is tangent to an isovariance curve. We call this point X (E). If we let E vary, X(E traces out a curve Algebraic considerations(which we omit here) show us that this cu a straight line. We will call it the critical line Z. The critical line passes through X for this point minimizes V for all points with E(X1, X2)=E As we go along Z in either direction from X, v increases. The segment of the critical line from X to the point where the critical line crosses direction of increasing E the boundary of the attainable set is part of the efficient set. The rest of the efficient set is (in the case illustrated) the segment of the ab line from d to b b is the point of maximum attainable E. In Figure 3, X lies outside the admissible area but the critical line cuts the admissible area. The efficient line begins at the attainable point with minimum variance(in this case on the ab line). It moves toward b until it inter- sects the critical line, moves along the critical line until it intersects a boundary and finally moves along the boundary to b. The reader mayPortfolio Selection 85 A is tangent to an isovariance curve. We call this point X(E). If we let h E vary, X(E) traces out a curve. Algebraic considerations (which we omit here) show us that this curve is a straight line. We will call it the critical line I. The critical line passes through X for this point minimizes V for all points with E(X1, Xz) = E. As we go along l in either direction from X, V increases. The segment of the critical line from X to the point where the critical line crosses *direction of increasing E depends on p,. p:. p3 FIG.2 the boundary of the attainable set is part of the efficient set. The rest of the efficient set is (in the case illustrated) the segment of the 3 line from d to b. b is the point of maximum attainable E. In Figure 3, X lies outside the admissible area but the critical line cuts the admissible area. The efficient line begins at the attainable point with minimum variance (in this case on the Z line). It moves toward b until it inter￾sects the critical line, moves along the critical line until it intersects a boundary and finally moves along the boundary to b. The reader may