TABLE OF CONTENTS In this section we continue to pursue the idea that a rational investor will prefer to hold a portfolio that delivers the highest expected return for a given level of risk, but now we extend the notion of preference to include the possibility that one portfolio will deliver a higher expected return more often than another. Thus we extend the preference relation of the previous section to produce a unique efficient portfolio that is economically superior to the others in a certain well-defined sense.
The previous section s preference relation ranks one portfolio relatively higher than another if its expected return is greater than the other s across all expected returns consistent with the portfolio sort. The previous section completely analyzes the situation in which an investor prefers one portfolio to another when it is 100% certain that the portfolio will have a higher expected return. This section develops the theory further by providing a methodology for choosing among the portfolios within the efficient set.
To accomplish this, we refine the preference relation on portfolios by relaxing the requirement of 100% certainty and positing that a rational investor will prefer one portfolio to another if the portfolio delivers a greater expected return a greater percentage of the time. Of course, the challenge is to put meaning to the notion of one portfolio delivering a higher expected return than another a greater percentage of the time. To do this we are forced to study probability measures on the...
