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Jensen’s Inequality in Finance

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  • Samih Azar

Abstract

The purpose of this paper is to measure the size and the statistical significance of three inequalities in the field of financial economics. The three are variants of Jensen’s inequality. The first inequality is a comparison of the expected value of a ratio to the ratio of the expected value, a problem that arises in pricing foreign exchange rates. The second is a comparison of the log of the expected value to the expected value of the log, a problem that arises in testing forward market efficiency, money demand, production functions, and trade gravity models. The third is a comparison of the expected utility to the utility of the expected value, and helps in determining the importance of the expected utility paradigm, and the magnitude of the equity risk premium. The methodology used is by simulation of random normal variables, thereby introducing sampling error. Despite this sampling error the conclusion is general: all three inequalities are economically material, and stand statistically as inequalities. The major conclusion is that Jensen’s inequality is not a theoretical and superfluous exercise in finance as some have advocated. Copyright International Atlantic Economic Society 2008

Suggested Citation

  • Samih Azar, 2008. "Jensen’s Inequality in Finance," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 14(4), pages 433-440, November.
    • Handle: RePEc:kap:iaecre:v:14:y:2008:i:4:p:433-440:10.1007/s11294-008-9172-9
    DOI: 10.1007/s11294-008-9172-9
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    References listed on IDEAS

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    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Jeremy J. Siegel, 1972. "Risk, Interest Rates and the Forward Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 86(2), pages 303-309.
    3. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    4. Eugene F. Fama & Kenneth R. French, 2002. "The Equity Premium," Journal of Finance, American Finance Association, vol. 57(2), pages 637-659, April.
    5. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    6. Goetzmann, William N. & Ibbotson, Roger G., 2006. "The Equity Risk Premium: Essays and Explorations," OUP Catalogue, Oxford University Press, number 9780195148145.
    7. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    8. Mehra, Rajnish & Prescott, Edward C., 2003. "The equity premium in retrospect," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 14, pages 889-938, Elsevier.
    9. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 1.
    10. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 2.
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    Cited by:

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    More about this item

    Keywords

    Jensen’s inequality; Concave and convex functions; Foreign exchange markets; Expected utility; Simulation of random normal variables; Equity risk premium; Power functions; CCAPM; D81; E44; F31; C15;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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