Expected Return, Firm Fundamentals, and Aggregate Systemic Risk: An Analysis for the Brazilian Market using an Accounting-Based Valuation Model.
| Autor | da Silva Carvalho Mikosz, Karina |
1 Introduction
This paper examines the capacity of the accounting-based valuation model of Lyle, Callen, and Elliott (2013) to predict returns (cost of capital) in the Brazilian capital market. Specifically, the work of Lyle et al. (2013), henceforth LCE, proposes: i) an expansion of the Feltham and Ohlson (1999) (FO) model, which already considered risk aversion, to incorporate dynamic expectations about the level of systemic risk in the economy; ii) to theoretically evidence the empirical findings of Ang, Hodrick, Xing, and Zhang (2006) that stocks with a high negative covariance with changes in the aggregate risk of the economy should have higher average returns; and iii) to express, through the derived accounting-based valuation model, cost of capital (expected return) as a function of a linear combination of accounting variables and company fundamentals, which are book-to-market, price-earnings, price-future profit, size, and dividend yield.
The theoretical construction of LCE is based on impartial accounting, where in terms of expectations the rate of return of an asset converges to the underlying cost of capital. Using cross-sectional regressions, the authors' proved that the proposed model was superior to conventional ones based on historical estimates, such as the Capital Asset Pricing Model (CAPM) and the Fama and French 3-factor model (1993), henceforth FF, since it produced fewer forecasting errors in comparison with the other models mentioned. LCE argues that the estimates generated by the CAPM and FF may not be adequate for calculating expected return since they do not include information on risk expectations or future states of the economy. However, the authors tested data from firms listed in the American stock market, and until now, there have been no studies that empirically verify how well the model captures the dynamics of shares of Brazilian firms.
In this article, we intend to verify the possibility of using the LCE accounting-based valuation framework to predict cost of capital (expected return) through cross-sectional regressions. We consider the evidence that asset returns have different relationships during periods of growth (booms) and recession (busts). Just as Pastor and Veronesi (2009) expand their analysis to also test the role of cyclical effects in expected return forecasts, here it was further investigated how periods of growth and recession affect the model's ability to predict returns in the Brazilian stock market.
Furthermore, the study by Ang et al. (2006) demonstrates that companies with more negative coefficients with regard to changes in aggregate risk measured by the Volatility Index (VIX) produce high future stock returns. They show that the sensitivity to aggregate risk in the entire economy is negatively related to returns, while LCE theoretically reveals this negative relationship. Thus, here the LCE results on how the sensitivity of firms to different risk factors can be useful in the process of forecasting returns were also explored. The VIX, released by the Chicago Board Options Exchange (CBOE), is employed because it is a good representation for the expected risk (systemic) of the entire economy, as previously reported by Ang et al. (2006). In Brazil, there is no official index with these characteristics. Yet, the work of Astorino, Chaguez, Giovannetti, and Silva (2015) proposed a calculation for "VIX BRASIL," IVol-BR, which was considered in this research and had daily data available from August 2011. Other risk factors employed were the betas of the CAPM and the 3-factor FF model, as well as the aggregated idiosyncratic risk using the Cross-Sectional Variance (CSV) as the representative variable.
On the whole, in developed markets, such as the United States of America (USA), valuation models based on fundamental variables are extensively used to predict expected returns (Ang et al., 2006; Ang, Hodrick, Xing, & Zhang, 2009; Fama & French, 1993, 2015; Lyle et al., 2013). Thus, using data from a different economy, such as Brazil, for example, can mitigate the bias that occurs as a result of snooping data (Lo & Mackinlay, 1990).
Moreover, the level of market efficiency in emerging economies is still a matter of debate, and this factor can significantly influence the results. In the short term, problems that can reduce market efficiency are more pronounced in countries like Brazil (Lopes & Alencar, 2010). Lopes (2002) observes some characteristics that distinguish the Brazilian capital market from developed economies, such as its shareholding structure and institutional factors, sources of funding, and state participation in the economy. Ownership control in Brazil is highly concentrated, and there is no differentiation between who the owners and managers are. Previous research (La Porta, Lopes-de-Silanez, Shleifer, & Vishny, 2000; La Porta, Lopez-de-Silanes, Shleifer, & Vishny, 2002) has shown that concentrated ownership is an inherent characteristic of poorly protected environments. Lopes and Alencar (2010) report that this characteristic is a determining aspect of the Brazilian environment when compared to the USA and has a strong effect on the relationship between disclosure and the cost of capital, for example. Thus, this work offers an independent empirical validation of the proposed model, extrapolating the regional limitation using a sample of Brazilian firms.
The main results showed that the LCE model is not well suited for forecasting returns in the Brazilian capital market, based on the sample and period researched. The robustness tests carried out by stratifying the sample based on four different characteristics of the firm (market capitalization, number of analysts that follow the firm, effort that the analysts make to cover a particular company, and accuracy of the analysts' forecast) demonstrated that the results remained the same.
The article is organized as follows. Section 2 describes the main theories concerning valuation models that use accounting data. In section 3, the methodological procedures are described, the results and their analysis are included in sections 4 and 5, and the conclusions are provided in section 6.
2 theoretical Foundations
2.1 Risk Aversion Models
Ohlson's (1995) model, called OM from hereon, and Feltham and Ohlson's (1995) model, consist of evaluating asset prices using accounting information (net equity and abnormal earnings) and a vector of other relevant information, where Linear Information Dynamics (LID) is used to predict abnormal profits. In the model, it is assumed that investors are risk-neutral, and interest rates are non-stochastic and fixed. The OM uses Residual Income Valuation (RIV), which is based on three support variables: i) use of profits, ii) book value of shareholders' equity, and iii) the Clean Surplus relationship, known as tidy profit. Edwards and Bell (1961) and Peasnell (1982) refer to the RIV as a model for evaluating companies based on accounting data, while Cupertino and Lustosa (2006) determine that the great innovation of the RIV in relation to the OM lies in it linking the model with LID.
Callen (2016) shows that some empirical applications of the OM replace the risk-free rate with other measures based on the CAPM or the 3-factor FF model. However, the study by Morel (2003) already showed that the parameters estimated using the OM are not consistent with those estimated in these models, as their assumptions are incompatible with each other. therefore, it would be incorrect to measure the cost of capital of the OM at a rate other than the risk-free one.
In this context, but taking into account risk aversion, other approaches have emerged, for example, the analysis of Feltham and Ohlson (1999) (FO), which extended the RIV model to include a risk aversion dynamic and was based on only two hypotheses: non-arbitrage in the financial markets and clean profit accounting. Recently, LCE theoretically extended the work of Ohlson (1995) and FO to incorporate changing expectations about the level of systemic risk in the economy and developed a linear model of accounting valuation that determines the price of the asset.
To this end, they made assumptions in the construction of the model, assuming that abnormal profits ([x.sup.a.sub.t]) and the "other information" vector ([v.sub.t]) follow an autoagressive linear dynamic. Specifically, abnormal profits for the next period ([x.sup.a.sub.t-1]) are a weighted average of current abnormal profits ([x.sup.a.sub.t]) and long-term abnormal profits ([x.sup.a.sub.L]), and the "other information" vector is a function of its behavior in the previous period. LCE also added a linear dynamic for the stochastic discount factor, [m.sub.t,t+1], which made it possible to incorporate The term that represents the level of aggregate (systematic) risk, [[sigma].sub.m,t], which is one of the pillars of the analysis. Formally, we have the following:
[x.sup.a.sub.t+1] = [omega][x.sup.a.sub.t+1] + (1 - [omega]) [x.sup.a.sub.L] + [e.sub.t+1] (t)
[v.sub.t+1] = [gamma][v.sub.t] + [u.sub.t+1] (2)
[m.sub.t,t+1] = [R.sup.-1.sub.f](1 - [[sigma].sub.m,t][e.sub.t-1]). (2)
The authors assumed that the error term [u.sub.t+1] is idiosyncratic and has no correlation with the stochastic discount factor. The error term [[member of].sub.t+1] is homoscedastic with a variance of [[sigma].sup.2.sub.x] (where [[sigma].sub.x] the volatility of abnormal profits), and both are considered as zero means. In practical terms, LCE established that ([[sigma].sub.m,t]) follows a random walk. As Callen (2016) and LCE argue, the formulation in Equations 1 and 2 consist of the same dynamic as that of Ohlson (1995). However, the latter was idealized in a risk-neutral world, where the company's cost of capital is an equal risk-free rate. In this case, if the return on equity is by chance equal to the company's cost of capital, abnormal long-term profits converge to zero. In the LCE methodology...
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