Knowledge that Transforms

Although investors face multiperiod decision problems, there are conditions under which the results of the one-period two-parameter model apply period by period. In addition to the assumptions made in the development of the two-parameter model itself (a perfect capital market, investor risk aversion, and normal distributions of one-period portfolio returns), the critical assumption in a multiperiod context is that, for any t, returns on portfolio assets from t−1 to t are independent of stochastic elements of the state-of-the-world at time t that affect investor tastes for given levels of wealth to be obtained at t. One such element of the state-of-the-world is the nature of investment opportunities to be available at t. For example, if the level of expected returns on investment portfolios to be available at time t is uncertain at time t−1, and if the returns from t−1 to t on some investment assets are more strongly related to the level of expected returns at t than returns on other assets, then the former assets are better vehicles for hedging against the level of expected returns at t. This can affect the demands for assets and their prices in such a way that the simple results of the one-period two-parameter model do not hold. The empirical tests of this paper reveal no evidence of measurable relationships between the returns on portfolio assets from t−1 to t and the level of expected returns to be available at t. Indeed, in our opinion there is no reliable evidence that the level of expected returns changed during the 1953–1972 period.

Much controversy surrounds the use of the portfolio investment rules induced by maximizing the expected logarithm of terminal wealth (henceforth referred to as the MEL policy). It has been thought that the MEL policy is a good approximation to the optimal investment program when the utility of terminal wealth function is bounded and when the time horizon is long. However, I exhibit a class of bounded utility of terminal wealth functions for which the MEL policy is a very poor approximation to the optimal program. Hence, the wholesale use of the MEL policy as an approximation to the optimal program is unwarranted.

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 relationship between prices of puts and calls on securities that is suggested by the theory of efficient markets is developed and empirically tested in this paper. We find that the basic model is not supported unless rather large transactions costs are included. Moreover, the transactions costs that must be assumed to make the model consistent with the data are so large as to raise troublesome questions as to whether there were unexploited profit opportunities in the options market at least during the 1967–1969 period. We also find that similar deviations from the efficient market hypothesis have shown up in related work by other researchers but that their explanations of these results appear to be incorrect on theoretical grounds or too sanguine.

Alternative sets of sufficient conditions are developed under which equilibrium security rates of return are determined as if there exist only identical individuals whose resources, beliefs, and tastes are a composite of the actual individuals in the economy. These conditions include as special cases all those previously examined in the literature (including conditions sufficient to produce the two-parameter mean-variance model), as well as others. Whenever such a composite individual exists it is shown that (1) valuation equations take a specific form and contain only exogenous parameters of the economy; (2) market exchange arrangements are Pareto-optimal; and (3) competitive value-maximizing firms make completely specified Pareto-optimal production decisions both over dates and states. These results rely on the observation that under popular homogeneity assumptions regarding beliefs and tastes, even though the securities market may be incomplete, equilibrium rates of return are determined as if there were an otherwise similar Arrow-Debreu economy.

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.

Security market regulators, among others, are concerned to know whether or not dealers are natural monopolists. Based on a randomly drawn sample of 314 over-the-counter stocks, the results of this study suggest that while there are economies of scale, they are not on the dealer level. In addition, both systematic and unsystematic risk were tested for association with the transaction costs in this market. The evidence suggests unsystematic risk is related to spread.

This study examines the market for acquisitions and the impact of mergers on the returns to the stockholders of the constituent firms. While employing the two-factor market model as recently developed and applied by Black-Jensen-Scholes and Fama-MacBeth, this study also considers changes in risk in analyzing the impact of mergers on stock prices. The results of the study are consistent with the hypothesis that the market for acquisitions is perfectly competitive and with the hypothesis that information regarding mergers is efficiently incorporated in the stock prices. Stockholders of acquiring firms seem to earn normal returns from mergers as from other investment-production activities with commensurate risk levels. Stockholders of acquired firms earn abnormal returns of approximately 14%, on the average, in the seven months preceding the merger.