The cross-section of expected stock returns in Brazil/ Evidencias seccionais dos retornos esperados das acoes no Brasil.
| Autor | Varga, Gyorgy |
| Cargo | Ensayo |
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Introduction
Fama and French (1992)--hereafter F&F--and Jegadeesh and Titman (1993) convincingly summarized the evidence that "diversifiable" individual characteristics, like book-to-market, size and momentum, could capture important cross-sectional variation in average stock returns. Whether their combination of such characteristics capture some common risk factors, as in Fama and French (1993, 1996) three factor model, or some inefficiency as in Daniel and Titman (1997) is still being debated until today (see Campbell, 2014). If stocks with these characteristics are fundamentally riskier, we might expect them to continue to pay return premiums in the future. Investors who are less sensitive to these sources of risk will continue to enjoy their high returns. If, on the other hand, return premiums arose because of mispricing, we might expect these excess returns to fade away along time as investors learn about them.
Inspired by F&F, Costa Jr. and Neves (2000) studied the Brazilian stock market for the period from March 1988 to February 1996 and found that not only the size and the book-to-market, but the portfolios'[beta] s and earnings-to-price ratios were individually and jointly significant. The results of Braga and Leal (2003) are a little different, confirming that high book-to-market firms porfolios have greater average returns, but not that small size firms porfolios have greater average returns for the period July 1991-June 1998. (1)
Regarding the momentum characteristic in Brazil, to the best of our knowledge, it has not been studied in a cross-section of individual stocks, but in the context of long-short strategies of good-bad momentum portfolios. For example, Bonomo and Dall'Agnol (2003) and Kimura (2003) do not find significant excess returns from these long-short strategies, while Piccoli et al. (2015) claim they do generate significant profits in normal periods that are used up during crises.
The short time span of data available in the early 2000s bounded deeper analyses. Qualitative and quantitative differences in this pioneering literature seem due to the inclusion or exclusion of a couple of years, given the influential weight of each included observations (1/N), what is specially an issue in a period of inflation stabilization that affected nominal returns (i.e., likely, changed the data generating process).
In this article, we review the explanatory power of the size, book-to-market, leverage, and earnings-to-price characteristics of individual firms in Brazil, using a reliable sample of monthly stock returns and fundamentals variables from July 1999 to June 2015. Like F&F, we find that the book-to-market of individual firms capture some of the cross-sectional variation in average stock returns. In general, the patterns documented by F&F hold for the Brazilian stock market, with the qualification of less significance. Through the F&F approach, we additionally document that the momentum of individual stocks measured as the cumulated returns over the past 2 to 12 months--has some explanatory ability. We find that the book-to-market is the most significant characteristic explaining the cross-section of stock returns in our most comprehensive sample, but that the momentum pattern is more evident in the subsample of more liquid stocks. When the July 1999--June 2014 period is split into two subperiods, none of the variables shows explanatory power in both sub-periods. The book-to-market relation with the cross-section of returns disappears in the later sub-period, when the momentum relation becomes noticeable. This last result is similar to Schwert (2002), who found that the abnormal return for characteristics such as size effect, value and others documented seem to have weakened, or simply disappeared, after the papers that highlighted them were published. Thus, through practitioners' exploration of these uncovered premiums, the research findings may have caused the market to become more efficient.
To more convincingly dismiss the market [beta] and size as sources of premiums, like F&F in the Appendix, we look for the continuation of their premiums into the longer 27-year period, from July 1988 to June 2015, available at another database. Given the Brazilian inflation was much higher and variable before 1999, for comparability along different inflation regimes, we choose to work with real variables, i.e., constant prices instead of current nominal prices. We confirm that the market [beta] and size are not important for this whole longer period. Although they are significant in single characteristic regressions for the sub-period July 1999-June 2007, given the high correlation between the market [beta] and size, none of them is individually significant when they are used together.
Finally, we speculate on the issues of liquidity and government-controlled firms. Liquidity and state governance risk are characteristics of special concern to investors in Brazil. For example, if growth stocks are more liquid (or less government-controlled) than value stocks, the value premium may in part reflect a compensation for the lower liquidity (or for greater state management inefficiency) of value firms.
We reveal traces that liquidity reduces the value premium, supporting the covariance hypothesis with liquidity risk. In the other direction, the momentum premium strengthens in the more liquid subsample, suggesting it is fostered by investors' active interest. Regarding government-control, we find no evidence of covariance with the firms' characteristics. Because government-controlled firms - which are larger in size and book-to-market--rewarded stockholder below the market average in the sample studied, their exclusion decreases the importance of the size effect and increases the importance of the value effect.
The article proceeds as follows: The F&F methodology used in this study is reviewed in section 2. We describe our sample in section 3 and discuss our results in section 4. In section 5, we present some conclusions and suggest next steps in this research agenda.
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Methodology
According to the efficient market hypothesis, all expected return in excess to the risk-free rate should be the "fair" reward to the investment's exposition to non-diversifiable systematic risk. In the CAPM, the most popular market efficient asset pricing model, all systematic risk is summarized in the market portfolio, thus implying that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where: E([[??].sub.it] - [R.sub.f,t]) is asset's i expected excess return over the risk-free rate [R.sub.ft] during period t and E([[??].sub.Mt] - [R.sub.f,t]) is the market portfolio expected excess return over the risk-free rate. In words, the CAPM states that asset i's premium comes from its covariance with the market portfolio--[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and not from its own variance--and is linear in the systematic risk incurred.
Since Black, Jensen and Scholes (1972) and Fama and MacBeth (1973), many tests of the CAPM have been proposed. Intuitively, they all boil down in estimating regressions like:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (2)
and testing whether the intercept [[alpha].sub.i] equals zero, with varying degrees of econometric sophistication and power (see also Gibbons Ross and Shanken 1989).
Alternatively, given that only non-diversifiable risks should be priced in efficient markets, non-arbitrage in the CAPM implies that:
E([[??].sub.i,t] - [R.sub.f,t]) = [[lambda].sup.M][[beta].sub.i], [for all] i (3)
where: [[lambda].sup.M] is the price of the stock market risk (or, the market reward per unit of the stock market risk factor incurred).
One can thus, similar to Fama and MacBeth (1973), run the crosssection regression:
[bar.[R.sub.i,t]] = [[lambda].sup.0.sub.t] + [[lambda].sup.M.sub.t] [[beta].sub.i] + [v.sub.i] [for all] i, for each t (4)
where [bar.[[R.sub.i,t]] is the proxy for stock i expected return (that can vary through time), (2) and test if [[lambda].sup.0.sub.t] = [R.sub.f,t] and [[lambda].sup.m.sub.t] > 0 on average; i.e., [bar.[[gamma].sup.0]] = ([T.sup.-1][[summation].s p.T.subt=1] [R.sub.f,t]) and [bar.[[gamma].sup.M]] = ([T.sup.-1] [[summation].sup.T.sub.t=1] [[lambda].sup.M.sub.t]) > 0. A [bar.[[gamma].sup.0]] significantly different from the average risk-free interest rate ([T.sup.-1] [[summation].sup.T.sub.t=1] [R.sub.f,t]) means that stocks returned different than justified by their [[beta].sub.i]s sensitivities to the non-diversifiable risk, i.e., there is an arbitrage opportunity if this same pattern of average return can be extrapolated into the future.
Other risk factors or individual characteristics hypothesized to explain expected returns can also be included in (4) and allowed to vary over time. For example, F&F regressed the month-by-month cross-section of returns on size and book-to-market, in addition to the market [beta], allowing these regressors to vary annually according their previous year estimate (i.e., they are known by the investors before the return realization):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where t is every July, (t - 1) is every June, [tau] = 0, 1, ..., 11 means (t + t) goes from July to June of the following year, [ME.sub.i,t-1] is the market value of equity and [BME.sub.i,t-1] = ([BE.sub.i,t-1]/[ME.sub.i,t-1]) is the book value of equity to its market value; and test if [bar.[[lambda].sup.M]], [bar.[[lambda].sup.ME]], [bar.[[lambda].sup.BM]] are significantly different from zero. (3) They thus examine whether the size and book-to-market characteristics of firms are priced among stocks, in addition to the [[beta].sub.i]s sensitivities to the market risk. Insignificant [bar.[[lambda].sup.MB]] and [bar.[[lambda].sup.ME]] mean that these diversifiable characteristics are not priced in the market, as it should be in an efficient market where the CAPM model is true model of risk. (4) That is the main...
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