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Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?

Author

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  • Robert A. Jarrow
  • Dilip B. Madan

Abstract

We show in any economy trading options, with investors having mean-variance preferences, that there are arbitrage opportunities resulting from negative prices for out of the money call options. The theoretical implication of this inconsistency is that mean-variance analysis is vacuous. The practical implications of this inconsistency are investigated by developing an option pricing model for a CAPM type economy. It is observed that negative call prices begin to appear at strikes that are two standard deviations out of the money. Such out-of-the money options often trade. For near money options, the CAPM option pricing model is shown to permit estimation of the mean return on the underlying asset, its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data covering the period January 1992–September 1994. It is found that the mean rate of return though positive, is poorly identified. The estimates for the volatility are stable and average 11%, while those for the planning horizon average 0.95. The hypothesis that the planning horizon is a year can not be rejected. The one parameter Black–Scholes model also marginally outperforms the three parameter CAPM model with average percentage errors being respectively, 3.74% and 4.5%. This out performance of the Black–Scholes model is taken as evidence consistent with the mean-variance analysis being vacuous in a practical sense as well.

Suggested Citation

  • Robert A. Jarrow & Dilip B. Madan, 1997. "Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?," Review of Finance, European Finance Association, vol. 1(1), pages 15-30.
    • Handle: RePEc:oup:revfin:v:1:y:1997:i:1:p:15-30.
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    File URL: http://hdl.handle.net/10.1023/A:1009779113922
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    Citations

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    Cited by:

    1. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini & Marco Taboga, 2009. "Portfolio Selection With Monotone Mean‐Variance Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 487-521, July.
    2. Husmann, Sven & Todorova, Neda, 2011. "CAPM option pricing," Finance Research Letters, Elsevier, vol. 8(4), pages 213-219.
    3. Cayton, Peter Julian & Ho, Kin-Yip, 2015. "A Nonparametric Option Pricing Model Using Higher Moments," MPRA Paper 79134, University Library of Munich, Germany.
    4. Marco Taboga, 2014. "The Riskiness of Corporate Bonds," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 46(4), pages 693-713, June.
    5. He, Ying & Dyer, James S. & Butler, John C. & Jia, Jianmin, 2019. "An additive model of decision making under risk and ambiguity," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 78-92.
    6. Yuchen Li & Zongxia Liang & Shunzhi Pang, 2022. "Continuous-Time Monotone Mean-Variance Portfolio Selection," Papers 2211.12168, arXiv.org, revised Jan 2024.
    7. Bell, Peter N, 2014. "On the optimal use of put options under trade restrictions," MPRA Paper 62155, University Library of Munich, Germany.
    8. Husmann, Sven, 2005. "On Estimating an Asset's Implicit Beta," Discussion Papers 238, European University Viadrina Frankfurt (Oder), Department of Business Administration and Economics.
    9. Thorsten Hens & Marc Oliver Rieger, 2014. "Can utility optimization explain the demand for structured investment products?," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 673-681, April.
    10. Buchner, Axel, 2015. "Equilibrium option pricing: A Monte Carlo approach," Finance Research Letters, Elsevier, vol. 15(C), pages 138-145.
    11. Chen, Son-Nan & Chiang, Mi-Hsiu & Hsu, Pao-Peng & Li, Chang-Yi, 2014. "Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model," Finance Research Letters, Elsevier, vol. 11(2), pages 161-172.

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