In this paper we demonstrate that robust estimators improve the reliability of estimates of beta coefficients on small, thinly traded stock markets. We outline several different types of robust and bounded influence regression estimators and assess them using a jackknife methodology on data from the Johannesburg Stock Exchange. The empirical evidence confirms the hypothesis that robust estimators are more efficient than least squares estimators and indicates that least squares estimators may over-estimate systematic risk in some cases. Copyright Blackwell Publishers Ltd 1998.

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In this article we focus on beta estimation in the thinly-traded environment of the Johannesburg Stock Exchange (JSE). We build on existing literature by evaluating a beta estimation procedure known as the trade-to-trade which has not until now been considered in the context of the JSE. We contrast our results with two known estimation procedures, i.e. the Cohen et al. and the traditional ordinary least squares (OLS). The trade-to-trade methodology, the estimator proposed by Cohen et al. and OLS are objectively assessed for shares typical of the JSE on the basis of unbiasedness and efficiency in the controlled environment of a simulation study. The trade-to-trade technique is found to be superior on both counts and is recommended as the appropriate technique for beta estimation on the JSE.

This note derives analytic expressions for annuities based on a class of parametric mortality “laws” (the so-called Makeham–Beard family) that includes a logistic form that models a decelerating increase in mortality rates at the higher ages. Such models have been shown to provide a better fit to pensioner and annuitant mortality data than those that include an exponential increase. The expressions derived for evaluating single life and joint life annuities for the Makeham–Beard family of mortality laws use the Gauss hypergeometric function and Appell function of the first kind, respectively.

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