Determinants of the implied equity risk premium in Brazil.

AutorSanvicente, Antonio Zoratto
  1. Introduction

    Any stock's risk premium, or "equity risk premium" (ERP), is given by the difference between the expected return on the market portfolio and the rate of return on the market's risk-free asset. From one stock to another, the actual risk premium varies with the particular stock's beta, or sensitivity to returns on the market portfolio.

    In many important applications, estimates of the market risk premium are made using averages of historical differences between returns on a stock market index, such as the Standard & Poor's 500 (S&P500) and a return on a riskless asset, such as U.S. Treasury notes or bonds.

    In Brazil, those important applications include (a) the determination of discount rates in order to value stocks of firms in acquisition and/or going-private offers (OPAs); (b) the setting of so-called "regulatory internal rates of return" for companies in regulated sectors, such as electric power generation and distribution, highways, and natural gas distribution, among others. Internally, firms may need to calculate their cost of equity capital as part of variable compensation schemes, or in the computation of their weighted-average cost of capital when valuing new investment opportunities. This is done because the Sharpe (1964), Lintner (1965), and Mossin (1966) version of the capital asset pricing model (CAPM) is used in the construction of the relevant security market line for estimating the appropriate opportunity cost of equity.

    Two main issues stand out. First, the already-mentioned use of historical return averages, as opposed to current levels of the market portfolio's expected return, is in stark conflict with the concept of an opportunity cost. For an individual or a firm that needs to make an investment decision, the relevant cost should be that prevailing at the moment the decision must be made, and not an average of what occurred in the past. (1) Second, since the available history for the Brazilian stock market is considered "short," when compared to that of the U.S. market, for example, it is claimed that one should use a U.S. market index as a proxy for the market portfolio, and not Brazilian stock prices and returns, even when calculating an equity risk premium for the Brazilian market.

    In the present paper, we explain how to get around using historical averages as a basis of estimating expected returns on the market portfolio, by describing a straightforward procedure for obtaining the required expectation from current stock market prices. This is known as an "implied" equity risk premium. We then present the resulting series for the January 1995-December 2019 period, pointing out special situations, or "crises" in which the expected market portfolio return spiked, as would be natural, as compensation for sharp increases in the general level of risk perceived in the market.

    We also test the significance and direction of the relationship between easily-observed market fundamentals and our estimate for the market portfolio's return, and show that the results are significant for certain fundamentals, and in the appropriate direction.

    An alternative manner in which one can point out problems with the use of historical returns in the computation of equity risk premiums is to mention that the approach is based on the assumption that information surprises involving business firms tend to cancel each other over time, so that past behavior would become an unbiased estimator of future behavior. Elton (1999) questions this idea, demonstrating that, in practice, this has not occurred. Damodaran (2011) points out that this methodology puts us at a crossroad: if we use a very long historical period in order to have a representative sample (as does Ibbotson (2010), whose series starts in 1926), we would have to assume that investors' risk profiles and/or market fundamentals remained constant throughout that period. On the other hand, if we reduce the period to the last 20 or 40 years, say, high return volatility would produce unacceptably high standard errors. If that is the case for a mature and liquid market such as the United States, that effect would certainly be amplified in emerging markets such as Brazil. In addition, there is survivorship bias. Market histories are studied using stock indices, and clear evidence for this bias in successful stock markets is presented and discussed by Brown et al. (1995).

    The use of an implied premium is predicated on the idea that valuation and analysis exercises must look forward in time and incorporate market expectations. Gebhardt et al. (1999) use residual income models to estimate the implied cost of equity as the internal rate of return produced by forecasted earnings, and implicit in current stock prices. Claus & Thomas (1999) use the same idea in the aggregate. Damodaran (2011) calculates the implied premium for the American and Brazilian markets.

    The fact that implied risk premium and cost of equity calculations are gaining relevance at the expense of the historical return approach is emphasized by Nekrasov & Ogneva (2011), who enumerate some of the following applications: shedding light on the equity premium puzzle (Claus & Thomas, 2001; Easton et al., 2002); the market's perception of equity risk (Gebhardt et al., 2001); risk associated with accounting restatements (Hribar & Jenkins, 2004); legal institutions and regulatory regimes (Hail & Leuz, 2006); and tests of the inter-temporal CAPM (Pastor et al., 2008), among others.

    More recently, the cost of equity estimated with an implied risk premium has been used as a dependent variable in corporate finance research. For example, Javakhadze et al. (2016) see the influence of managerial social capital. That is, capital constructed by developing managers' networks benefits a firm by reducing its cost of equity. The cost of equity was estimated using the dividend discount model, with data for 729 firms on all continents. Lima & Sanvicente (2013) present evidence that better governance reduces the cost of equity in the Brazilian market.

    Hsing et al. (2011) apply the EGARCH model to the Brazilian stock index from 1997 to 2010 and find correlations with a few aggregate economic variables. The market seems to be positively affected by industrial production, the ratio of M2 money supply to GDP and the U.S. stock market index. They also find a negative impact of the lending rate, currency depreciation and domestic inflation.

    Camacho & Lemme (2004) compare a set of 22 Brazilian companies with investments abroad using two models: Global CAPM and Local CAPM, to investigate whether the cost of equity capital of Brazilian companies employed in the evaluation of overseas investments should be greater than that used for local projects, assuming an integrated market. They conclude that it is not correct to add any risk premiums to the cost of domestic equity capital.

    Ferreira (2011) computes correlations between Brazilian macroeconomic variables and the implied risk premium calculated using monthly data for stocks traded on the Bovespa from January 2005 to December 2010. The equity risk premium demanded by investors is positively affected by the unexpected inflation rate, the growth in money supply, the real interest rate, and the output gap, and it is negatively affected by GDP growth.

    Ferreira (2017) uses an implied risk premium for the Brazilian market as part of an investigation into whether publicly-owned firms had created shareholder value in the 2008-2015 period. The equity risk premium was calculated in the determination of a firm's cost of equity, itself a component of the firm's weighted-average cost of capital (WACC). The sample involved 134 listed firms, and for approximately 75% of such firms the author concludes that there had been value creation for their respective shareholders.

    A methodology for estimating the implied equity risk premium for the Brazilian market is suggested by Minardi et al. (2007). The proposal is to use business firm fundamentals such as return on equity and payout ratio as inputs to the Gordon formula. This is how the ERP for the Brazilian market is measured in the present paper.

    The paper is organized as follows: Section 2 reviews the literature, including previous uses and tests of determinants of the ERP; Section 3 describes the methodology for the calculation of the ERP as implied by current stock prices; Section 4 presents the methodology for the analysis of risk premium determinants, including both the model specification and the data used; results are provided in Section 5; and Section 6 concludes and discusses both limitations and possible extensions.

  2. Literature review: implied equity risk premium and cost of equity

    Claus & Thomas (1999) propose a new approach to estimating the equity risk premium for the U.S. market. This involves aggregating individual firm data and determining the equity risk premium implied in current stock prices for a number of firms, ranging from 1,559 in 1985 to 3,673 in 1998. Hence, they estimate a so-called "implied market risk premium." The implied equity risk premium is obtained as the internal rate of return (k), in the following equation:

    [p.sub.0] = [bv.sub.0] + [5.summation over (t=1)] [ae.sub.t]/[(1 + k).sup.t] + ([ae.sub.5](1 + g")/(k - g") [(1 + k).sup.5]) (1)

    where, for the end of each year (t = 0,..., 5):

    [p.sub.0] = current stock market price;

    [bv.sub.0] = book value of the firm's equity, as disclosed in its financial statements;

    [ae.sub.t] = abnormal earnings, equal to reported earnings minus a charge for the cost of equity, i.e., the product of beginning book value of equity and the implied rate of return; this means that projected earnings for year t are given by [e.sub.t] = [bv.sub.t-1] + 0.5 * [e.sub.t-1], where the et are analysts' earnings forecasts; this is the so-called "clean surplus" approach, with the added assumption of a common 50% payout ratio for all firms;

    g" = the assumed constant growth...

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