Abstract
The Campbell and Vuolteenaho (Am Econ Rev 94(5):1249–1275, 2004) two–beta model decomposes the systematic risk in the sensitivity of cash flow and discount rate change. We employed this model, which we call the Two Beta Decomposition Model (TBDM) and found that this model is useful to compute the cost of capital for unlisted companies (UCs) via a proxy from listed companies. This model includes not only the accounting return reaction to long-term changes in consumption, but also links fundamental reactions to temporal changes in risk aversion. We test this model along with three traditional alternatives that are potentially useful in computing the cost of equity for UCs: accounting betas (AB), unlevered betas (UB), and operational betas (OB). Our results show that AB, UB and TBDM can partially explain the cross-sectional variations of stock returns. Additionally, using a series of non-parametric ranking test along with several statistics of goodness of fit, we found that the TBDM is the model that produces the best fit among competing models followed by the UB which is currently the most used among proxy methods.
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We use databases available online.
Notes
Note that the model is set to allow an ex-post analysis since future shocks are not observable. This change implies the usual bias of ex-post models (Brown and Walter 2013).
Income Statement information in thousands.
The null hypothesis that the mean of our sample is equal to 15.5% was rejected for the t-test and the Wilcoxon signed rank test even with a statistical significance of 10%.
In Sect. 4, we provide a detailed explanation regarding how the variables in panel B are estimated.
The outputs of the Shapiro–Wilk normality test are presented in Table 7.
Most annual financial statements are released from February to March. Therefore, April market prices should reflect the accounting information of the preceding year.
P/E ratio has been made available by Professor Shiller at his web page.
The discussion regarding the theoretical implications of including taxes in the unlevered betas is still an open question. However, Sarmiento-Sabogal and Sadeghi (2014) find that models including this factor outperform those that omit it.
Available by Professor French at his web page.
We require at least three observations for each risk class to compute\(\overline{b}_{y}^{u}\), which do not present cases.
Note that AB definition in OB context is similar but not equal to the one we use in Eq. (9).
Since we work with excess returns and the price of any risk should be positive.
In the appendix section we present the results running OLS regressions with standard errors in Table 8 and reports the output of MacKinnon–White heteroskedasticity-consistent standard errors estimators in small samples in Table 9. In general, the results seem to be not sensitive to the selection of the standard errors estimators for all the models. Also, in Table 8 we present the Breusch–Pagan/Cook–Weisberg test for the homoscedasticity of the residuals.
The estimations are presented in Table 10 of the “Appendix” section.
See Table 11 in “Appendix” section.
In the “Appendix” section, we present the estimation for 20 value-weighted portfolios of BE/E in Table 12.
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We thank the support of Macquarie University, Pontificia Universidad Javeriana, and CESA Business School as well as the helpful comments provided by the peer reviewers.
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Appendices
Appendix A: compustat items for variables calculation
Debt = current liabilities (Compustat item # 34) + long-term debt (# 9)
EBIT = Operating Income after Depreciation (# 178).
EBITDA = Operating Income before Depreciation (# 13) if available; otherwise, we use EBIT plus Depreciation and Amortization (# 14).
Book Value of Equity (BE) = Stock Holders Equity—Preferred Stock + Deferred Taxes (#74, if available) + Investment Tax Credits (#208, if available) + Post-Retirement Benefit Liabilities (# 330, if available).
Stock Holders Equity = Stock Holders Equity (# 216), or
Stock Holders Equity = Common Equity (# 60) + Preferred Stock, or
Stock Holders Equity = Total Assets (# 6)—Total Liabilities (# 181).
Preferred Stock is selected from the first non-missing option of redemption value (# 56), liquidating value (# 10), or book value (# 130).
Deferred taxes are taken from its Deferred Taxes (# 74) or Investment Tax Credit (# 208, if available).
BE based on (Daniel and Titman 2006), and (Cohen et al. 2009).
Tax rate (τ) = USA top rate of statutory corporate taxes each year: 48% between 1972 and 1978, 46% from 1979 to 1986, 40% in 1987, 34% between 1988 and 1992, and 35% thereafter. Based on (Kemsley and Nissim 2002).
Appendix B
See Tables
7,
8,
9,
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11,
12.
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Sarmiento, J., Sadeghi, M., Sandoval, J.S. et al. The application of proxy methods for estimating the cost of equity for unlisted companies: evidence from listed firms. Rev Quant Finan Acc 57, 1009–1031 (2021). https://doi.org/10.1007/s11156-021-00968-3
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DOI: https://doi.org/10.1007/s11156-021-00968-3
Keywords
- Unlisted companies
- Cost of equity
- Accounting betas
- Unlevered betas
- Operational betas
- Two beta decomposition model