shares on the exchange are resources shares, it is unsurprising that a marked shift from Financial-Industrials to Resources shares is found for optimal benchmarks as fund size increases. It is also found that, as fund size increases, the degree of deviation fund managers can take from these optimal benchmarks decreases significantly. It is noted that the constraints imposed on benchmarks by the new unit trust regulations have little impact on the results and were not violated at any stage of the optimisation. In contrast, pension fund regulations were violated prior to the maximum viable fund size indicating the limitations the proposed regulations impose on the holdings of large pension fund managers. Given the deficiencies observed in existing equity benchmarks, the methodology adopted in this paper attempts to optimise the interplay between (i) concentration, (ii) liquidity, (iii) fund size and (iv) regulatory constraints in their construction. While the specific analysis was conducted in the context of the practical issues that came to the fore with the 24 June 2002 introduction of the new FTSE/JSE Africa index series, the methodology introduced in this paper is capable of contributing to the explicit construction of more efficient benchmarks in the future.

PAIA Manual