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The Derivation of Probabilistic Information for the Evaluation of Risky Investments

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  • Frederick S. Hillier

    (Stanford University, Stanford, California)

Abstract

The amount of risk involved is often one of the important considerations in the evaluation of proposed investments. This paper is concerned with the derivation of the type of explicit, well-defined, and comprehensive information that is essential for an accurate appraisal of a risky investment. It is shown how, under certain assumptions, such information in the form of the probability distribution of the present worth, annual cost, or internal rate of return of the proposed investment can be derived. The derivation and use of this information is then illustrated by an example.

Suggested Citation

  • Frederick S. Hillier, 1963. "The Derivation of Probabilistic Information for the Evaluation of Risky Investments," Management Science, INFORMS, vol. 9(3), pages 443-457, April.
    • Handle: RePEc:inm:ormnsc:v:9:y:1963:i:3:p:443-457
    DOI: 10.1287/mnsc.9.3.443
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    Cited by:

    1. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    2. Marcin Dec, 2021. "From point through density valuation to individual risk assessment in the discounted cash flows method," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5621-5635, October.
    3. Klein, Martin & Deissenroth, Marc, 2017. "When do households invest in solar photovoltaics? An application of prospect theory," Energy Policy, Elsevier, vol. 109(C), pages 270-278.
    4. Van Groenendaal, Willem J. H. & Kleijnen, Jack P. C., 2002. "Deterministic versus stochastic sensitivity analysis in investment problems: An environmental case study," European Journal of Operational Research, Elsevier, vol. 141(1), pages 8-20, August.
    5. Constantin Zopounidis & Michalis Doumpos & Dimitrios Niklis, 2018. "Financial decision support: an overview of developments and recent trends," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 63-76, June.
    6. Manel Baucells & Emanuele Borgonovo, 2013. "Invariant Probabilistic Sensitivity Analysis," Management Science, INFORMS, vol. 59(11), pages 2536-2549, November.
    7. Reid, Donald W. & Skees, Jerry R., 1985. "Some Potential Effects of Changing From a Progressive to a Flat Income Tax Rate Structure," 1985 Annual Meeting, August 4-7, Ames, Iowa 278654, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Lau, Hon-Shiang & Lau, Amy Hing-Ling & Kottas, John F., 2000. "A comparison of procedures for estimating the parent probability distribution from a given set of fractiles," European Journal of Operational Research, Elsevier, vol. 120(3), pages 657-670, February.
    9. Uwe Kehrel & Walter Schmitting, 2008. "Jenseits der Grenzen der klassischen Investitionsrechnung: Integration von Vollständigen Finanzplänen, flexibler Planung und Simulation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 19(1), pages 59-83, May.
    10. Hon-Shiang Lau & Amy Hing-Ling Lau & Chrwan-Jyh Ho, 1998. "Improved Moment-Estimation Formulas Using More Than Three Subjective Fractiles," Management Science, INFORMS, vol. 44(3), pages 346-351, March.
    11. Marcin Dec, 2019. "From point through density valuation to individual risk assessment in the discounted cash flows method," GRAPE Working Papers 35, GRAPE Group for Research in Applied Economics.
    12. Rajaratnam, Myuran & Rajaratnam, Bala & Rajaratnam, Kanshukan, 2014. "A novel equity valuation and capital allocation model for use by long-term value-investors," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 483-494.
    13. Christian Toll, 2018. "Zur Bewertung einer Unternehmensspaltung aus Sicht der Anteilseigner des zu spaltenden Unternehmens [Valuation of a Corporate Demerger from the Shareholders’ Point of View]," Schmalenbach Journal of Business Research, Springer, vol. 70(1), pages 155-204, March.
    14. Jean-Paul Paquin & Alain Charbonneau & David Tessier, 2015. "The derivation of the NPV variance of a risky capital investment project with first-order autoregressive cash flows and autoregressive conditional heteroscedastic variances," Applied Economics, Taylor & Francis Journals, vol. 47(12), pages 1170-1186, March.
    15. Borgonovo, Emanuele & Gatti, Stefano, 2013. "Risk analysis with contractual default. Does covenant breach matter?," European Journal of Operational Research, Elsevier, vol. 230(2), pages 431-443.
    16. Nibouche Fatima & Belmokhtar Oumhani, 2009. "Corporate Model of the Algerian National Marble Company," Folia Oeconomica Stetinensia, Sciendo, vol. 8(1), pages 19-48, January.
    17. Montes, Germán Martínez & Martín, Enrique Prados, 2007. "Profitability of wind energy: Short-term risk factors and possible improvements," Renewable and Sustainable Energy Reviews, Elsevier, vol. 11(9), pages 2191-2200, December.
    18. Anderson, J.R., 1989. "Forecasting, uncertainty, and public project appraisal," Policy Research Working Paper Series 154, The World Bank.
    19. Grubbström, Robert W., 2022. "On the net present value distribution affected by a random walk process," International Journal of Production Economics, Elsevier, vol. 250(C).
    20. Carmichael, David G. & Ballouz, Joseph J. & Balatbat, Maria C.A., 2015. "Improving the attractiveness of CDM projects through allowing and incorporating options," Energy Policy, Elsevier, vol. 86(C), pages 784-791.
    21. Zopounidis, C., 1999. "Multicriteria decision aid in financial management," European Journal of Operational Research, Elsevier, vol. 119(2), pages 404-415, December.
    22. van Groenendaal, W.J.H. & Kleijnen, J.P.C., 1997. "On the assessment of economic risk : Factorial design versus Monte Carlo methods," Other publications TiSEM fd2a2307-0812-4543-8151-7, Tilburg University, School of Economics and Management.

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