The empirical review test of conditional CAPM using expected returns of Brazilian, Argentinean, Portugal and united states of American portfolio.

• Author: Garcia, Fabio Gallo
• Position: Report

1. INTRODUCTION

   The last two decades witnessed a growth in numbers of empirical studies which examined the product capacity of the static version of Capital Asset Pricing Models (CAPM). Conclusions from these studies demonstrated that static CAPM was unable to give a reasonable explanation to cross-sectional variation of the average returns of the analyzed portfolios.

   Costa Jr. (1996) emphasized this idea when he mentioned that an original version of CAPM of absolute simplicity, recognized information of a greater relevance and applied it in a comprehensible manner. What happens is that the hypothesis that surrounds this original version requires a market of a perfect competition, which makes one to fear for lack of realism. Answers to this skeptism could be found in the empirical test done in the current study, that is, what is important is not the realism of the hypothesis of startup, but, to know if it is capable of concluding for the adjustment of the models to reality.

   Fama and French (1992) the ferrous critics of CAPM performed multivariate tests (multiple regression) and found two variables that explain the greater part of cross-section variation of medium returns: Book Value/Market Value index have a positive correlation with the returns of stocks while the variable as a whole is negative and significantly correlated and the beta appeared insignificant in this test.

   Fama and French (1993) found in their model three statistically associated factors that are significant as different from zero. This result suggests that the proxy of the factors associate's risks to returns of the human capital and the betas are unstable. Notwithstanding, this model was able to explain the cross-sectional of the expected returns.

   The CAPM and it static version were and are of great importance in finance. Therefore, in today's applications we find complex adaptations of CAPM that enables one to envisage results for questions that are yet to be resolved in finance.

   Based on this panorama therefore, and considering the whole scope of discussion that surrounds the validity of CAPM, this study aims to present the advantages of the conditional or dynamic model (models that incorporate variances and co-variances that changes during a space of time), in relation to a static model.

   Therefore, we study the tests of conditional models (beta variance during a period) that are not commonly studied in literature. These tests are convenient in order to incorporate variances and co-variances and changes in a future period. In the conditional model test, we highlight the studies of Jagannathan and Wang (1996), and Ferson and Harvey (1999).

   Bonomo (2002) mentioned yet, important studies about conditional CAPM among these, we cite Bodurtha and Mark (1991) where a beta of a group of assets is defined as a conditional covariance of error committed upon forecast of the returns on assets and the error on forecasted market returns. These models have various beta coefficients while the standard CAPM has only one.

   Finally, this study is structured in five sections, firstly, being contemplation of introductory aspects of the study; the second section has the background of Conditional Capital Asset Pricing Model, thirdly, about the methodological approach of Fama and MacBeth (1974). Fourthly we discuss details about Conditional CAPM for Brazil, Argentina, Portugal and US. Fifthly, we present the results found as related to the Brazilian market, Argentinean, Portuguese and the US market. And last but not the least, we present the final considerations about the study.

2. BACKGROUND OF CONDITIONAL CAPITAL ASSET PRICING MODEL

   CAPM is defined as a model which relates an expected profitability of an asset in a certain market and equilibrium with its undiversified risks, also known as beta. . Besides Sharpe, other authors also formulate CAPM, in its static version. Among these authors are Lintner (1965), Mossin (1966) and Treynor. This version of static CAPM or conditional has some consistent results when we perform empirical tests in order to verify the adherence capacity of the model to the reality of some economies.

   In all tests of non-conditional CAPM such as that of Fama and MacBeth (1974), Black, Jensen and Scholes (1972) it was supposed that beta would be static, that is, the assets systematic risk would not change.

   Haugen (1986) shows that Black, Jensen and Scholes considers that there is a positive linear relationship between beta and the expected return. As a consequence of this fact, Black, Jensen and Scholes (1972) encounter in their test of CAPM a positive relationship between profitability and the beta.

   Merton (1973) shows that the Consumption Capital Asset Pricing Model (ICAPM) had as an objective, generalize the CAPM model of Sharpe (1964) for an intertemporal context. The original ICAPM takes the hypothesis that the investors consumed all the reaches after a period, such that the said reaches and the consumptions are confused.

   The static CAPM of Sharpe- Lintner-Black, given as [R.sub.i] which denotes the returns on shares [sub.l] and [R.sub.m] the portfolio market returns for all shares of the economy. The version of Black (1972) is:

   E[R.sub.i] = [[gamma].sub.0] + [[gamma].sub.1][[beta].sub.i] (2.1)

   where [[gamma].sub.0] and [[gamma].sub.1] are defined as expected market returns and risk Premium expected from the market respectively, and where [[beta].sub.i] is defined as:

   [[beta].sub.i] = Cov([R.sub.i], [R.sub.m])/Var[[R.sub.m]], (2.2)

   Fama and French (1992) followed Black (1972) and examined empirically the static CAPM, arriving at a conclusion that, there is a weak relationship between medium return and the beta, and finding a strong evidence against static CAPM.

   Thus, Jagannathan and Wang (1996) developed a study which partially contradicts these evidences. In these same studies they observed that, upon application of CRSP index as a base for market portfolio, they found in their non-conditional model, implicit in the conditional CAPM, an explanation close to 30% of cross-sectional variation of the medium returns of 100 market portfolios, similar to that used by Fama and French (1992). For the implementation of CAPM therefore, is commonly used as proxy all the shares that are enlisted in the New York Stock Exchange (NYSE) and the American Stock Exchange (AMEX), which could be considered as a reasonable proxy for the market returns on portfolio of all assets. However, Fama and French (1992) found that, upon usage of that proxy, the same was not sufficient for a satisfactory analysis of the performance of CAPM.

   As a result of this fact and in order to ameliorate the proxy, Jagannathan and Wang (1996) followed Mayers (1972) and included in their models returns on human capital. When human capital is also included in the portfolio of the market, the non-conditional model implicit in conditional CAPM conditional is then capable of explaining more than 50% of the cross-sectional variation of the medium return. Besides this, the statistics tests where unable to give answers as they reject the model.

3. METHODOLOGY OF FAMA AND MACBETH (1974)

   Haugen (1986) shows that Fama and MacBeth (1974) methodology introduced a significant difference as related to the former tests, since they arrived at coherent results concerning fundamental forecasts of CAPM (Black, 1973 version).

   Fama and MacBeth (1974) constituted 20 portfolios which contain shares enlisted in NYSE for the period of 1926 through 1929. Latter, they estimated the beta of each of the portfolios and highlighting the monthly returns of the market index for the period of 1930 through 1934. They used the betas of each of the portfolios of the prior periods to forecast the monthly returns of the portfolios for the periods subsequent to 1935 through 1938. The process estimating the market beta was repeated nine times until 360 estimations were ascertained which was in the January 1935 through June of 1968.

   Haugen (1986) showed that in this case, Fama and MacBeth adopted betas and returns from different periods. The estimated beta in a period is used to estimate interest rate of returns for a future period. The results of these tests were very comforting, in that, CAPM gained the supports of scientists after the publication of this study.

   Even though the critics of the model are yet to find in various studies that takes it as literary support, amongst these, one would observe the model produced by Jagannathan and Wang (1996) through Fama and MacBeth (1974) that utilizes the same methodology.

4. THE CONDITIONAL CAPM MODEL FOR BRAZIL, ARGENTINA, & PORTUGAL.

   Brazil, Argentina and Portugal were chosen considering their potential in the market and their representativeness. Portugal has achieved the investment grade and, as a consequence, it also has a diverse range of investments throughout the country. In relation to Argentina and Brazil, we might state that both countries have a considerable volume of transactions in the stock exchange market.

   The selected variables (in the first place) are consisted of integral part of the Conditional CAPM Model for Brazil. It refers to the portfolios constructed through the monthly share returns negotiated at the Stock Market of Sao Paulo (Bovespa), GDP of the market and, for the...