Real Options Valuation Based on Certainty Equivalents
Main Article Content
Keywords
real options, utility function, certainty equivalent, incomplete markets, CRRA
Abstract
This purpose of this research is to identify appropriate rates to discount the flows from real options in situations in which the risk-free rate does not apply, in particular, in incomplete markets. A methodology is proposed for valuing real options based on certainty equivalence, which requires as a principal condition the consideration of preferences represented with utility functions. A constant relative risk aversion (CRRA) utility function is used to represent these preferences. The results indicate that this methodology adequately reflects how the value of a real option changes in accordance with an investor´s preferences.
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References
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Arrow, K. J. (1966). Aspects of the Theory of Risk-Bearing. Helsinki: Yrjo Jahnssonin Saatio.
Beedles, W. L. (1978). On the Use of Certainty Equivalent Factors as Risk Proxies. The Journal of Financial Research, 1, 1, 15-21.
Chu, R., & Chu, Y. P. (1990). The Subsidence of Preference Reversals in Simplified and Marketlike Experimental Settings: A Note. The American Economic Review, 80, 4, 902-11.
Clemen, R. T., & Reily, T. (2001). Making Hard Decisions with Decision Tools. Pacific Grove, CA: Duxbury Thomson Learning.
Cochrane, J. H. (2001). Asset Pricing. Princeton: Princeton University Press.
Cohn, R. A., et al. (1975). Individual Investor Risk Aversion and Investment Portfolio Composition. The Journal of Finance, 30, 2, 605-20.
Copeland, T., & Antikarov, V. (2003). Real Options: A practitioner`s Guide. Nueva York: Texere.
Damodaran, A. (1999). Estimating Equity Risk Premiums. Consultado el 15 de febrero de 2014. Recuperado de papers.ssrn.com/abstract=2238064
Debreu, G. (1959). The Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Nueva York: Yale University Press.
Dohmen, T., et al. (2005). Individual Risk Attitudes: New Evidence from a Large, Representative, Experimentally-Validated Survey. IZA, 1730, 1-59.
Erb, C. B., Harvey, C. R., & Viskanta, T. E. (1995). Country Risk and Global Equity Selection. The Journal of Portfolio Management, 74-83.
Estrada, J. (2000). The Cost of Equity in Emerging Markets: A Downside Risk Approach. Emerging Markets Quarterly, 4, 3, 1-20.
Estrada, J. (2002). Systematic Risk in Emerging Markets: The D-CAPM. Emerging Markets Review, 3, 4, 365-79. Consultado el 16 de enero de 2014. Recuperado de http://linkinghub.elsevier.com/retrieve/pii/S1566014102000420
Fried, I., & Blume, M. E. (1975). The Demand for Risky Assets. American Economic Review, 65, 5, 900-22. Consultado el 15 de febrero de 2014. Recuperado de http://www.ncbi.nlm.nih.gov/pubmed/ 20888544
Fuenzalida, D., Mongrut, S., & Nash, M. (2007). Evaluación de proyectos en mercados de capitales incompletos. El trimestre económico, LXXIV, 293, 69-121.
Godfrey, S., & Espinosa, R. (1996). A Practical Approach to Calculating Costs of Equity for Investments in Emerging Markets. Journal of Applied Corporate Finance, 9, 3, 80-9.
Grasselli, M. R. (2011). Getting Real with Real Options: A Utility-Based Approach for Finite-Time Investment in Incomplete Markets. Journal of Business Finance & Accounting, 38, 5-6, 740-64. Consultado el 15 de febrero de 2014. Recuperado de http://doi.wiley.com/10.1111/j.1468-5957.2010.02232.x
Harrison, G. W., et al. (2005). Eliciting Risk and Time Preferences Using Field Experiments: Some Methodological Issues. Research in Experimental Economics, 10.
Harrison, G. W., et al. (2005). Risk Aversion and Incentive Effects: Comment. The American Economic Review, 95, 3, 897-901.
Harrison, G. W., Harstad, R. M., & Rutstrom, E. E. (2004). Experimental Methods and Elicitation of Values. Experimental Economics, 7, 2, 123-40. Consultado el 15 de febrero de 2014. Recuperado de http://link.springer.com/10.1023/B:EXEC.0000026975.48587.f0
Harrison, G. W., Lau, M. I., & Rutström, E. E. (2007). Estimating Risk Attitudes in Denmark: A Field Experiment. Scandinavian Journal of Economics, 109, 2, 341-68. Consultado el 17 de enero de 2014. Recuperado de http://doi.wiley.com/10.1111/j.1467-9442.2007.00496.x
Harrison, G. W., & List, J. A. (2004). Field Experiments. Journal of Economic Literature, XLII, 1, 1009-55.
Harvey, C. R., & Bekaert, G. (1995). Time-Varying World Market Integration. The Review of Economic Studies, 50, 2, 403-44.
Hearings, J., & Klubber, F. (2000). The Robustness of CAPM - A Computational Approach. Consultado el 21 de enero de 2014. Recuperado de www.fep.up.pt/investigacao/cempre/.../54.pdf
Henderson, V. (2007). Valuing the Option to Invest in an Incomplete Market. Mathematics and Financial Economics, 1, 2, 103-28. Consultado el 21 de enero de 2014. Recuperado de http://link.springer. com/10.1007/s11579-007-0005-z
Hertz, D. B. (1979). Risk Analysis in Capital Investment. Harvard Business Review, 169-81.
Hirshleifer, J. (1964). Efficient Allocation of Capital in an Uncertain World. The American Economic Review, 54, 3, 77-85.
Holt, C., & Laury, S. K. (2002). Risk Aversion and Incentive Effects. American Economic Review, 92, 5, 1644-55. Consultado el 21 de enero de 2014. Recuperado de http://pubs.aeaweb. org/doi/abs/10.1257/000282802762024700
Hugonnier, J., & Morellec, E. (2004). Investment Under Uncertainty and Incomplete Markets. International Center of Financial Asset Management and Engineering, 122.
Lessard, D. R. (1996). Incorporating Country Risk in the Valuation of Offshare Projects. Journal of Applied Corporate Finance, 9, 3, 52-63.
Mehra, R., & Prescott, E. C. (1985). The Equity Premium: A Puzzle. Journal of Monetary Economics, 15, 2, 145-61.
Merton, R. C. (1991). Continuous-Time Finance. The Economic Journal, 101, 406, 643-44.
Morin, R. A., & Suárez, A. F. (1983). Risk Aversion Revisited. The Journal of Finance, 38, 4, 1201-16.
Mukherjee, T. K., Belle, M. Van, & Baker, H. K. (2003). Using Certainty Equivalents to Evaluate Project Risk. Corporate Finance Review, 7, 4, 20-4.
Myers, S. C. (1968). A Time-State-Preference Model of Security Valuation. The Journal of Financial and Quantitative Analysis, 3, 1, 1-33.
NcNamee, P., & Celona, J. (1988). Decision Analysis for the Professional. The Journal of Risk and Insurance, 55, 4, 774-5.
Neuman, J. Von, & Morgenstern, O. (1947). Theory of Games and Economic Behavior. Princeton: Princeton University Press.
Noronha, C. et al. (2009). Optimal Strategies for Investment in Generation of Electric Energy through Real Options. MPRA, 18000.
Palacios-Huerta, I. (2003). An Empirical Analysis of the Risk Properties of Human Capital Returns. The American Economic Review, 93, 3, 948-64.
Pereiro, L. E., & Galli, M. (2000). La determinación del costo del capital en la valuación de empresas de capital cerrado: una guía práctica. Consultado el 21 de enero de 2014. Recuperado de www.slideshare.net/
Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Journal of Econometric Society, 32, 1, 122-36.
Rabin, M. (2000). Risk Aversion and Expected-Utility Theory: A Calibration Theorem. Journal of the Econometric Society, 68, 5, 1281-92.
Reyck, B. de, Degraeve, Z., & Gustafsson, J. (2004). Valuing Real Options in Incomplete Markets, 44, 1-2. Consultado el 21 de enero de 2014. Recuperado de www.ifd.dauphine. fr/fileadmin/.../Henderson.pdf
Riley, W. B., & Chow, K. V. (1992). Asset Allocation and Individual Risk Aversion. Financial Analysts Journal, 48, 6, 32-7.
Siegel, F. W., & Hoban, J. P. (1982). Relative Risk Aversion Revisited. The Review of Economic and Statistics, 64, 3, 481-7.
Smith, J. E., & Nau, R. F. (1995). Valuing Theory Risky and Projects: Decision Option Analysis Pricing. Management Science, 41, 5, 795-816.
Suen, R. M. H. (2009). Bounding the CRRA Utility Functions, 13260. Consultado el 21 de enero de 2014. Recuperado de mpra.ub.uni-muenchen.de/13260/
Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Massachusetts: The MIT Press.
Arrow, K. J. (1964). The Role of Securities of in the Optimal Allocation. The Review of Economic Studies, 31, 2, 91-6.
Arrow, K. J. (1966). Aspects of the Theory of Risk-Bearing. Helsinki: Yrjo Jahnssonin Saatio.
Beedles, W. L. (1978). On the Use of Certainty Equivalent Factors as Risk Proxies. The Journal of Financial Research, 1, 1, 15-21.
Chu, R., & Chu, Y. P. (1990). The Subsidence of Preference Reversals in Simplified and Marketlike Experimental Settings: A Note. The American Economic Review, 80, 4, 902-11.
Clemen, R. T., & Reily, T. (2001). Making Hard Decisions with Decision Tools. Pacific Grove, CA: Duxbury Thomson Learning.
Cochrane, J. H. (2001). Asset Pricing. Princeton: Princeton University Press.
Cohn, R. A., et al. (1975). Individual Investor Risk Aversion and Investment Portfolio Composition. The Journal of Finance, 30, 2, 605-20.
Copeland, T., & Antikarov, V. (2003). Real Options: A practitioner`s Guide. Nueva York: Texere.
Damodaran, A. (1999). Estimating Equity Risk Premiums. Consultado el 15 de febrero de 2014. Recuperado de papers.ssrn.com/abstract=2238064
Debreu, G. (1959). The Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Nueva York: Yale University Press.
Dohmen, T., et al. (2005). Individual Risk Attitudes: New Evidence from a Large, Representative, Experimentally-Validated Survey. IZA, 1730, 1-59.
Erb, C. B., Harvey, C. R., & Viskanta, T. E. (1995). Country Risk and Global Equity Selection. The Journal of Portfolio Management, 74-83.
Estrada, J. (2000). The Cost of Equity in Emerging Markets: A Downside Risk Approach. Emerging Markets Quarterly, 4, 3, 1-20.
Estrada, J. (2002). Systematic Risk in Emerging Markets: The D-CAPM. Emerging Markets Review, 3, 4, 365-79. Consultado el 16 de enero de 2014. Recuperado de http://linkinghub.elsevier.com/retrieve/pii/S1566014102000420
Fried, I., & Blume, M. E. (1975). The Demand for Risky Assets. American Economic Review, 65, 5, 900-22. Consultado el 15 de febrero de 2014. Recuperado de http://www.ncbi.nlm.nih.gov/pubmed/ 20888544
Fuenzalida, D., Mongrut, S., & Nash, M. (2007). Evaluación de proyectos en mercados de capitales incompletos. El trimestre económico, LXXIV, 293, 69-121.
Godfrey, S., & Espinosa, R. (1996). A Practical Approach to Calculating Costs of Equity for Investments in Emerging Markets. Journal of Applied Corporate Finance, 9, 3, 80-9.
Grasselli, M. R. (2011). Getting Real with Real Options: A Utility-Based Approach for Finite-Time Investment in Incomplete Markets. Journal of Business Finance & Accounting, 38, 5-6, 740-64. Consultado el 15 de febrero de 2014. Recuperado de http://doi.wiley.com/10.1111/j.1468-5957.2010.02232.x
Harrison, G. W., et al. (2005). Eliciting Risk and Time Preferences Using Field Experiments: Some Methodological Issues. Research in Experimental Economics, 10.
Harrison, G. W., et al. (2005). Risk Aversion and Incentive Effects: Comment. The American Economic Review, 95, 3, 897-901.
Harrison, G. W., Harstad, R. M., & Rutstrom, E. E. (2004). Experimental Methods and Elicitation of Values. Experimental Economics, 7, 2, 123-40. Consultado el 15 de febrero de 2014. Recuperado de http://link.springer.com/10.1023/B:EXEC.0000026975.48587.f0
Harrison, G. W., Lau, M. I., & Rutström, E. E. (2007). Estimating Risk Attitudes in Denmark: A Field Experiment. Scandinavian Journal of Economics, 109, 2, 341-68. Consultado el 17 de enero de 2014. Recuperado de http://doi.wiley.com/10.1111/j.1467-9442.2007.00496.x
Harrison, G. W., & List, J. A. (2004). Field Experiments. Journal of Economic Literature, XLII, 1, 1009-55.
Harvey, C. R., & Bekaert, G. (1995). Time-Varying World Market Integration. The Review of Economic Studies, 50, 2, 403-44.
Hearings, J., & Klubber, F. (2000). The Robustness of CAPM - A Computational Approach. Consultado el 21 de enero de 2014. Recuperado de www.fep.up.pt/investigacao/cempre/.../54.pdf
Henderson, V. (2007). Valuing the Option to Invest in an Incomplete Market. Mathematics and Financial Economics, 1, 2, 103-28. Consultado el 21 de enero de 2014. Recuperado de http://link.springer. com/10.1007/s11579-007-0005-z
Hertz, D. B. (1979). Risk Analysis in Capital Investment. Harvard Business Review, 169-81.
Hirshleifer, J. (1964). Efficient Allocation of Capital in an Uncertain World. The American Economic Review, 54, 3, 77-85.
Holt, C., & Laury, S. K. (2002). Risk Aversion and Incentive Effects. American Economic Review, 92, 5, 1644-55. Consultado el 21 de enero de 2014. Recuperado de http://pubs.aeaweb. org/doi/abs/10.1257/000282802762024700
Hugonnier, J., & Morellec, E. (2004). Investment Under Uncertainty and Incomplete Markets. International Center of Financial Asset Management and Engineering, 122.
Lessard, D. R. (1996). Incorporating Country Risk in the Valuation of Offshare Projects. Journal of Applied Corporate Finance, 9, 3, 52-63.
Mehra, R., & Prescott, E. C. (1985). The Equity Premium: A Puzzle. Journal of Monetary Economics, 15, 2, 145-61.
Merton, R. C. (1991). Continuous-Time Finance. The Economic Journal, 101, 406, 643-44.
Morin, R. A., & Suárez, A. F. (1983). Risk Aversion Revisited. The Journal of Finance, 38, 4, 1201-16.
Mukherjee, T. K., Belle, M. Van, & Baker, H. K. (2003). Using Certainty Equivalents to Evaluate Project Risk. Corporate Finance Review, 7, 4, 20-4.
Myers, S. C. (1968). A Time-State-Preference Model of Security Valuation. The Journal of Financial and Quantitative Analysis, 3, 1, 1-33.
NcNamee, P., & Celona, J. (1988). Decision Analysis for the Professional. The Journal of Risk and Insurance, 55, 4, 774-5.
Neuman, J. Von, & Morgenstern, O. (1947). Theory of Games and Economic Behavior. Princeton: Princeton University Press.
Noronha, C. et al. (2009). Optimal Strategies for Investment in Generation of Electric Energy through Real Options. MPRA, 18000.
Palacios-Huerta, I. (2003). An Empirical Analysis of the Risk Properties of Human Capital Returns. The American Economic Review, 93, 3, 948-64.
Pereiro, L. E., & Galli, M. (2000). La determinación del costo del capital en la valuación de empresas de capital cerrado: una guía práctica. Consultado el 21 de enero de 2014. Recuperado de www.slideshare.net/
Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Journal of Econometric Society, 32, 1, 122-36.
Rabin, M. (2000). Risk Aversion and Expected-Utility Theory: A Calibration Theorem. Journal of the Econometric Society, 68, 5, 1281-92.
Reyck, B. de, Degraeve, Z., & Gustafsson, J. (2004). Valuing Real Options in Incomplete Markets, 44, 1-2. Consultado el 21 de enero de 2014. Recuperado de www.ifd.dauphine. fr/fileadmin/.../Henderson.pdf
Riley, W. B., & Chow, K. V. (1992). Asset Allocation and Individual Risk Aversion. Financial Analysts Journal, 48, 6, 32-7.
Siegel, F. W., & Hoban, J. P. (1982). Relative Risk Aversion Revisited. The Review of Economic and Statistics, 64, 3, 481-7.
Smith, J. E., & Nau, R. F. (1995). Valuing Theory Risky and Projects: Decision Option Analysis Pricing. Management Science, 41, 5, 795-816.
Suen, R. M. H. (2009). Bounding the CRRA Utility Functions, 13260. Consultado el 21 de enero de 2014. Recuperado de mpra.ub.uni-muenchen.de/13260/
Trigeorgis, L. (1996). Real Options: Managerial Flexibility and Strategy in Resource Allocation. Massachusetts: The MIT Press.