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An Economic Index of Relative Riskiness

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  • Amnon Schreiber

Abstract

In their seminal works, Arrow (1965) and Pratt (1964) defined two aspects of risk aversion: absolute risk aversion and relative risk aversion. Based on their definitions, we define two aspects of risk: absolute risk and relative risk. We consider situations in which, by making an investment, an agent exchanges a certain amount of wealth w by a random distributed level of wealth W. In such situations, we define absolute risk as the riskiness of a gamble that is distributed as W-w, and relative risk as the riskiness of a security that is distributed as W/w. We measure absolute risk by the Aumann and Serrano (2008) index of riskiness and relative risk by an equivalent index that we develop in this paper. The two concepts of risk do not necessarily agree on which one of two investments is riskier, and hence they capture two different aspects of risk.

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  • Amnon Schreiber, 2012. "An Economic Index of Relative Riskiness," Discussion Paper Series dp597, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp597
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    References listed on IDEAS

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    1. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    2. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    3. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    4. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    5. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    7. , P. & ,, 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society, vol. 8(2), May.
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    Cited by:

    1. , & ,, 2015. "The Foster-Hart measure of riskiness for general gambles," Theoretical Economics, Econometric Society, vol. 10(1), January.
    2. Moti Michaeli, 2014. "Riskiness for sets of gambles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 515-547, August.
    3. Yang, Jen-Wei, 2024. "Benchmark-based strategy for minimizing Riskiness," Finance Research Letters, Elsevier, vol. 60(C).
    4. Chen, Yi-Ting & Ho, Keng-Yu & Tzeng, Larry Y., 2014. "Riskiness-minimizing spot-futures hedge ratio," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 154-164.
    5. , P. & ,, 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society, vol. 8(2), May.

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