Knowledge that Transforms

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.

This paper develops general overtaking techniques for studying the asymptotic properties of portfolio policies optimal with respect to a terminal utility valuation. For a restricted class of utility functions the sequence of optimal constant (non-revised) portfolio policies formed as the horizon recedes into the future is shown to converge. Furthermore, for utility functions unbounded above and below, this turnpike policy need not be the policy associated with the minimal constant relative risk aversion function that bounds the valuation function from above. Finally, an analogy between the portfolio turnpike problem and the turnpike problem of growth theory is studied.

This paper outlines models of capital market equilibrium when there are explicit barriers to international investment in the form of a tax on holdings of assets in one country by residents of another country. There is a corresponding subsidy on short positions in foreign assets. Asset prices deviate from the predictions of the world capital asset pricing model. Investors do not hold a mixture of national market portfolios, but the mix of risky assets is the same for every investor in a country. Optimal portfolios tend to be heavy in domestic assets, and light in foreign assets. Tax free investors, however, tend to hold assets anywhere in the world that are taxed heavily. Estimates of the magnitude of the average tax (or the magnitude of effective barriers to international investment) can be made by comparing the average return on the minimum variance zero β portfolio, z, with the average across countries and time of the short-term interest rate. When barriers are ineffective, the expected return on portfolio z will be the average short-term interest rate, and the world capital asset pricing model will hold.

This paper presents some of the implications of modern portfolio theory for the equilibrium structure of wages under conditions of uncertainty. The primary model presented is a model of wage uncertainty and hence the equilibrium structure is derived in terms of expected wages. The equilibrium structure with the assumption of a perfect labor market (e.g., labor units are infinitely divisible and costlessly mobile) and a perfect capital market is shown to have a very simple linear form. The model assumes homogeneous labor units as well as the usual single-period capital asset pricing model assumptions.

This paper suggests that it is not possible to demonstrate, using the best available empirical methods, that the expected returns on high yield common stocks differ from the expected returns on low yield common stocks either before or after taxes. A taxable investor who concentrates his portfolio in low yield securities cannot tell from the data whether he is increasing or decreasing his expected after-tax return by so doing. A tax exempt investor who concentrates his portfolio in high yield securities cannot tell from the data whether he is increasing or decreasing his expected return. We argue that the best method for testing the effects of dividend policy on stock prices is to test the effects of dividend yield on stock returns. Thus the fact that we cannot tell, using the best available methods, what effects dividend yield has on stock returns implies that we cannot tell what effect, if any, a change in dividend policy will have on a corporation's stock price.

This paper considers the problem of the investor who has numerous opportunities for revising his portfolio and whose choices are governed by a utility function defined on ‘terminal’ wealth, U0(x0). Attention is focussed on the behavior of the induced utility functions of intermediate wealth with n periods to go, Un(xn), and the associated investment policies. Conditions under which the functions Un(xn) will tend to isoelasticity have previously been given by Mossin and by Leland. In this paper, the conditions for convergence are weakened further, to the point where they appear sufficiently broad to encompass perhaps most utility functions of practical interest.