448 The Journal of Business Taking the derivative of this expression with respect to xki, we have xcov(RR)一SE(R)-T=0 (10) This set of equations, for i=1, 2 n, determines the of xu. If we write Dy for the inverse of the covariance matrix RA), then the solution to this set of equations may be written xM=S8∑DE()+T2D Note that the subscript k, referring to the individual investor, appears on the right-hand side of this equation only in the multipliers Sk and Tk. Thus very investor holds a linear combination of two basic portfolios, and every efficient portfolio is a linear combination of these two basic port folios. In equation(11), there is no guarantee that the weights on the individual assets in the two portfolios sum to one. If we normalize these eights, then equation (11) may be written (12) In equation(12), the symbols are defined as follows w=s∑∑DE(); DiE(R,)/ DEc (Ri) 1; Wkp+ Wig=1 k=1, 2, The last equation in (14)follows from the fact that the xki,s must also sum to one his content downloaded from 202.. 18.13 on Wed, 1 1 Sep 2013 02: 46: 59 AM All use subject to JSTOR Terms and Conditions448 The Journal of Business Taking the derivative of this expression with respect to Xki, we have N Z Xkj CoV(Ri, Rj) - SkE(Ri) - Tk (10) j~l This set of equations, for i - 1, 2, , N, determines the values of Xki. If we write Dij for the inverse of the covariance matrix cov(Ri, Rj), then the solution to this set of equations may be written N N XW- Sk DE(Rj) + Tk Di. (11) j=:l j=:l Note that the subscript k, referring to the individual investor, appears on the right-hand side of this equation only in the multipliers Sk and Tk. Thus every investor holds a linear combination of two basic portfolios, and every efficient portfolio is a linear combination of these two basic port￾folios. In equation (11), there is no guarantee that the weights on the individual assets in the two portfolios sum to one. If we normalize these weights, then equation (11) may be written Xki WkpXpi + WkqXqi. (12) In equation (12), the symbols are defined as follows: N N Wkp Sk DjE(Rj); i~_i j=:l N N Wkq Tk E D-j i==1 j=1 (13) N N N XPi DjjE(R)/ DijE(Rj); j==1 i==l j=1 N N N Xqi Dtjj 1 Dip. j==1 i==1 j=1 Thus we have N - pi1; (14) N Xqj =1; i= 1 Wkp + Wkq 1 k- 1 2, ..., L. The last equation in (14) follows from the fact that the Xki'S must also sum to one. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:46:59 AM All use subject to JSTOR Terms and Conditions