Extreme Events in Finance

Chapter 17The Sortino Ratio and Extreme Value Theory: An Application to Asset Allocation

G. Geoffrey Booth¹ and John Paul Broussard²

¹Eli Broad Graduate School of Management, Michigan State University, East Lansing, MI, United States

²School of Business – Camden, Rutgers, The State University of New Jersey, Camden, NJ, United States

17.1 Introduction

Modern portfolio theory has its genesis in the seminal works of Markowitz (1952) and Roy (1952).¹ Before their works, the notion of considering investments in the portfolio context was known by academicians and practitioners but lacked a coherent theory.² Combining stocks and other assets to create diversified portfolios with desired risk and return characteristics quickly caught on and was extended to describe the behavior of the stock market using the capital asset pricing model (CAPM) (Sharpe, 1964; Lintner, 1965; Mossin, 1966). This model (often referred to simply as the CAPM), provides the theoretical basis for the Sharpe ratio (Sharpe, 1966, 1994), a performance measure that relates the return of a portfolio in excess of the risk-free rate to the risk of the portfolio as measured by its volatility, or more precisely, the standard deviation of its returns. This ratio has remained popular since its introduction and has proven to be robust in many environments.

Following the finance orthodoxy initiated by Bachelier (1900), the CAPM and the Sharpe ratio assume that the returns distribution is Gaussian, a distribution that is ...