STOCHASTIC

78 THE REVIEW OF ECONOMICS AND STATISTICS
the investor's portfolio must simultaneously lie
within the opportunity set and satisfy the probability
constraint (6), it must lie above the
line AB and below the line RT. The feasible
set of portfolios is therefore given by the set
RST and is illustrated in figure 3.
FIGURE 3. — "MAXIMUM /I" SAFETY-FIRST
CRITERION : No RISKLESS ASSET
1 ' »
i M
It is easy to see that the portfolio which maximizes
expected returns among those included
in this set is the one represented by T, which is
therefore the one selected by the Telser safetyfirster.
It also can be seen that this portfolio
is less conservative (in the sense that it leads
the investor to select a portfolio with a larger
mean and larger standard deviation) than that
selected by a "minimum a" investor who selects
the same disaster level z, or by a "maximum
2" investor who selects the same probability
level a. They will select the points W,S respectively.
On the other hand, the "maximum /u"
approach does create problems of feasibility
that the other two variants do not have. By
selecting both a and 2, the investor fixes the
position of the line RT and it is quite possible
that the values of these parameters he selects
are such that this line fails to intersect the
opportunity locus. In this case the "maximum
fi." principle breaks down for there is no portfolio
which will permit the investor to meet his
disaster level with the required probability.
indifference curves in the mean-standard deviation plane for
the "maximum p." approach as could be done for the other
approaches. The reason is that in this approach the optimality
criterion, which is to maximize the expected return,
does not involve a. Consequently, one cannot get a very
sensible "balancing off" between fi and cr such as portrayed
by normal mean-standard deviation indifference curves.
l/s
We are now in a position to study the relationship
between portfolio analysis based on
expected utility maximization and that based
on the safety-first principle. Referring to figure
1, imagine that an investor who maximizes expected
utility chooses the portfolio P. Since the
set of attainable portfolios bounded by APB is
a convex set and since the set of points preferable
to those lying along Ij also forms a convex
set, by the separating hyperplane theorem
there exists a straight line CD passing through
P which is tangential to both APB and I,. If
we use the "minimum a" safety-first criterion,
we can equate the slope of this line to the slope
given by (9),