Practical Financial Optimization: Decision Making for Financial Engineers

Chapter 2

Basics of Risk Management

The modes of causation are many, though when brought under heads they too can be reduced in number. Thus we must inquire what chance and spontaneity are, whether they are the same or different, and how they fit into our division of causes.

Aristotle, Physics

The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature.

Peter Bernstein, Against the Gods

2.1 Preview

In this chapter we introduce basic concepts of risk measurement and risk management, and lay the foundations for the development of financial optimization models. We start with a classification of the risk factors that face an enterprise in today's financial markets, and define appropriate risk metrics. We also give measures of reward for performance evaluation. The chapter concludes with a classification of the optimization models used in risk management.

2.2 A Classification of Financial Risks

What is financial risk? It is the uncertainty surrounding the value of assets due to unforeseen and unforecastable future events. The causes of uncertainty are many, and financial risk is multidimensional. In this section we classify the risk factors so that the causes of uncertainty fit into a few categories.

Assume that there is available a universe U of n financial assets from which we can construct a portfolio by investing a fraction ...