On the use of the Cauchy distribution to describe price fluctuations in R&D and other forms of real assets

Abstract

An improved model for describing the returns of assets that result from R&D efforts is needed. Such a model may lead

to better decision support tools to monetize the value of R&D activities for both public and private sector technology

managers. Real option pricing methodologies are often used to gauge appropriate funding levels for assets such as

R&D projects that contain large time-dependent uncertainties. A study of the commonly used Black-Scholes equation

finds that the Gaussian distribution assumption used to describe the behaviour of the underlying assets’ fluctuations

is not appropriate for R&D. This conclusion is based on a study of 43 military R&D projects and 100 micro-cap

technology intensive small firms. A power law, such as the Cauchy distribution, is shown to be more accurate in

describing fluctuations in returns on R&D investments. Using historical data we find that the Cauchy distribution is a

better representation of the underlying assets’ behaviour in military R&D projects and in technology intensive firms

with small market capitalization (i.e., single project firms that are commercializing R&D).