Capital Asset Price the value of rab. If the two investments are perfectly correlated, the combinations will lie along a straight line between the two points, since in this case both ere and oRe will be linearly related to the proportions invested in the two plans. 1 If they are less than perfectly positively cor- elated, the standard deviation of any combination must be less than that obtained with perfect correlation (since rab will be less); thus the combi- nations must lie along a curve below the line aB. azb shows such a curve for the case of complete independence (rab=0); with negative correlation the locus is even more U-shapec The manner in which the investment opportunity curve is formed is relatively simple conceptually, although exact solutions are usually quite difficult. 14 One first traces curves indicating Er, or values available with imple combinations of individual assets, then considers combinations of combinations of assets. The lower right-hand boundary must be either linear or increasing at an increasing rate(d2 or/dER>0). As suggested earlier, the complexity of the relationship between the characteristics of individual assets and the location of the investment opportunity curve makes it difficult to provide a simple rule for assessing the desirability of individual assets, since the effect of an asset on an investor s over-all investment opportunity curve depends not only on its expected rate of return (Eri)and risk (ori), but also on its correlations with the other by the equilibrium conditions for the model, as we will show in parteo available opportunities (ru, I2,...., rin). However, such a rule is implie The Pure rate of interest We have not yet dealt with riskless assets let p be such an asset; its risk is zero (ORp=0) and its expected rate of return, ERp, is equal(by definition) to the pure interest rate. If an investor places a of his wealth Ere =aERa t(1-a)er.= ERb+ ER,a but rab =1, therefore the expression under the square root sign can be factored qe=√/[aa+(1-a)ox2 a+(1一a)ckb = ORb+(oBa-oRb)a 12. This curvature is, in es 13. When rab =0, the slope of the curve at point a is Erh-E., at point B it is - When Iab=-1, the curve degenerates to two straight lines to 14. Markowitz has shown that this is a problem in parametric quadratic programmin (March and June, 1956), 111-133. A solution method for a special case is given in the author's"A Simplified Model for Portfolio Analysis, "op cit