While the normality assumption is restrictive, it allows us to (1) understand the determinants of the difference between the unconstrained and constrained HJ-bounds, (2) establish a connection between the minimum-variance frontier and the constrained HJ-bound; and (3) conduct finite sample inference on the sample HJ-bounds.
and a = [mu]'[V.sup.-1][mu], b = [1'.sub.N][V.sup.-1][mu], and c = [1'.sub.N][V.sup.-1][1.sub.N] are the three efficiency set constants that characterize the minimum-variance frontier of the N risky assets.
Hansen and Jagannathan (1991) provide a linkage between the minimum-variance frontier and the unconstrained HJ-bound.
In order to locate the portfolio with minimum second moment, we draw a circle with its center at the origin, and the location of the minimum second moment portfolio [p.sup.*] can be obtained from the point where the circle is tangent to the minimum-variance frontier of the risk-free and risky assets.