Extreme Events in Finance

Chapter 19The Choice of the Distribution of Asset Returns: How Extreme Value Can Help?¹

François Longin

Department of Finance, ESSEC Business School, Cergy-Pontoise Cedex, France

19.1 Introduction

The statistical distribution of asset returns plays a central role in financial modeling. Assumptions on the behavior of market prices are necessary to test asset pricing theories, to build optimal portfolios by computing risk/return-efficient frontiers, to value derivatives and define the hedging strategy over time, and to measure and manage financial risks. However, neither an economic theory nor a statistical theory exists to assess the exact distribution of returns. Distributions used in empirical and theoretical research are always the result of an assumption or estimation using data. The paradigm adopted in finance is the Gaussian distribution. In the 1950s and 1960s, Markowitz (1952) and Sharpe (1964) assumed normality for asset returns when studying portfolio selection and deriving the capital asset pricing model. In the beginning of the 1970s, Black and Scholes (1973) and Merton (1973) derived the price and the hedging strategy of an option by assuming a Brownian motion for the price of the underlying asset, implying a Gaussian distribution for returns. More recently, with the changes in the banking and financial regulation on risks and capital, value-at-risk models developed and implemented by financial institutions also rely intensively on the Gaussian distribution.²