The likelihood of various stock market return distributions, part 2: Empirical results

Abstract

The present article shows how Bayesians should shift beliefs among a family of models concerning the probability distribution of daily changes in the Standard & Poor 500 Index, given a particular sample. The preceding article in this issue showed that classical (R.A. Fisher, Neyman-Pearson) inference can be highly misleading for Bayesians, as can the assumption of a diffuse prior. The present article discusses how to bound Bayesian shifts in belief for compound hypotheses generally, as well as the specific shifts in beliefs among simple and compound hypotheses implied by the particular sample.

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

“…These principles are illustrated in an application of practical significance in a companion article, Markowitz and Usmen (1996), which follows.…”

“…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.…”

“…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.…”

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.…”

Portfolio selection with higher moments

“…But it is well known that many financial returns are not normally distributed. Studying a single asset at a time, empirical evidence suggests that asset returns typically have heavier tails than implied by the normal assumption and are often not symmetric (Kon 1984, Mills 1995, Markowitz and Usmen 1996, Peiro 1999, Premaratne and Tay 2002. Also, we argue that the relevant probability model is the posterior predictive distribution, which in general is not normal, even under an assumed normal sampling model.…”