Abstract

One of the most important developments in modern investment theory is the market hypothesis. Market efficiency refers to the speed with which information is rationally absorbed. Thus, statements about market efficiency are always made with respect to a particular set of information. Three information sets with respect to which the market mayor may not be have been defined, resulting in the weak, semi-strong, and strong form market hypothesis. Weak form efficiency refers to efficiency with respect to past prices, semi-strong form to all publicly available information, and strong form to all available information, public or private. All three forms of the market hypothesis have been tested by researchers. For an excellent review see Fama [5]. Only the weak-form hypothesis is of concern in this paper. The study compares the performance of the market portfolio with those of portfolios that are mean-beta on the basis of historical means and betas. The tests are important because they have implications for both the multi-security weak-form market hypothesis and the construction of portfolios. It is unfortunate that the word efficient is used to convey very different concepts in portfolio theory and the market hypothesis. What is even more ironic is that the two concepts are actually contradictory. If the market is truly efficient, it does not matter if portfolios are derived with historical return and risk measures, historical measures adjusted for other publicly or privately available information, or completely subjective measures. The portfolios cannot be expected to consistently earn returns superior to that yielded by the market portfolio. On the other hand, if any of these portfolios can earn consistently superior returns, then the market cannot be efficient. Although this paradox has not been addressed directly before, studies by Cohen and Pogue [3] and Frankfurter [8] do contain some relevant results. Cohen and Pogue found that portfolios outperformed random portfolios of 50 securities. Frankfurter, on the other hand, found portfolios to perform only as well as the market portfolio. Since Evans and Archer [4] have shown that random porfolios of the size used by Cohen and Pogue are essentially equivalent to the market portfolio, the two sets of results are contradictory. A problem with the results is that the tests were both conducted on a very limited number of securities and for only one time period. For example, although Frankfurter utilized a sample of 522 stocks to construct his portfolios, he selected only one portfolio for comparison with the market portfolio, the portfolio being one with the risk equal to that of the market portfolio. When the portfolio was found to be insignificantly different from the market portfolio, the conclusion was drawn that the portfolios only perform as well as the market portfolio. It should be remembered, of course, that the main purpose of

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