A Test of a Generalized Stochastic Calculus

31 Pages Posted: 31 Aug 2015 Last revised: 11 Dec 2018

Date Written: November 27, 2018

Abstract

It has been in the literature since 1963 when Mandelbrot published The Variation of Certain Speculative Prices that returns on equity securities have heavy tails. In a 2014 article, Harris derives a mathematical reason these tails must be heavy. This proof in turn excludes mean-variance finance as either a model or as an approximation of reality. This paper tests the two competing sets of models treating the model itself as a parameter. Following the work of Alan Turing and IJ Good, this paper does a population study of all annual returns in the CRSP universe of securities from 1925-2013 and excludes mean-variance based models with a probability sufficiently close to unity that further discussion of mean-variance models is no longer necessary.

Keywords: Mean-Variance Finance, Capital Asset Pricing Model, Arbitrage Pricing Theory, Central Limit Theorem, Black-Scholes Option Pricing Model, Cauchy distribution, Bayesian methods

JEL Classification: C11, G10, G12

Suggested Citation

Harris, David E., A Test of a Generalized Stochastic Calculus (November 27, 2018). Available at SSRN: https://ssrn.com/abstract=2653151 or http://dx.doi.org/10.2139/ssrn.2653151

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