STOCHASTIC

MEAN-STANDARD PORTFOLIO ANALYSIS 77
curves which will have the indicated curvature. 6
The equilibrium portfolio P, is then found
where a tangency occurs between an indifference
curve and the efficiency frontier, AB. If
the indifference curve passing through P is
given by
V(i>.,a) = V
the slope of the indifference curve at P is found
by substituting the coordinates of P into the
equation
Since any monotonic transformation of the expected
utility function V will also have a slope
given by (7), it follows that there is an infinity
of indifference curves which are tangential to
AB at P.
Turning now to the safety-first principle, we
shall commence with the "minimum a" criterion.
The indifference curves corresponding to (4)
are given by
Z — /I
= *, (8)
owhere
k is a constant. We have already argued
that one would expect a to be small, in which
case 2 < p. and k < 0. As k varies (4) defines
a series of curves in the (/i,