  Given two random realized returns on an investment, which is to be preferred?
This is a fundamental problem in finance that has no definitive solution except
in the case one investment always returns more than the other. In 1952
Markowitz and Roy introduced the following criterion for risk vs. return in
portfolio selection: if two portfolios have the same expected realized return
then prefer the one with smaller variance. An efficient portfolio has the least
variance among all portfolios having the same expected realized return.
  The primary contribution of this short note is observation that the CAPM
formula holds for realized returns as random variables, not just their
expectations. This follows directly from writing down a mathematical model for
one period investments.
