Skip to main content
SpringerLink
Log in

Unconstrained estimates of the equity risk premium

  • Published:
Review of Accounting Studies Aims and scope Submit manuscript

Abstract

Estimates of the equity risk premium implied by analyst forecasts—generally 2–4 %—are often significantly below realized equity returns of 6 %. Measurement error could result from conservative assumptions, reliance upon consensus rather than detailed forecasts, the use of market rather than target prices, and regression analysis, which can be influenced by a small number of observations. We address these potential sources of measurement error. Our estimates are consistent with subsequently realized returns and capture systematic risk exposure. Alternative techniques could capture another form of priced risk or identify firm characteristics associated with systematic mispricing. From 1999 to 2008, we estimate an average equity risk premium in the United States of 5.3 %. The estimate increases from 3.1 % for 1999–2000 to 5.9 % from 2001 to 2008, comparable to the historical average of realized equity returns.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. The valuations referred to here are in-sample valuations computed by applying the estimated cost of capital in a residual income valuation and comparing the resulting valuation to target or market price.

  2. We present results for estimates compiled from target prices and market prices, for calibrated and uncalibrated estimates, as well as equal- and market capitalization-weighted analysis. With respect to our calibration, we also present results where the calibration relies upon risk proxy ranks rather than the level of risk proxies.

  3. In cases where target price is less than the current price, this is the percentage difference between the minimum price over 12 months and the target price.

  4. This figure is the arithmetic mean of annual equity market returns in the US relative to government bond yields, presented in Table 3, p. 18. It is an extension of the 103-year average ending in 2002 presented in Dimson et al. (2003), Table 1, p. 12).

  5. The lower bound for the cost of equity capital is motivated by the average yield on US Treasury bonds of 4.7 percent over the sample period.

  6. This range for ROE estimates is much larger than the 5–20 percent allowable ROE range used in Gode and Mohanram (2003).

  7. We performed analysis using even higher long-term growth estimates but these higher assumptions did not show up as best estimates according to our bias and precision criteria.

  8. Very similar equity risk premium estimates are generated if the median, rather than the mean, yield on US Treasury bonds is used, or if we use the yield on five-year bonds.

  9. Gebhardt et al. (2001) perform their analysis on an equal-weighted basis, while Easton and Sommers (2006) rely upon value-weighted estimates.

  10. The use of a five-year or 15-year explicit forecast horizon did not materially impact on the results.

  11. This constraint is the same as that in Bradshaw (2004), and the assumption of a constant payout ratio over the explicit forecast period is consistently adopted in prior studies. The reason we do not use the dividend per share forecasts of individual analysts is that there are a relatively low number of these forecasts recorded in the I/B/E/S database. We prefer to use a consistent estimation technique for forecasting dividends across all observations.

  12. There will always be a small number of cases in which there is enough dispersion of analyst expectations such that there is no set of parameter estimates that, on average, result in valuations that approximate target prices. These cases represent less than 2 percent of our sample.

  13. The standard error of the beta estimate could be interpreted as a proxy for company-specific risk, or alternatively could represent the imprecision in the beta estimate.

  14. We use an in-sample estimate of the market return in order to avoid making spurious inferences about market risk exposure, purely because our sample happens to comprise a set of stocks that differ from a broader market index. We repeat our analysis on a market capitalization-weighted basis.

  15. The estimates that appear in Table 4 are compiled from the uncalibrated estimates of the cost of equity capital. The calibrated estimates only have an minor impact on the value-weighted market-wide estimates. For analysis based on target prices, the mean and standard deviation of the value-weighted market risk premiums are 5.3 percent and 1.6 percent according to our estimation technique, 2.7 percent and 1.7 percent for the Easton et al. (2002) technique, and 1.1 and 2.0 percent for the Nekrasov and Ogneva (2011) technique. The corresponding means (standard deviations) for estimates based on market prices are 7.6 percent (3.0 percent), 5.3 percent (2.7 percent), and 3.0 percent (2.3 percent).

  16. For example, Gray, Hall, Klease, and McCrystal (2009) report that, regardless of the length of estimation procedure, OLS beta estimates perform no better in predicting future stock returns than the naïve assumption that all firms have a beta estimate equal to one.

  17. For this variable, it is not appropriate to compare the magnitude of coefficients from the rank regressions across estimation techniques. Specifically, the coefficients of 6.95, 8.55, and −0.91 from Table 10 are not comparable because the dispersion of the long-term growth estimates is substantially lower for the Nekrasov and Ogneva (2011) technique. The other independent variables are the same across estimation techniques, so the coefficients can be compared across estimation techniques for both the levels regression and rank regression.

  18. In the appendix, Tables 11, 12, 13, 14, 15, 16, we present regression results for market capitalization-weighted portfolios, as well as portfolios based on uncalibrated estimates of the cost of equity capital.

References

  • Asquith, P., Mikhail, M., & Au, A. (2005). Information content of equity analyst reports. Journal of Financial Economics, 75, 245–282.

    Article  Google Scholar 

  • Bandyopadhyay, S., Brown, L., & Richardson, G. (1995). Analysts’ use of earnings forecasts in predicting stock returns—Forecast horizon effects. International Journal of Forecasting, 11, 429–445.

    Article  Google Scholar 

  • Block, S. (1999). A study of financial analysts: Practice and theory. Financial Analysts Journal, 55, 86–95.

    Article  Google Scholar 

  • Botosan, C., & Plumlee, M. (2005). Assessing alternative proxies for the expected risk premium. Accounting Review, 80, 21–53.

    Article  Google Scholar 

  • Bradshaw, M. (2001). The use of target prices to justify sell-side analysts’ stock recommendations. Harvard Business School, Working Paper.

  • Bradshaw, M. (2004). How do analysts use their earnings forecasts in generating stock recommendations? Accounting Review, 79, 25–50.

    Article  Google Scholar 

  • Brav, A., & Lehavy, R. (2003). An empirical analysis of analysts’ target prices: Short-term informativeness and long-term dynamics. Journal of Finance, 58, 1933–1967.

    Article  Google Scholar 

  • Chen, F., Jorgensen, B. N., & Yoo, Y. K. (2004). Implied cost of equity capital in earnings-based valuation: International evidence. Accounting and Business Research, 34, 323–344.

    Article  Google Scholar 

  • Cheng, Q. (2005). What determines residual income? Accounting Review, 80, 85–112.

    Article  Google Scholar 

  • Clarkson, P., Simon, A., & Tutticci, I. (2009). What influences analysts’ target prices? University of Queensland, Working Paper.

  • Claus, J., & Thomas, J. (2001). Equity premia as low as three percent? Evidence from analysts’ earnings forecasts for domestic and international stock markets. Journal of Finance, 56, 1629–1666.

    Article  Google Scholar 

  • Courteau, L., Kao, J. L., & Richardson, G. (2001). Equity valuation employing the ideal versus ad hoc terminal value expressions. Contemporary Accounting Research, 18, 625–661.

    Article  Google Scholar 

  • Cowen, A., Groysberg, B., & Healy, P. (2006). Which types of analyst firms are more optimistic? Journal of Accounting and Economics, 41, 119–146.

    Article  Google Scholar 

  • Dimson, E., Marsh, P., & Staunton, M. (2003). Global evidence on the equity risk premium. Journal of Applied Corporate Finance, 15, 8–19.

    Article  Google Scholar 

  • Dimson, E., Marsh, P., & Staunton, M. (2006). The worldwide equity premium: A smaller puzzle. Zurich: European Finance Association Meetings.

    Google Scholar 

  • Easton, P. (2004). PE ratios, PEG ratios, and estimating the implied expected rate of return on equity capital. Accounting Review, 79, 73–95.

    Article  Google Scholar 

  • Easton, P. (2006). Use of forecasts of earnings to estimate and compare cost of capital across regimes. Journal of Business Finance and Accounting, 33, 374–394.

    Article  Google Scholar 

  • Easton, P. (2007). Estimating the cost of capital implied by market prices and accounting data. Foundations and Trends in Accounting, 2, 241–364.

    Article  Google Scholar 

  • Easton, P., & Sommers, G. (2006). Effect of analysts’ optimism on estimates of the expected rate of return implied by earnings forecasts. Journal of Accounting Research, 45, 983–1015.

    Article  Google Scholar 

  • Easton, P., Taylor, G., Shroff, P., & Sougiannis, T. (2002). Using forecasts of earnings to simultaneously estimate growth and the rate of return on equity investment. Journal of Accounting Research, 40, 657–676.

    Article  Google Scholar 

  • Fama, E., & French, K. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56.

    Article  Google Scholar 

  • Fama, E., & French, K. (1995). Size and book-to-market factors in earnings and returns. Journal of Finance, 50, 131–155.

    Article  Google Scholar 

  • Fama, E., & French, K. (2002). Equity risk premium. Journal of Finance, 57, 637–659.

    Article  Google Scholar 

  • Fama, E., & MacBeth, J. (1973). Risk, return and equilibrium—Empirical tests. Journal of Political Economy, 81, 607–642.

    Article  Google Scholar 

  • Francis, J., Olsson, P., & Oswald, D. R. (2000). Comparing the accuracy and explainability of dividend, free cash flow and abnormal earnings value estimates. Journal of Accounting Research, 38, 45–70.

    Article  Google Scholar 

  • Gebhardt, W. R., Lee, C. M., & Swaminathan, B. (2001). Toward an implied cost of capital. Journal of Accounting Research, 39, 135–176.

    Article  Google Scholar 

  • Gode, D., & Mohanram, P. (2003). Inferring the cost of capital using the Ohlson–Juettner model. Review of Accounting Studies, 8, 399–431.

    Article  Google Scholar 

  • Gordon, J., & Gordon, M. (1997). The finite horizon expected return model. Financial Analysts Journal, 53, 52–61.

    Article  Google Scholar 

  • Gray, S., Hall, J., Klease, D., & McCrystal, A. (2009). Bias, stability and predictive ability in the measurement of systematic risk. Accounting Research Journal, 22, 220–236.

    Article  Google Scholar 

  • Grullon, G., & Michaely, R. (2002). Dividends, share repurchases and the substitution hypothesis. Journal of Finance, 57, 1649–1684.

    Article  Google Scholar 

  • Liu, J., Nissim, D., & Thomas, J. (2002). Equity valuation using multiples. Journal of Accounting Research, 40, 135–172.

    Article  Google Scholar 

  • Loh, R., & Mian, M. (2006). Do accurate earnings forecasts facilitate superior investment recommendations? Journal of Financial Economics, 33, 3–56.

    Google Scholar 

  • Lundholm, R., & O’Keefe, T. (2001). Reconciling value estimates from the discounted cash flow model and the residual income model. Contemporary Accounting Research, 18, 311–335.

    Article  Google Scholar 

  • Mehra, R., & Prescott, E. C. (1985). The equity premium: A puzzle. Journal of Monetary Economics, 15, 145–161.

    Article  Google Scholar 

  • Moyer, C., & Patel, A. (1997). The equity market risk premium—A critical look at alternative ex ante estimates. Review of Accounting Studies, 10, 133–170.

    Google Scholar 

  • Nekrasov, A., & Ogneva, M. (2011). Using earnings forecasts to simultaneously estimate firm-specific cost of equity and long-term growth. Review of Accounting Studies, 16, 414–457.

    Article  Google Scholar 

  • Ohlson, J. A. (1995). Earnings, books values and dividends in equity valuation. Contemporary Accounting Research, 11, 661–687.

    Article  Google Scholar 

  • Ohlson, J. A., & Juettner-Nauroth, B. E. (2005). Expected EPS and EPS growth as determinants of value. Review of Accounting Studies, 10, 349–365.

    Article  Google Scholar 

  • Petersen, M. A. (2009). Estimating standard errors in finance panel data sets: Comparing approaches. Review of Financial Studies, 22, 435–480.

    Article  Google Scholar 

  • Ramnath, S., Rock, S., & Shane, P. (2008). The financial analyst forecasting literature: A taxonomy with suggestions for further research. International Journal of Forecasting, 24, 34–75.

    Article  Google Scholar 

  • Schipper, K. (1991). Analyst forecasts. Accounting Horizons, 5, 105–131.

    Google Scholar 

  • Sharpe, S. (2005). How does the market interpret analysts’ long-term growth forecasts? Journal of Accounting, Auditing and Finance, 20, 147–166.

    Google Scholar 

Download references

Acknowledgments

We appreciate the feedback from participants at the 2009 AFAANZ Conference and the 2010 Australasian Finance and Banking Conference, and an anonymous referee.

Author information

Authors and Affiliations

  1. UQ Business School, The University of Queensland, St Lucia, Brisbane, QLD, 4072, Australia

    Tristan Fitzgerald, Stephen Gray, Jason Hall & Ravi Jeyaraj

Authors
  1. Tristan Fitzgerald
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen Gray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jason Hall
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ravi Jeyaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jason Hall.

Appendix

Appendix

See Tables 10, 11, 12, 13, 14, 15, 16.

Table 10 Regression of cost of capital estimates on risk proxy ranks
Full size table
Table 11 Market capitalization weighted returns to stocks sorted by cost of capital estimates
Full size table
Table 12 Equal weighted returns to stocks sorted by uncalibrated cost of capital estimates
Full size table
Table 13 Market capitalization-weighted returns to stocks sorted by uncalibrated cost of capital estimates
Full size table
Table 14 Regression of market capitalization-weighted portfolio returns on market returns
Full size table
Table 15 Regression of equal-weighted portfolio returns on market returns where portfolios are formed from uncalibrated cost of capital estimates
Full size table
Table 16 Regression of market capitalization-weighted portfolio returns on market returns where portfolios are formed from uncalibrated cost of capital estimates
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fitzgerald, T., Gray, S., Hall, J. et al. Unconstrained estimates of the equity risk premium. Rev Account Stud 18, 560–639 (2013). https://doi.org/10.1007/s11142-013-9225-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11142-013-9225-z

Keywords

JEL classification

Search

Navigation