The Valuation Handbook: Valuation Techniques from Today's Top Practitioners

CHAPTER 22

Lower Risk and Higher Returns

Linking Stable Paretian Distributions and Discounted Cash Flow

 

Rawley Thomas

President, LifeCycle Returns, Inc.

Dandan Yang

President’s Research Associate, LifeCycle Returns, Inc.

Robert J. Atra

Chair of the Finance Department, Lewis University

 

 

The nonnormality of security returns has reemerged due to the recent crisis in the financial markets. In just October 2008, the Dow Jones Industrial Average experienced five days where the average moved more than ±5 percent. Given a daily standard deviation of around 1 percent, these returns should be extraordinarily rare, if not impossible, assuming the normal distribution (De Grauwe, Iania, Rovira, and Kaltwasser 2008). These rare events traditionally predicted by the normal distribution are not nearly rare enough.

October 2008 is not an isolated event. The crash of October 1987 was approximately a 20 standard deviation event. The 1987 event should never have occurred, not only in our lifetime but in the universe’s lifetime, assuming normality. Furthermore, international borders do not confine these extraordinary episodes. The 1987 crash, as well as the recent crisis, represents a worldwide phenomenon. As disastrous as October 1987 was for the U.S. stock market, in reality it performed the fifth best of the 23 major country markets (Roll 1989) during that depressing month.

Given the doubt cast upon applications of the normal distribution in finance, two questions arise: (1) What is an ...