776 JAN MOSSIN lso observe that if an individual holds any risky assets at all (i. e, if he is not so averse to risk as to place everything in the riskless asset), then he holds some of every asset. (The analysis assumes, of course, that all assets are perfectly divisible. Looked at from another angle, 13)states that for any two individuals r and s, and any two risky assets j and k, we have xilxk=x/xk, i.e., the ratio between the holdings of two risky assets is the same for all individuals With these properties of equilibrium portfolios, we can return to the problem of onnegativity of the solution. With risk aversion it follows from (5) that P The sum of such positive terms must also be positive, i.e. ∑σn又2/ >0 But then also, 2, 2/Eajaia>0, so that the a' of footnote 4 is positive, which then implies z>0. Hence, negative asset holdings are ruled out Our results are not at all unreasonable. at any set of prices, it will be rational for investors to diversify. Suppose that before the exchange takes place investors generally come to the conclusion that the holdings they would prefer to have of some asset are small relative to the supply of that asset. This must mean that the price of this asset has been too high in the past. It is then only natural to expect the exchange to result in a fall in this price, and hence in an increase in desired holdings What the relations of (14)do is simply to give a precise characterization of the ultimate outcome of the equilibrating effects of the market process 5. THE MARKET LINE The somewhat diffuse concept of a"price of risk"can be made more precise and meaningful through an analysis of the rate of substitution between expected yield and risk(in equilibrium). Specification of such a rate of substitution would imply line in a mean-standard deviation plane and characterizes it by saying: In equi librium, capital asset prices have adjusted so that the investor, if he follows rational procedures(primarily diversification), is able to attain any desired point along a capital market line"(p 425). He adds that". some discussions are also consistent with a nonlinear(but monotonic)curve"(p. 425, footnote) We shall attempt to formulate these ideas in terms of our general equilibrium ystem. As we have said earlier, a relation among points in a mean-variance diagram makes sense only when the means and variances refer to some unit common to all assets,for example, a dollar's worth of investment. We therefore had to reject such has content downl ued stube to sT oR ems aecondtp23013020-0 AM776 JAN MOSSIN also observe that if an individual holds any risky assets at all (i.e., if he is not so averse to risk as to place everything in the riskless asset), then he holds some of every asset. (The analysis assumes, of course, that all assets are perfectly divisible.) Looked at from another angle, (13) states that for any two individuals r and s, and any two risky assets j and k, we have xJ/x =xJ/x', i.e., the ratio between the holdings of two risky assets is the same for all individuals. With these properties of equilibrium portfolios, we can return to the problem of nonnegativity of the solution. Withl risk aversion it follows from (5) that The sum of such positive terms must also be positive, i.e., E fa X ( q)>?- But then also, IXx/ Z >aj0xc> 0, so that the a' of footnote 4 is positive, which then implies z >0. Hence, negative asset holdings are ruled out. Our results are not at all unreasonable. At any set of prices, it will be rational for investors to diversify. Suppose that before the exchange takes place investors generally come to the conclusion that the holdings they would prefer to have of some asset are small relative to the supply of that asset. This must mean that the price of this asset has been too high in the past. It is then only natural to expect the exchange to result in a fall in this price, and hence in an increase in desired holdings. What the relations of (14) do is simply to give a precise characterization of the ultimate outcome of the equilibrating effects of the market process. 5. THE MARKET LINE The somewhat diffuse concept of a "price of risk" can be made more precise and meaningful through an analysis of the rate of substitution between expected yield and risk (in equilibrium). Specification of such a rate of substitution would imply the existence of a so-called "market curve." Sharpe illustrates a market curve as a line in a mean-standard deviation plane and characterizes it by saying: "In equi￾librium, capital asset prices have adjusted so that the investor, if he follows rational procedures (primarily diversification), is able to attain any desired point along a capital market line" (p. 425). He adds that "... some discussions are also consistent with a nonlinear (but monotonic) curve" (p. 425, footnote). We shall attempt to formulate these ideas in terms of our general equilibrium system. As we have said earlier, a relation among points in a mean-variance diagram makes sense only when the means and variances refer to some unit common to all assets, for example, a dollar's worth of investment. We therefore had to reject such 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