THE DEMAND FOR ASSETS UNDER CONDITIONS OF RISK: REPLY

Abstract

IN HIS COMMENT Professor Aivazian claims that one cannot derive the demand for assets unless one incorporates the investor's preferences in the analysis. This is, obviously, a correct assertion, and one can readily see that indifference curves play a central role in my graphical exposition. While it is true that there is no transparent link between my mathematical analysis and my graphical demonstration I take this opportunity to clarify several points which misled Professor Aivazian and may mislead other readers. Equation (9), a key equation in my paper, is mathematically valid and can be interpreted in either of the following two ways: I. If u in my equation (3) denotes the market expected return, then p9 is identical for all investors independent of their preferences. In this case Xi (see my equation (9)) is the proportional demand for asset i, that is to say, the amount of money invested in the ith asset divided by the total amount of money invested in all risky assets. Clearly, to derive the proportional demand one does not need the knowledge of indifference curves. II. Alternatively, if u in equation (3) is taken to be the portfolio expected return chosen by the particular investor under consideration, then Xi is the demand for the ith asset in absolute value. Please notice that in this case one does not need the second maximization step (the inclusion of the investor's preferences) since the investor's indifference curves are taken into account by the information that a particular mean u has been chosen. Obviously, in this case p1 is a function of his choice and represents the investor's preference. In such an analysis we determine not only the efficiency locus, but also the exact point on this locus, i.e., the optimal (u,a2) combination for this particular investor. If one repeats the analysis for another value u (see my equation (3)), one obtains another point on the efficiency locus which represents the preferences of another investor. Professor Aivazian is correct in claiming that my mathematical definition of the income and substitution effects are not the classical definitions of consumer demand theory. (He could see my comment on this point on page 86.) To be more specific in deriving the substitution effect I hold EW1 and a2( WI) constant. This of course -implies that U(EWI, a2(W1)) is held constant. However, my definition of the substitution effect is too restrictive since U can be held constant by changing EW1 and a2(W1) simultaneously. Professor Aivazian claims that the mathematical treatment of income and substitution effect in my paper is incorrect since deriving the substitution effect I do not hold expected wealth and variance as constants. Though I did not show explicitly that I hold EW1 and a2(W1) constant, they were actually treated as