The likelihood of various stock market return distributions, part 1: Principles of inference

Abstract

This is the first of two articles which apply certain principles of inference to a practical, financial question. The present article argues and cites arguments which contend that decision making should be Bayesian, that classical (R. A. Fisher, Neyman-Pearson) inference can be highly misleading for Bayesians as can the use of diffuse priors, and that Bayesian statisticians should show remote clients with a variety of priors how a sample implies shifts in their beliefs. We also consider practical implications of the fact that human decision makers and their statisticians cannot fully emulate Savage's rational decision maker.A companion article (Markowitz and Usmen, 1996) which follows in this issue describes how remote Bayesian clients should shift beliefs among various hypotheses concerning the probability distribution of daily changes in the Standard and Poor (S&P) 500 Index of stock prices, given a particular sample. The original motivation for the study was methodological. We wanted to see if useful data analysis could be performed on practical financial problems within constraints imposed by certain philosophical principles, namely, that financial research is primarily to improve financial decisions; rational decision making is Bayesian; the commonly used, commonly published classical (R.A. Fisher, Neyman-Pearson) inference methods are highly unreliable guides to Bayesians; the conjugate or diffuse priors frequently assumed in Bayesian studies are either restrictive (few hypotheses admit nontrivial conjugates) or are possibly highly misleading; and the Bayesian statistician should show remote clients, with a wide variety of priors, the extent to which they should shift beliefs, from prior to posterior, given the sample at hand (as opposed to assuming a single set of priors and showing the posterior beliefs implied by the sample mad these priors).

Portfolio Theory: As I Still See It

“…I never-at any time!-assumed that return distributions are Gaussian. To the contrary, on the one occasion that a colleague and I investigated the form of the return-generating distribution we concluded (in Markowitz & Usmen 1996a, 1996b) that, among the very broad class of distributions in the Pearson Family, daily log returns on the S&P 500 were most likely generated by a student-t distribution with between four and five degrees of freedom.…”

Unimodal density estimation using Bernstein polynomials

“…The S&P 500 is one of the most commonly followed stock market indices and is based on common stock prices of 500 top publicly traded American companies, which are determined by S&P. It is considered one of the best indicators of the state of the market and economy (Markowitz and Nilufer, 1996).…”

Allocation of Assets on the Ghana Stock Exchange (GSE)

“…Evidence of studying single asset at a time show that, a typical asset returns have heavier tails than implied by the normal assumption and are often not symmetric (see. Kon (1984), Mills (1995), Markowitz and Usmen (1996) and Peiro (1999). Because of the fat tail in the distribution of returns, several researchers have suggested the adoption of the third and the fourth moments in the Markowitz optimization model.…”