Modern Portfolio Theory: Foundations, Analysis, and New Developments, + Website

Chapter 3

Risk and Diversification

Chapter 2 briefly introduces topics such as risk, dominant asset, efficient asset, opportunity set, and capital market line (CML), naive diversification, and Markowitz diversification. These topics are discussed intuitively. Later chapters reexamine the topics in more depth.

3.1 Reconsidering Risk

The common dictionary definition of risk says it is the chance of injury, damage, or loss. Although this definition is correct, it is not highly suitable for scientific analysis. Analysis cannot proceed very far using verbal definitions, for several reasons. (1) Verbal definitions are not exact; different people interpret them in different ways. (2) Verbal definitions do not yield to analysis; they can only be broken down into more verbose verbal definitions and examples. (3) Verbal definitions do not facilitate ranking or comparison because they are usually not explicit enough to allow measurement. A quantitative risk surrogate is needed to replace the verbal definition of risk if risk analysis and portfolio analysis are to proceed very far. Most sciences are moving to refine and quantify their studies. For example, biometrics, econometrics, and psychometrics are focusing on quantification of the studies of biology, economics, and psychology, respectively.

The model used here for analyzing risk focuses on probability distributions of quantifiable outcomes. Because the rate of return from an investment is the most relevant outcome from an investment, ...