Formal Criteria for Investment Decisions

Abstract

T His paper attempts to solve certain remaining problems in the theory of optimal investment decisions. It is a formal analysis designed to clarify certain matters on which discussion has remained confused and confusing, without regard to potential practical importance. The problems to be discussed concern ambiguities and paradoxes connected with the criterion of marginal productivity or rate of return, especially in cases in which the receipts stream of an investment extends over more than two periods. The literature on this subject and present knowledge of it have been summarized by J. Hirshleifer in his recent article, which contains a definitive analysis of the two-period case.' Hirshleifer's analysis is not sufficient to solve the multiperiod case in full generality, since it does not deal adequately with multiperiod investment opportunities. However, since his analysis is applicable as far as it goes, it is useful to review his main conclusions and their direct corollaries. First, when an investment lasts for only two periods-that is, when it is entirely disinvested in the second period-its marginal productivity or rate of return is unambiguously defined. Rates of return may therefore be used to rank different possible two-period investments. Second, if unlimited borrowing and lending are possible at a given rate of interest, the investor should undertake all investments that have a positive present value at that rate of interest (that have a net product not less than that rate of interest), if all investments are independent. If there are mutually exclusive or interdependent investments, he should choose that investment portfolio that has the highest present value at the given rate of interest. In either case he should then borrow (or lend) the difference between his production plan and his consumption plan. Third, if unlimited borrowing and lending are not possible at a given rate of interest, the investor's investment and borrowing-lending opportunities can be combined into an over-all opportunity set (in a system of co-ordinates in which one axis represents first-period consumption and the other represents secondperiod consumption). He should select the point in this set that touches his highest indifference curve. In this case the ranking of investments by their productivity or rate of return is an integral part of the construction of the production-opportunity curve (in the case in which there is no borrowing or lending, this is also the over-all opportunity curve). However, the indiscriminate use of either the rate-of-return criterion or the present-value criterion, as these are ordinarily understood, for determining which investments are selected could in some cases give wrong answers. In the ranking process, mutually exclusive or interdependent investment opportunities give rise to multiple production-opportunity curves; but these have an envelope, which is the interesting curve. These last points are discussed further below. l "On the Theory of Optimal Investment Decision," Journal of Political Economy, LXVI (August, 1958), 329-52.