Knowledge that Transforms

This paper examines stock market efficiency with respect to money supply data by testing (1) regression models of stock returns on monetary variables and (2) trading rules based on money supply data. The evidence indicates no meaningful lag in the effect of monetary policy on the stock market and that no profitable security trading rules using past values of the money supply exist. Therefore this evidence is consistent with the efficient market model. Current security returns incorporate all information contained in past money supply data and, in addition, appear to anticipate future changes in the money supply. A number of previous studies have concluded that lags exist and can be used in profitable trading rules. Analysis of these studies demonstrates that for a variety of reasons the evidence in these past studies does not sustain such conclusions.

The fallacy that a many-period expected-utility maximizer should maximize (a) the expected logarithm of portfolio outcomes or (b) the expected average compound return of his portfolio is now understood to rest upon a fallacious use of the Law of Large Numbers. This paper exposes a more subtle fallacy based upon a fallacious use of the Central-Limit Theorem. While the properly normalized product of independent random variables does asymptotically approach a log-normal distribution under proper assumptions, it involves a fallacious manipulation of double limits to infer from this that a maximizer of expected utility after many periods will get a useful approximation to his optimal policy by calculating an efficiency frontier based upon (a) the expected log of wealth outcomes and its variance or (b) the expected average compound return and its variance. Expected utilities calculated from the surrogate log-normal function differ systematically from the correct expected utilities calculated from the true probability distribution. A new concept of ‘initial wealth equivalent’ provides a transitive ordering of portfolios that illuminates commonly held confusions. A non-fallacious application of the log-normal limit and its associated mean-variance efficiency frontier is established for a limit where any fixed horizon period is subdivided into ever more independent sub-intervals. Strong mutual-fund Separation Theorems are then shown to be asymptotically valid.

Peer Reviewed

Presented at the American Finance Association Meeting, New York, December 1973.