A portfolio frontier superior to the Markowitz one-period buy-and hold efficient frontier does exist. Such a superior frontier can be generated by pursuing a rebalancing policy, even under the conditions of random walk. By rebalancing we mean that an investor maintains a fixed but optimal set of weights among the securities in a portfolio throughout an investment period by buying and selling securities at the end of some predetermined intervals.

Tp wo forces, relatively unimportant several decades ago, have influenced the destiny of the consumer dollar in the years following the Second World War. The first of those forces is the growth of installment and mortgage credit relative to disposable income, and the second is the growth of contractual savings relative to the total amount of personal saving. It is argued in this paper that these two forces, even though stabilizing contractual savings and payments, have altered the pattern of nondurable goods consumption in certain undesirable ways. Since the end of World War II, the phenomenal rise in installment and mortgage credit and its possible de-stabilizing effect on the economy has been a subject of much discussion among economists. But in this paper, our attention is mainly directed to the neglected aspect of how durable goods financing has affected, surreptitiously, the consumption expenditures for nondurable goods and services and how the change may adversely affect the stability of the economy. The change is measured in this paper by comparing two periods the most recent decade, that is, the fifties, and the twenties, a decade selected for statistical convenience as well as for cyclical comparability. The relative importance of these two forces in the two periods and appropriate analytical framework are presented in Section I; the results of empirical investigations and tests are summarized in Section II; and policy implications are examined in Section III.

In our 1980 paper we tested the joint hypothesis that prices are determined by the mean-variance (MV) capital asset pricing model (CAPM) and that beliefs are stationary. By focusing on the Invariance Law of Prices we avoided the questionable practice of estimating ex ante expectations with ex post returns. Moreover, we circumvented the need to identify the true market portfolio and hence avoided the ambiguity, noted by Richard Roll (1977), in the traditional security market line (SML) tests of the same joint hypothesis. However, Stuart Turnbull and Ralph Winter (T-W) and Richard Sweeney point to a further inconsistency in the joint hypothesis, that they believe can be removed by relaxing the stationarity assumption. This new concern is fundamental in that it applies to all empirical tests which assume stationarity of the return distribution, whether they are simply tests of the CAPM or tests employing the CAPM. The concern would apply a fortiori to tests that assume stationary betas as well. Both comments also suggest that the ad hoc addition of a random error term to our Invariance Law equation and the subsequent statistical tests of it are unnecessary. We first address these two criticisms and then address some further criticisms raised separately by T-W and Sweeney.