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A statistical investigation of a stock valuation model

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Abstract

The Federal Reserve (FED) model is an empirical approach commonly used for valuation of the stock market. The model compares the earnings yield of the stock market with the nominal yield of long-term government bonds. This work investigates the validity of the FED model using Brazilian financial data. To achieve our goal, we utilized an empirical model called Vector Error Correction model (VECM), that allows to investigate the hypothesis of cointegration and causality aspects between the variables. The main results indicate the existence of favorable evidence to the long run relationship between the yields in Brazil. Also, in Brazil, there is a clear causality effect from the fixed income yields to the stock market ones.

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Notes

  1. The origin of the name “FED model” is generally attributed to the following statement given by the Federal Reserve Chairman Alan Greenspan in a Monetary Policy Report for July 22nd, 1997: “\(\ldots\) the ratio of prices in the S  & P 500 to consensus estimates of earnings over the coming 12 months has risen further from levels that were already unusually high. Changes in this ratio have often been inversely related to changes in long-term Treasury yields \(\ldots\)”.

  2. The authors presumed \(EP = M\times {{\mathcal {Y}}},\) where \(M> 1\) denotes a multiplier on \({{\mathcal {Y}}}\).

  3. https://www.bloomberg.com/professional/solution/bloomberg-terminal/.

  4. https://www.cnbc.com/2013/08/30/how-a-brazilian-billionaire-lost-25-billion-in-18-months.html.

  5. https://www.euromoney.com/article/b12kjqzr9rhfms/petrobras-walks-the-debt-capital-tightrope.

  6. As discussed in Zakamulin and Hunnes (2021), the relationship between EP and Y likely changes over time, which is consequence of changes in the economy and regulatory reforms, for example. This assumption implies some restrictions on the long-run relationship between these two variables. In this sense, as observed in Fig. 3 and discussed in Sect. 3, there is a clear outlier in \(EP_{t}\) series; besides, there are sub-periods for which the correlation between the Brazilian stock earnings and \(Y_t\) seems to be significant. These facts lead us to suspect structural breaks in the \(EP_{t}\) and \(Y_{t}\) long-run relationship. Thus, in addition to applying the widely used (Dickey and Fuller 1981) unit root tests, our stationary analysis is based on the developments of Zivot and Andrews (2002) and Lee and Strazicich (2003) (see Sect. 4.2).

  7. Unlike the \(R^2\) criterion, the Adj-\(R^2\) can increase or decrease when the number of parameters increases. This measure is not a proportion and can even assume negative values. As a model selection criterion, the greater the Adj-\(R^2\) value the better.

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Acknowledgements

The authors thank an anonymous referees for comments and suggestions that led to a much improved manuscript. They also gratefully acknowledge partial financial support from CNPq, Brazil.

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Authors and Affiliations

  1. Department of Accounting and Actuarial Sciences, Universidade Federal de Pernambuco, Cidade Universitária, Recife, PE, 50740–540, Brazil

    Wilton Bernardino

  2. Graduated Program in Economics (PIMES), Universidade Federal de Pernambuco, Cidade Universitária, Recife, PE, 50740–540, Brazil

    João B. Amaral, Nelson L. Paes, Raydonal Ospina & José L. Távora

  3. Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Cidade Universitária, Recife, PE, 50740–540, Brazil

    Raydonal Ospina

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  1. Wilton Bernardino
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  2. João B. Amaral
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Correspondence to Raydonal Ospina.

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Bernardino, W., Amaral, J.B., Paes, N.L. et al. A statistical investigation of a stock valuation model. SN Bus Econ 2, 106 (2022). https://doi.org/10.1007/s43546-022-00270-x

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