VOL 68 No. 4 LEVY: PORTFOLIO EQUILIBRIUM K A C Standard deviation Standard deviation FIGURE FIGURE 2 and the riskless asset. Obviously, the in- curities'efficient sets need to be tangent vestor's welfare will decrease if no more the market line rkK. a sufficient condition than nk securities may be included in the for the market to be cleared out, in this ex- portfolio, since for a given expected return, ample, is for two out of three efficient sets he will be exposed to higher risk (see given in Figure 2(i.e, AB, BC, AC) to be Figure 1) tangent to the line rkk. In other words In the specific case in which all investors each of the three assets must be included in hold the same number of risky assets nk in some two-asset portfolio which is tangent to equilibrium, all these interior efficient sets the straight line will be tangent to the same straight line. To In the more realistic case. which will be illustrate, suppose that nk =2 for all k and dealt with below, the kth investor has the that there are n= 3 risky assets available constraint of investing in no more than nk in the market. Figure 2 shows this possibility risky assets when nk varies among investors sing A, B, and C to indicate the three risky securities Without any constraints, all investors E hold portfolio m(i.e, the market portfolio), and all efficient portfolios lie on line rmM that all investors decide to g include only two risky assets in their port- 0 folio. Investors who hold securities A and b a are faced with opportunity line rkK. If all investors decide to include two risky assets in their portfolio, this situation will represent an equilibrium situation, since no one will purchase security C(see Figure 2) Hence the price of securlty C will decline, r and its expected return will increase, until we get a new efficient curve between B and C(or C and A)which will be tangent to line rkk. In this case, however, the market may Standard deviation be cleared out. Note that not all two se- FIGURE 3 0m3303038ANVOL. 68 NO. 4 LEVY: PORTFOLIO EQUILIBRIUM 645 a) B mB /, t</A' r Standard deviation FIGURE I and the riskless asset. Obviously, the in￾vestor's welfare will decrease if no more than nk securities may be included in the portfolio, since for a given expected return, he will be exposed to higher risk (see Figure 1). In the specific case in which all investors hold the same number of risky assets nk in equilibrium, all these interior efficient sets will be tangent to the same straight line. To illustrate, suppose that nk = 2 for all k and that there are n = 3 risky assets available in the market. Figure 2 shows this possibility using A, B, and C to indicate the three risky securities. Without any constraints, all investors hold portfolio m (i.e., the market portfolio), and all efficient portfolios lie on line rmM. Now suppose that all investors decide to include only two risky assets in their port￾folio. Investors who hold securities A and B are faced with opportunity line rkK. If all investors decide to include two risky assets in their portfolio, this situation will not represent an equilibrium situation, since no one will purchase security C (see Figure 2). Hence the price of security C will decline, and its expected return will increase, until we get a new efficient curve between B and C (or C and A) which will be tangent to line rkK. In this case, however, the market may be cleared out. Note that not all two se- . J K Stand ar i V~~ r Standard deviation FIGURE 2 curities' efficient sets need to be tangent to the market line rkK. A sufficient condition for the market to be cleared out, in this ex￾ample, is for two out of three efficient sets given in Figure 2 (i.e., AB, BC, AC) to be tangent to the line rkK. In other words, each of the three assets must be included in some two-asset portfolio which is tangent to the straight line. In the more realistic case, which will be dealt with below, the kth investor has the constraint of investing in no more than nk risky assets when nk varies among investors m 4-J2 0~ r Standard deviation FIGURE 3 This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:07:38 AM All use subject to JSTOR Terms and Conditions