STOCHASTIC

its mathematical convenience, multivariate normality
is doubtless also suspect, especially perhaps
in considering common stocks.
It is, consequently, very relevant to note that
by using the Bienayme-Tchebychefi inequality,
Roy [19] has shown that investors operating on
his "Safety First" principle (i.e. make risky investments
so as to minimize the upper bound of
the probability that the realized outcome will fall
below a pre-assigned "disaster level") should
maximize the ratio of the excess expected portfolio
return (over the disaster level) to the
standard deviation of the return on the portfolio
21 — which is precisely our criterion of max
g when his disaster level is equated to the riskfree
rate r*. This result, of course, does not
depend on multivariate normality, and uses a
different argument and form of utility function.
The Separation Theorem, and its Corrolaries
(t) and (ii) above — and all the rest of our following
analysis which depends on the maximization
w