http://ijfr.sciedupress.com International Journal of Financial Research Vol. 7, No. 5; 2016 Published by Sciedu Press 1 ISSN 1923-4023 E-ISSN 1923-4031 Is S&P100 Index a Mean-Variance Efficient Portfolio? Mohammad G. Robbani 1 & Ajeet Jain 1 1 Department of Accounting and Finance, Alabama A&M University, Normal, USA Correspondence: Mohammad G. Robbani, Professor of Finance, Department of Accounting and Finance, Alabama A&M University, Normal, AL 35762, USA. Tel: (256) 372-5095. Received: July 13, 2016 Accepted: August 2, 2016 Online Published: October 8, 2016 doi:10.5430/ijfr.v7n5p1 URL: http://dx.doi.org/10.5430/ijfr.v7n5p1 Abstract This paper investigates whether Standards and Poors’ 100 stock index (henceforth, S&P100) is a mean-variance efficient portfolio. In other words, the paper examines if there is any other portfolio allocation rule that provides better risk-return scenario than one that is achieved under value-weighted strategy used in S&P100 index. Our results show that the realized risk of the S&P100 index is not the lowest for the return at any other portfolio combinations using all stocks in index. There are other portfolio combinations that provide lower risk for the same realized rate of return. Similarly, the realized return of S&P100 index is not the highest for the standard deviations at any other portfolio combinations. Based on these results, we conclude that the S&P100 index may not be considered to be a mean-variance efficient portfolio. Keywords: S&P100 index, mean-variance efficiency, portfolio 1. Introduction To select a portfolio, Markowitz (1952) and Tobin (1958) proposed that risk-averse investors must follow the mean-variance principle to maximize their utility. Under this rule, investors choose any alternative portfolio that includes a set of securities available in the market that can be combined in a linear combination in infinite possible ways. These chosen portfolios will include the portfolios that are efficient in the context of mean and variance. In other words, investors will discard those portfolio combinations that have lower mean and higher variance compared to any other given member of the set of portfolios. Under the mean-variance efficiency rule, a rational investor will select a portfolio that provides highest return for a given amount of risk or lowest risk for a given amount of return. This selection rule guarantees that investors are always better-off in the portfolio decision-making process. Fama (1965) defined the efficient portfolio as a portfolio that has the minimum variance for any given rate of return or that has maximum return for any given variance. Efficiency of a portfolio can be measured by evaluating its risk and return relationship over a period of time. In this paper, we use the Standard and Poor’s 100 stock index (henceforth, S&P100) to estimate the risk and return relationship by using its value-weighted portfolio allocation method. S&P100 index contains the top 100 companies from the US stock markets in terms of their market value. It is well-known that the index composition is revised from time to time to accurately represent the value of the overall market. Our purpose is to empirically investigate if the S&P100 index, is in fact, a mean-variance efficient portfolio. According to the argument presented by Markowitz (1952), Tobin (1958) and Fama (1965), if the S&P100 index is a mean-variance efficient portfolio, its value-weighted rate of return should be the highest at the realized risk level compared to portfolios constructed under any other weighting scheme or its standard deviation should be lowest under value-weighted method at the realized return compared to portfolios under any other weighting scheme. That means, there should not be any other combination of those stocks in the S&P100 that should provide higher return than the realized return of the index at the same risk level or there should not be any other portfolios that should offer lower standard deviation at the same return realized from S&P100 index. The purpose of this paper is to examine whether there is any other portfolio allocation rule that provides better risk-return scenario than one that is achieved under value-weighted strategy. By using the daily return for all stocks in the index, we estimate the annualized return and risk for the portfolio that includes all stocks in the S&P100 index. The empirical literature surprisingly does not directly address the performance of this very popular stock index. However, there have been a large body of research on the conditional mean-variance efficiency of U.S. and other