EMPIRICAL STUDY ON THE EFFICIENCY OF A THEORETICAL PORTFOLIO OF THE BOVESPA INDEX

Abstract

The use of proxies for the market portfolio is a common practice in the finance field. Some scientific studies covering the basics of the theory of capital markets depend on the consideration of the market portfolio, which is treated as the benchmark portfolio for the entire capital market, especially when using theories derived from the so-called "portfolio theory", whose precursor was Harry Markowitz (1952, 1959), who created the basis for nearly everything that is studied in relation to investment decisions under uncertainty. Markowitz made an important contribution in the field of study of the relationship between risk and return, defining key concepts such as diversification effect, the efficient set and the tangency portfolio among others. His first study in the field of modern finance theory was an article published in 1952 in The Journal of Finance, entitled Portfolio Selection. Later, in 1959 he wrote a book on the subject with the same title as the original article. Despite the fact that capital market modern theory defines and uses the market portfolio, especially when dealing with the equilibrium model of bond prices called the capital asset pricing model (CAPM) as it is known, it is impossible to observe the true market portfolio. It is understood as market portfolio that portfolio which is formed by all assets that could be traded in the economy. Therefore, it comprehends all the so-called financial assets which involve primary rights on future cash flows and other assets representing wealth from the standpoint of the investor, such as real estate, artwork, rarities etc. It's easy to see how difficult it is if not impossible from a practical standpoint, to build the market portfolio, even periodically. As to organized markets, it is easier to get the value and asset prices as it happens, for example, with the stock market. But in other markets, even when lacking a clearing system, it is impossible to assert correct values to the assets traded. Inevitably what ends up happening is the creation of proxies, i.e., approximate representations of real market portfolio, especially when studying empirically or applying in practice the theories related to capital markets. Roll (1977), in his famous critique to the empirical tests of CAPM, argues it is impossible to observe the market portfolio, which in turn implies a lack of objectivity to conclude the validity of the model quoted. The CAPM empirical tests eventually end up being, according to Roll, efficiency tests of the market portfolio, once the mentioned model requires that such tests, to which all titles are referenced, be efficient in terms of mean and variance. In this study we try to evaluate the Bovespa index portfolio performance, which is the main market index used in Brazil in terms of risk and return. It would be desirable that the proxy of our market was a good representation of the true market portfolio, which means to position itself on the efficient frontier related to the risky assets traded in our market. However, by the construction methodology of the index theoretical portfolio it is difficult to imagine that the same is part of such frontier. The efficiency of the index was statistically tested using procedures detailed in the article.