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How to Discount Cashflows with Time-Varying Expected Returns

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  • Andrew Ang
  • Jun Liu

Abstract

While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time-varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk-free rates, predictable risk premiums and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large mis-valuations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time-variation in risk-free rates and factor loadings.

Suggested Citation

  • Andrew Ang & Jun Liu, 2003. "How to Discount Cashflows with Time-Varying Expected Returns," NBER Working Papers 10042, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:10042
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    References listed on IDEAS

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    1. Wayne E. Ferson & Campbell R. Harvey, 1999. "Conditioning Variables and the Cross Section of Stock Returns," Journal of Finance, American Finance Association, vol. 54(4), pages 1325-1360, August.
    2. Andrew Ang & Geert Bekaert, 2007. "Stock Return Predictability: Is it There?," The Review of Financial Studies, Society for Financial Studies, vol. 20(3), pages 651-707.
    3. Bakshi, Gurdip & Chen, Zhiwu, 2005. "Stock valuation in dynamic economies," Journal of Financial Markets, Elsevier, vol. 8(2), pages 111-151, May.
    4. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    5. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    6. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    7. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
    8. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    9. Campbell, John Y & Shiller, Robert J, 1988. " Stock Prices, Earnings, and Expected Dividends," Journal of Finance, American Finance Association, vol. 43(3), pages 661-676, July.
    10. Eugene F. Fama & Kenneth R. French, 2002. "The Equity Premium," Journal of Finance, American Finance Association, vol. 57(2), pages 637-659, April.
    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    12. M. J. Brennan, 1997. "The Term Structure of Discount Rates," Financial Management, Financial Management Association, vol. 26(1), Spring.
    13. Fama, Eugene F, 1996. "Discounting under Uncertainty," The Journal of Business, University of Chicago Press, vol. 69(4), pages 415-428, October.
    14. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    15. Robert Mundell, 1963. "Inflation and Real Interest," Journal of Political Economy, University of Chicago Press, vol. 71(3), pages 280-280.
    16. Fama, Eugene F. & French, Kenneth R., 1997. "Industry costs of equity," Journal of Financial Economics, Elsevier, vol. 43(2), pages 153-193, February.
    17. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    18. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    19. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
    20. Graham, John R. & Harvey, Campbell R., 2001. "The theory and practice of corporate finance: evidence from the field," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 187-243, May.
    21. Geert Bekaert & Steven R. Grenadier, 1999. "Stock and Bond Pricing in an Affine Economy," NBER Working Papers 7346, National Bureau of Economic Research, Inc.
    22. John Y. Campbell & Luis M. Viceira, 1999. "Consumption and Portfolio Decisions when Expected Returns are Time Varying," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 433-495.
    23. Ferson, Wayne E & Korajczyk, Robert A, 1995. "Do Arbitrage Pricing Models Explain the Predictability of Stock Returns?," The Journal of Business, University of Chicago Press, vol. 68(3), pages 309-349, July.
    24. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    25. Cochrane, John H, 1996. "A Cross-Sectional Test of an Investment-Based Asset Pricing Model," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 572-621, June.
    26. Zhiwu Chen & Gurdip Bakshi, 2001. "Stock Valuation in Dynamic Economics," Yale School of Management Working Papers ysm198, Yale School of Management.
    27. Ferson, Wayne E & Harvey, Campbell R, 1993. "The Risk and Predictability of International Equity Returns," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 527-566.
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    Cited by:

    1. Martin Lettau & Jessica A. Wachter, 2007. "Why Is Long‐Horizon Equity Less Risky? A Duration‐Based Explanation of the Value Premium," Journal of Finance, American Finance Association, vol. 62(1), pages 55-92, February.
    2. Sujata Behera, 2020. "Does the EVA valuation model explain the market value of equity better under changing required return than constant required return?," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-23, December.
    3. Xavier Gabaix, 2007. "Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices," NBER Working Papers 13430, National Bureau of Economic Research, Inc.
    4. Lior Menzly & Tano Santos & Pietro Veronesi, 2004. "Understanding Predictability," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 1-47, February.
    5. Wachter, Jessica A., 2005. "Solving models with external habit," Finance Research Letters, Elsevier, vol. 2(4), pages 210-226, December.

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    More about this item

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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