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Certainty equivalent, risk premium and asset pricing

Abstract

This paper attempts to determine the certainty equivalent of an uncertain future cash flow or value through the option pricing method, and builds models of certainty equivalent and certainty equivalent coefficient. Based on the model of certainty equivalent coefficient, this paper further derives models of risk premium and risk-adjusted discount rate. The latter is a new capital asset pricing model (CAPM) accounting for total risk rather than with only the systematic risk accounted for as in the current CAPM. The reliability in relevant financial analysis, valuation, decision making and risk management may be enhanced with these new models.

References

  • Becker J L, Sarin R K (1987). Lottery dependent utility. Management Science, 33: 1367–1382

    Article  Google Scholar 

  • Diamond P, Stiglitz J E (1974). Increases in risk and in risk aversion. Journal of Economic Theory, 8: 337–360

    Article  Google Scholar 

  • Fama E (1977). Risk-adjusted discount rates and capital budgeting under uncertainty. Journal of Financial Economics, 5(1): 3–24

    Article  Google Scholar 

  • Gollier C (2002a). Discounting an uncertain future. Journal of Public Economics, 85:149–166

    Article  Google Scholar 

  • Gollier C (2002b). Time diversification, liquidity constraints, and decreasing aversion to risk on wealth. Journal of Monetary Economics, 49(8): 1439–1459

    Google Scholar 

  • Gollier C (2002c). Time horizon and the discount rate. Journal of Economic Theory, 107(3):463–473

    Article  Google Scholar 

  • Gollier C, Pratt J W (1996). Risk vulnerability and the tempering effect of background risk. Econometrica, 64(6): 1109–1123

    Article  Google Scholar 

  • Gollier C, Zeckhauser R J (2002). Horizon length and portfolio risk. Journal of Risk and Uncertainty, 24(4): 195–212

    Article  Google Scholar 

  • Gordon A S (1986). A certainty-equivalent approach to capital budgeting. Financial Management, 15(4): 23–32

    Article  Google Scholar 

  • Gray D F, Merton R C, Bodie Z (2007). Contingent claims approach to measuring and managing sovereign credit risk. Journal of Investment Management, 5(4): 5–28

    Google Scholar 

  • Grinblatt M, Titman S (1998). Financial Markets and Corporate Strategy, Chapter 10. McGraw-Hill Inc.

  • Groom B, Koundouri P, Panopoulou E, Pantelidis T (2004). Model selection for estimating certainty equivalent discount rates. Working paper, University College London, London, UK

    Google Scholar 

  • Hong C S, Herk L F (1996). Increasing risk aversion and diversification preference. Journal of Economic Theory, 70(2): 180–200

    Google Scholar 

  • Kimball M S (1993). Standard risk aversion. Econometrica, 61(4): 589–611

    Article  Google Scholar 

  • Machina M J (1987). Choice under uncertainty: Problems solved and unsolved. Economic Perspectives, 1: 121–154

    Google Scholar 

  • Merton R C (2000). Future possibilities in finance theory and finance practice. Working paper, Harvard Business School

  • Myers S C, Turbull S M (1977). Capital budgeting and the capital asset pricing model: Good news and bad news. Journal of Finance, 32(2): 321–333

    Article  Google Scholar 

  • Ogaki M, Zhang Q (2001). Decreasing relative risk aversion and tests of risk sharing. Econometrica, 69(3): 515–526

    Article  Google Scholar 

  • Pearce D, Groom B, Hepburn C, Koundouri P (2003). Valuing the future: Recent advances in social discounting. World Economics, 4(3): 121–141

    Google Scholar 

  • Rabin M (2000). Risk aversion and expected-utility theory: A calibration theorem. Econometrica, 68(6): 1281–1292

    Article  Google Scholar 

  • Robichek A A, Myers S C (1966). Conceptual problems in the use of risk-adjusted discount rates. Journal of Finance, 21(1): 727–730

    Article  Google Scholar 

  • Samuelson A (1967). General proof that diversification pays. Journal of Financial and Quantitative Analysis, 2(2): 1–13

    Article  Google Scholar 

  • Schmalensee R (1981). Risk and return on long-lived tangible assets. Journal of Financial Economics, 2(2): 185–205

    Article  Google Scholar 

  • Trippi R R (1989). A discount rate adjustment for calculation of expected net present values and internal rates of return of investments whose lives are uncertain. Journal of Economics and Business, 41(2): 143–151

    Article  Google Scholar 

  • Turner A L, Weigel E J (1992). Daily stock market volatility: 1928–1989. Management Science, 38(11): 1586–1609

    Article  Google Scholar 

  • Weitzman M (1998). Why the far distant future should be discounted at its lowest possible rate. Journal of Environmental Economics and Management, 36: 201–208

    Article  Google Scholar 

  • Weitzman M (2001). Gamma discounting. American Economic Review, 91(1): 261–271

    Article  Google Scholar 

  • Zhang Z (2009). Determine optimal capital structure based on revised definitions of tax shield and bankruptcy cost. Frontiers of Business Research in China, 3(1): 120–144

    Article  Google Scholar 

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Correspondence to Zhiqiang Zhang.

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Zhang, Z. Certainty equivalent, risk premium and asset pricing. Front. Bus. Res. China 4, 325–339 (2010). https://doi.org/10.1007/s11782-010-0015-1

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  • DOI: https://doi.org/10.1007/s11782-010-0015-1

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