770 perceptions of these probability distributions. The yield on a whole portfolio is, of course,also a random variable. The portfolio analyses mentioned earlier assume that, in his choice among all the possible portfolios, the individual is satisfied to be guided by its expected yield and its variance only. This assumption will also be made in the present paper. It is important to make precise the description of a portfolio in these terms. It is obvious(although the point is rarely made explicit)that the holdings of the various assets must be measured in some kind of units. The Markowitz analysis, for exam ple, starts by picturing the investment alternatives open to the individual as a point set in a mean-variance plane, each point representing a specific investment opportunity. The question is: to what do this expected yield and variance of yield refer? For such a diagram to make sense, they must necessarily refer to some unit common to all assets. An example of such a unit would be one dollar's worth of investment in each asset. Such a choice of units would evidently be of little use for our purposes, since we shall consider the prices of assets as variables to be deter- mined in the market. Consequently, we must select some arbitrary"physical"unit of measurement and define expected yield and variance of yield relative to this unit.If, for example, we select one share as our unit for measuring holdings of Standard Oil stock and say that the expected yield is u and the variance o2,this means expected yield and variance of yield per share; if instead we had chosen a hundred shares as our unit, the relevant expected yield and variance of yield would have been 100 4, and 10,000 a, respectively. We shall find it convenient to give an interpretation of the concept of"yield by assuming discrete market dates with intervals of one time unit. The yield to be considered on any asset on a given market date may then be thought of as the value per unit that the asset will have at the next market date(including possible accrued dividends, interest, or other emoluments). The terms "yield""and"future value"may then be used more or less interchangeably ye shall, in general, admit stochas assets. But the specification of the stochastic properties poses the problem of identification of"different"assets. It will be necessary to make the convention that two units of assets are of the same kind only if their yields will be identical. 3 This assumption is not crucial for the analysis, but simplifies it a good deal. It also seems doubtful whether the introduction of subjective probabilities would really be useful for deriving propositions about market behavior. In any case, it may be argued as borch [3, p. 439] does Whether two rational persons on the basis of the same information can arrive at different evalua- tions of the probability of a specific event, is a question of semantics. That they may act differently on the same information is well known, but this can usually be explained assuming that the two 4 Acceptance of the von Neumann-Morgenstern axioms leading to their theorem on measur- able utility), together with this assumption, implies a quadratic utility function for yield(see (4D) But such a specification is not strictly necessary for the analysis to follow, and so by the principle of Occams razor has not been introduced has content downl ued stube to sT oR ems aecondtp23013020-0 AM770 JAN MOSSIN perceptions of these probability distributions.3 The yield on a whole portfolio is, of course, also a random variable. The portfolio analyses mentioned earlier assume that, in his choice among all the possible portfolios, the individual is satisfied to be guided by its expected yield and its variance only. This assumption will also be made in the present paper.4 It is important to make precise the description of a portfolio in these terms. It is obvious (although the point is rarely made explicit) that the holdings of the various assets must be measured in some kind of units. The Markowitz analysis, for exam￾ple, starts by picturing the investment alternatives open to the individual as a point set in a mean-variance plane, each point representing a specific investment opportunity. The question is: to what do this expected yield and variance of yield refer? For such a diagram to make sense, they must necessarily refer to some unit common to all assets. An example of such a unit would be one dollar's worth of investment in each asset. Such a choice of units would evidently be of little use for our purposes, since we shall consider the prices of assets as variables to be deter￾mined in the market. Consequently, we must select some arbitrary "physical" unit of measurement and define expected yield and variance of yield relative to this unit. If, for example, we select one share as our unit for measuring holdings of Standard Oil stock and say that the expected yield is ,u and the variance a2, this means expected yield and variance of yield per share; if instead we had chosen a hundred shares as our unit, the relevant expected yield and variance of yield would have been 100 4e, and 10,000 a2. respectively. We shall find it convenient to give an interpretation of the concept of "yield" by assuming discrete market dates with intervals of one time unit. The yield to be considered on any asset on a given market date may then be thought of as the value per unit that the asset will have at the next market date (including possible accrued dividends, interest, or other emoluments). The terms "yield" and "future value" may then be used more or less interchangeably. We shall, in general, admit stochastic dependence among yields of different assets. But the specification of the stochastic properties poses the problem of identification of "different" assets. It will be necessary to make the convention that two units of assets are of the same kind only if their yields will be identical. 3 This assumption is not crucial for the analysis, but simplifies it a good deal. It also seems doubtful whether the introduction of subjective probabilities would really be useful for deriving propositions about market behavior. In any case, it may be argued, as Borch [3, p. 439] does: "Whether two rational persons on the basis of the same information can arrive at different evalua￾tions of the probability of a specific event, is a question of semantics. That they may act differently on the same information is well known, but this can usually be explained assuming that the two persons attach different utilities to the event." 4 Acceptance of the von Neumann-Morgenstern axioms (leading to their theorem on measur￾able utility), together with this assumption, implies a quadratic utility function for yield (see [4]). But such a specification is not strictly necessary for the analysis to follow, and so, by the principle of Occam's razor, has not been introduced. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:20:50 AM All use subject to JSTOR Terms and Conditions