# 4

# The Characteristics of the Opportunity Set under Risk

In Chapter 1 we introduced the elements of a decision problem under certainty. The same elements are present when we recognize the existence of risk; however, their formulation becomes more complex. In the next two chapters we explore the nature of the opportunity set under risk. Before we begin the analysis we present a brief summary or road map of where we are going. The existence of risk means that the investor can no longer associate a single number or payoff with investment in any asset. The payoff must be described by a set of outcomes and each of their associated probabilities of occurrence, called a frequency function or return distribution. In this chapter we start by examining the two most frequently employed attributes of such a distribution: a measure of central tendency, called the expected return, and a measure of risk or dispersion around the mean, called the standard deviation. Investors should not and, in fact, do not hold single assets; they hold groups or portfolios of assets. Thus a large part of this chapter is concerned with how one can compute the expected return and risk of a portfolio of assets given the attributes of the individual assets. One important aspect of this analysis is that the risk on a portfolio is more complex than a simple average of the risk on individual assets. It depends on whether the returns on individual assets tend to move together or whether some assets give good returns when ...

Get *Modern Portfolio Theory and Investment Analysis, 9th Edition* now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.