Capital Asset Prices 433 from X to are dominated by some combination of investment in and lending at the pure interest rate. Consider next the possibility of borrowing.If the investor can borrow at the pure rate of interest,this is equivalent to disinvesting in P.The effect of borrowing to purchase more of any given investment than is possible with the given amount of wealth can be found simply by letting a take on negative values in the equations derived for the case of lending. This will obviously give points lying along the extension of line PA if borrowing is used to purchase more of A;points lying along the extension of PB if the funds are used to purchase B,etc. As in the case of lending,however,one investment plan will dominate all others when borrowing is possible.When the rate at which funds can be borrowed equals the lending rate,this plan will be the same one which is dominant if lending is to take place.Under these conditions,the invest- ment opportunity curve becomes a line (PZ in Figure 4).Moreover, if the original investment opportunity curve is not linear at point,the process of investment choice can be dichotomized as follows:first select the (unique)optimum combination of risky assets (point )and second borrow or lend to obtain the particular point on PZ at which an indiffer- ence curve is tangent to the line.15 Before proceeding with the analysis,it may be useful to consider alter- native assumptions under which only a combination of assets lying at the point of tangency between the original investment opportunity curve and a ray from P can be efficient.Even if borrowing is impossible,the investor will choose(and lending)if his risk-aversion leads him to a point below on the line P.Since a large number of investors choose to place some of their funds in relatively risk-free investments,this is not an un- likely possibility.Alternatively,if borrowing is possible but only up to some limit,the choice of would be made by all but those investors willing to undertake considerable risk.These alternative paths lead to the main conclusion,thus making the assumption of borrowing or lending at the pure interest rate less onerous than it might initially appear to be. III.EQUILIBRIUM IN THE CAPITAL MARKET In order to derive conditions for equilibrium in the capital market we invoke two assumptions.First,we assume a common pure rate of interest, with all investors able to borrow or lend funds on equal terms.Second, we assume homogeneity of investor expectations:16 investors are assumed 15.This proof was first presented by Tobin for the case in which the pure rate of interest is zero (cash).Hicks considers the lending situation under comparable conditions but does not allow borrowing.Both authors present their analysis using maximization subject to constraints expressed as equalities.Hicks'analysis assumes independence and thus insures that the solution will include no negative holdings of risky assets;Tobin's covers the general case,thus his solution would generally include negative holdings of some assets.The discussion in this paper is based on Markowitz'formulation,which includes non-negativity constraints on the holdings of all assets. 16.A term suggested by one of the referees. This content downloaded from 202.120.21.61 on Mon,06 Nov 2017 02:56:13 UTC All use subject to http://about.istor.org/termsCapital Asset Prices 433 from X to cP are dominated by some combination of investment in 4 and lending at the pure interest rate. Consider next the possibility of borrowing. If the investor can borrow at the pure rate of interest, this is equivalent to disinvesting in P. The effect of borrowing to purchase more of any given investment than is possible with the given amount of wealth can be found simply by letting a take on negative values in the equations derived for the case of lending. This will obviously give points lying along the extension of line PA if borrowing is used to purchase more of A; points lying along the extension of PB if the funds are used to purchase B, etc. As in the case of lending, however, one investment plan will dominate all others when borrowing is possible. When the rate at which funds can be borrowed equals the lending rate, this plan will be the same one which is dominant if lending is to take place. Under these conditions, the invest- ment opportunity curve becomes a line (POZ in Figure 4). Moreover, if the original investment opportunity curve is not linear at point c, the process of investment choice can be dichotomized as follows: first select the (unique) optimum combination of risky assets (point c), and second borrow or lend to obtain the particular point on PZ at which an indiffer- ence curve is tangent to the line.'5 Before proceeding with the analysis, it may be useful to consider alter- native assumptions under which only a combination of assets lying at the point of tangency between the original investment opportunity curve and a ray from P can be efficient. Even if borrowing is impossible, the investor will choose 4 (and lending) if his risk-aversion leads him to a point below 4) on the line Pq). Since a large number of investors choose to place some of their funds in relatively risk-free investments, this is not an un- likely possibility. Alternatively, if borrowing is possible but only up to some limit, the choice of 4) would be made by all but those investors willing to undertake considerable risk. These alternative paths lead to the main conclusion, thus making the assumption of borrowing or lending at the pure interest rate less onerous than it might initially appear to be. III. EQUILIBRIUM IN THE CAPITAL MARKET In order to derive conditions for equilibrium in the capital market we invoke two assumptions. First, we assume a common pure rate of interest, with all investors able to borrow or lend funds on equal terms. Second, we assume homogeneity of investor expectations:16 investors are assumed 15. This proof was first presented by Tobin for the case in which the pure rate of interest is zero (cash). Hicks considers the lending situation under comparable conditions but does not allow borrowing. Both authors present their analysis using maximization subject to constraints expressed as equalities. Hicks' analysis assumes independence and thus insures that the solution will include no negative holdings of risky assets; Tobin's covers the general case, thus his solution would generally include negative holdings of some assets. The discussion in this paper is based on Markowitz' formulation, which includes non-negativity constraints on the holdings of all assets. 16. A term suggested by one of the referees. This content downloaded from 202.120.21.61 on Mon, 06 Nov 2017 02:56:13 UTC All use subject to http://about.jstor.org/terms