Abstract
One of the most prominent mysteries of present day finance is the ample usage of such simple and dated concepts as the arithmetic and the geometric means as proxies for the aggregate price dynamics of leading international stock markets. While such undertakings may find their explanation, though not justification, in the inertia of the finance community to adopt more modern index concepts, it is even more astounding that during the last decade of the twentieth century some newly implemented stock market indexes are still constructed in the tradition of these principles.
It is known from theoretical analyses [Helmenstein and Haefke1995] that the arithmetic mean differs from the geometric mean in reflecting absolute and relative price changes of the index stocks. The two indexes may therefore offer distinct information to the investor. Building on this premise, we investigate whether the investor may profitably exploit trading signals which are solely due to different index construction principles whereas the underlying sample of index stocks is identical. If so, the choice of an index construction principle is by no means an insensitive issue, and our results have a substantial bearing for the validity of the efficient market hypothesis even in its weak form. According to a common criticism regarding the persistence of excess returns, it is a cheap and easy task to find promising trading rules and to exploit the buy and sell signals. Thus, it seems reasonable to expect that the profits will not be sustained and market efficiency in its weak form will be restored.
The set of alternatives how to exploit the information contained in the relationship between the two averages is richer, however. The efficienct market hypothesis, which has been the leading paradigm for at least two decades, finds itself on ever shakier grounds as the development of nonlinear forecasting techniques proceeds. Since White's [White1988] paper numerous empirical economists have tried to find counterexamples to the efficient market hypothesis. The NNCM workshop series [Refenes1993, Abu-Mostafa1994, Refenes1995], and the CIFEr conference (1995) provide a plethora of papers which in one way or another refute the efficient market hypothesis. Using a neural network forecast of the arithmetic and the geometric average, in the present paper we demonstrate that simulated trading of the underlying stocks yields higher cumulated returns over the out-of-sample evaluation period than a simple buy-and-hold strategy. or a 2-50 moving average trading rule.
The paper is organized as follows. Section 2 exposes the theoretical properties of the arithmetic and the geometric means. In Section 3 we investigate the time trend properties of the averages and construct the models used for forecasting. Section 4 presents the results, and Section 5 contains concluding remarks.
Keywords: Trading strategy, stock market index, neural networks, cointegration.
JEL-Classification: G14, C43, C45, C53.