Estimation Error in Mean Returns and the Mean-Variance Efficient Frontier

31 Pages Posted: 15 Sep 2014 Last revised: 16 Nov 2017

See all articles by Majeed Simaan

Majeed Simaan

Stevens Institute of Technology - School of Business

Yusif Simaan

Fordham University - Graduate School of Business

Yi Tang

Fordham University - Gabelli School of Business

Date Written: September 26, 2017

Abstract

In this paper, we build estimation error in mean returns into the mean-variance (MV) portfolio theory under the assumption that returns on individual assets follow a joint normal distribution. We derive the conditional sampling distribution of the MV portfolio along with its mean and risk return when the sample covariance matrix is equal to a constant matrix. We use the mean squared error (MSE) to characterize the effects of estimation error in mean returns on the joint sampling distributions and examine how such error affects the risk-return tradeoff of the MV portfolios. We show that the negative effects of error in mean returns on the joint sampling distributions increase with the decision maker’s risk tolerance and the number of assets in a portfolio, but decrease with the sample size.

Keywords: Portfolio Theory, Investment, Estimation Error, Multivariate Analysis

JEL Classification: C13, C44, C46, G11

Suggested Citation

Simaan, Majeed and Simaan, Yusif and Tang, Yi, Estimation Error in Mean Returns and the Mean-Variance Efficient Frontier (September 26, 2017). International Review of Economics & Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2495621

Majeed Simaan (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

Yusif Simaan

Fordham University - Graduate School of Business ( email )

113 West 60th Street
Bronx, NY 10458
United States
6462200652 (Phone)

Yi Tang

Fordham University - Gabelli School of Business ( email )

113 West 60th Street
New York, NY 10023
United States

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