Risk Measures

This chapter and Chapter 11 later are based on Merton (1990, Chapter 2) which is supposed to be an introductory chapter. However, there are many very important concepts of risk, risk measures and mutual fund theorems that are key to finance theories that deserve careful and detailed coverage to facilitate the development of new finance theories. Hence, it is now separated into two chapters. This chapter covers the concept of risk and riskiness following Rothschild and Stiglitz (1970, 1971) and those by Merton (1990). The Merton’s risk measure is for an individual utility function but has properties closely resemblance the CAPM beta in the general equilibrium setting. This whole area of work tends to focus only on the first two moments of risky returns distribution which is rather restrictive in the modern context. Rothschild and Stiglitz’s risk concept is very loosely defined using utility and is always valid disregarding the shape of the risky returns distribution. Though not discussed here, Rothschild and Stiglitz’s risk concept has now been extended to include higher order of risk preference such as prudence, cautiousness and downside risk aversion. In this chapter and Chapter 11, investment and asset pricing are evaluated in a static one-period framework without consumption.