The Market Portfolio Is NOT Efficient: Evidences, Consequences And Easy To Avoid Errors

Pablo Fernandez

University of Navarra – IESE Business School

Jose Paulo Carelli

ISE Business School

Alberto Ortiz Pizarro

University of Navarra, IESE Business School

March 14, 2016

Abstract:

The Market Portfolio is not an efficient portfolio. There are many evidences that tell us that: the equal weighted indexes have beaten their market-value weighted indexes for many years, many easy-to-build portfolios (some “smart-beta”, “multifactors”) have beaten market-value weighted indexes. We document evidences about seven Equal weighted indexes that have had higher returns than the corresponding market-value weighted index: S&P500, MSCI Emerging Markets, FTSE 100, MSCI World. MSCI, DAX 30 and IBEX 35.

However, many finance and investment books still recommend to diversify in the same relative proportions as in a broad market index such as the Standard & Poor’s 500, many funds compare their performance with the return of market-value weighted indexes.

Without homogeneous expectations, the market portfolio cannot be an efficient portfolio for all investors.

In this document we also cover: a) volatility and beta being bad measures of risk; b) the unhelpfulness of the Sharpe ratio; and c) common (and easy to avoid) errors in portfolio management and corporate finance.

The Market Portfolio Is NOT Efficient: Evidences, Consequences And Easy To Avoid Errors – Introduction

“Learning means being able to keep perceiving reality as it truly is: complex – and not trying to fit every new experience into a closed and pre-conceived notion or overall scheme”. Yepes (1993, pp. 17-18).

“Experience doesn’t consist of the number of things one has seen, but of the number of things on which one has reflected”. Pereda, Jose Maria. Writer. Santander. Spain

“Your truth? No, the truth. And come with me to look for it”. Antonio Machado. Spanish poet.

Unweighted (equal weighted) indexes have outperformed their “value-weighted indexes”

Although many finance and investment books still recommend “holding a diversified portfolio in which securities are held in the same relative proportions as in a broad market index such as the Standard & Poor’s 500” [see, for example, Bodie and Merton (2000)], we have a lot of available evidence that tell us that the Market Portfolio is not an efficient portfolio. Equal weighted indexes1 have beaten market-value weighted indexes and Equal weighted portfolios have beaten market weighted portfolios.

Exhibits 1 to 6 have evidences about seven ‘Equal weighted indexes’ that have had higher returns than the corresponding market-value weighted index2: S&P500, MSCI Emerging Markets, FTSE 100, MSCI World. MSCI, DAX 30 and IBEX 35. However, the CAPM suggests that the value-weighted portfolio should outperform the equal-weighted portfolios.

The Market Portfolio is not an efficient portfolio

With the data of the previous section, it is quite clear that the Market Portfolio cannot be an ‘efficient portfolio’. There are many papers that show that:

DeMiguel, Garlappi, and Uppal (2009) (see exhibit 8) show that the return of the equal-weighted portfolio is almost always higher than that of portfolios based on mean-variance optimization.

Jacobs, Muller, and Weber (2013) extend this finding to other datasets and asset classes and suggest easy-toimplement allocation guidelines for individual investors.

The Market Portfolio Is NOT Efficient: Evidences, Consequences And Easy To Avoid Errors

But according to Bodie, Kane and Marcus (2013, pg. 232), “the CML represent efficient investments”

Bloomfield, Leftwich, and Long (1977) show that sample-based mean-variance optimal portfolios do not outperform an equally-weighted portfolio.

Plyakha, Uppal and Vilkov (2014) (see exhibit 7) find that the equal-weighted portfolio outperforms the price- and value-weighted portfolios in terms of average return, four-factor alpha, Sharpe ratio, and certainty-equivalent return. They rebalance the portfolios monthly.

Adame-Garcia, Fernández and Sosvilla (2016) (see exhibit 9) show that in the period 2001-2014 the total return of the equal-weighted IBEX 35 (46.8%) was higher than the return of the value-weighted IBEX 35 (13.21%). They rebalance daily the equal-weighted IBEX 35.

Ernst, Thompson and Miao (2016) (see exhibit 10) show that the return of the equally weighted S&P 500 portfolio is higher than the return of the market capitalization weighted S&P 500 portfolio. They calculate that 100$ invested in the S&P500 in 1958 were worth $5,212 in 2014; while 100$ invested in the ‘equally weighted S&P 500 portfolio’ in 1958 were worth $27,601 in 2014. They rebalance daily the ‘equally weighted S&P 500 portfolio’ and exclude dividends from all calculations.

Brennan and Lo (2010), in their paper “Impossible Frontiers”, argue that “the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers “impossible,” and show that impossible frontiers are difficult to avoid”. “as the number of assets, n, grows… the expected minimum amount of short selling across frontier portfolios grows” and document it using daily and monthly U.S. stock returns.

Levy and Roll (2015) critique Brennan and Lo (2010), and point out that “starting from an impossible frontier, slight changes in asset prices, as they converge to an economic equilibrium, deliver a possible frontier, consistent with the CAPM”.

Brennan and Lo (2015) answer that “possible frontiers are not only rare, but they occupy an isolated region of mean-variance parameter space that becomes increasingly remote as n increases”. They also add: “like Ingersoll, the legendary Fischer Black was also partial to theory and once said that if the data disagreed with the theory, he would discard the data. There is a certain wisdom to this striking conclusion given that financial data are noisy, dirty, and often fraught with fat tails, nonstationarities, and other theoretical infelicities. However, having grappled with financial data and institutional details that are typically ignored by theory for the sake of tractability, we have developed a somewhat greater respect for empirical phenomena, especially when they are at odds with theoretical implications”.

Mei and Moses (2002) report that for the period 1875-2000 there is underperformance of art masterpieces, meaning expensive paintings tend to underperform the art market index.

Brealey, Myers and Allen (2014, pg. 202) say: “Since the stocks of small firms have provided higher average returns that those of large firms, the risk premium on an equally weighted index is higher than on a value-weighted index”. What do you think about it?

Market Portfolio

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