Chapter 2 - Financial risk and heavy tails

Abstract

Financial theory has long recognized the interaction of risk and reward. Financial asset returns often possess distributions with tails heavier than those of the normal distribution. This chapter briefly examines financial risk from an historical perspective. It reviews risk in the context of the mean–variance portfolio theory, the capital asset pricing model (CAPM) and the APT, and briefly discusses the validity of their assumption of normality. The most cherished tenet of modern day financial theory is the trade-off between the risk and return. The higher the expected return, the better the investment. Risk considerations were involved in the investment decision process, but only in a qualitative way; stocks are more risky than bond. The capital asset pricing model is an equilibrium-pricing model, which relates the expected return of an asset to the risk-free return, to the market's expected return, and to the covariance between the market and the asset. In addition to assuming that market participants use the mean–variance framework, the model makes two additional major assumptions. First, the market is assumed frictionless., which means that securities are infinitely divisible, there exist no transaction costs, no taxes, and there are no trading restrictions. Second, the investor's beliefs are homogeneous. This means investors agree on mean returns and covariances for all assets in the market.