In a recently published study in this JOURNAL, Dimson and Fraletti (I986) examined in detail the performance of stocks recommended by a leading broker. They concluded that they 'were unable to detect any significant abnormal performance by the recommended stocks'. Their study of the investment performance of an individual broker was a follow-up study to an earlier investigation (Dimson and Marsh, I984) into the forecasting skills of different financial advisers. What is surprising is that the earlier study had revealed statistically significant evidence of superior forecasting skills by some brokers. In contrast, in this follow-up study, when Dimson and Fraletti investigated, in detail, recommendations made by a broker with above average forecasting skills, they failed to find evidence that this superior forecasting skill resulted in superior investment performance. In this paper it will be argued that, with the sample sizes available to Dimson and Fraletti, then at all plausible levels of the broker's forecasting ability, a rejection of the hypothesis of superior investment performance was almost inevitable. The failure to detect abnormal performance in this case is illustrative of a more general problem with statistical tests of market efficiency. Stock markets are characterised by wide fluctuations in returns relative to the mean return. This results in the power of many statistical tests of market efficiency being weak. A natural consequence is that the statistical evidence is frequently insufficient to reject the null hypothesis that the market is efficient. Thus, when Summers (I986) and Poterba and Summers (I987) re-examined some of the standard tests of weak form efficiency, they concluded that the power of such tests was so weak that unavailably large sample sizes would be required to produce statistically significant positive findings. A similar conclusion would appear to apply to some studies of semi-strong and strong market efficiency. Ashton (I985) re-examined the data used by Jensen (I968) in his study of the performance of mutual fund managers. He concluded that the problem with the study did not arise so much from a misspecification of the null hypothesis, Dybvig and Ross (I985), but rather from the lack of power of the statistical test used. In his analysis oftheJensen study, Ashton (I985) was concerned with the detection of fund managers' ability to time the general rises and falls in the market. In contrast, the Dimson and Fraletti study is concerned with the ability of brokers to select securities which will perform well relative to the market and the analysis just cited does not apply. In this paper, a theoretical model of brokers' forecasts is developed, which enables brokers to identify those shares which will outperform a general market portfolio. This model is then used to derive the expected value and variance of
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