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On CAPM and Black–Scholes differing risk-return strategies

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  • McCauley, Joseph L.
  • Gunaratne, Gemunu H.

Abstract

In their path-finding 1973 paper, Black and Scholes presented two separate derivations of their famous option pricing partial differential equation. The second derivation was from the standpoint that was Black's original motivation, namely, the capital asset pricing model (CAPM). We show here, in contrast, that the option valuation is not uniquely determined; in particular, strategies based on the delta-hedge and CAPM provide different valuations of an option although both hedges are instantaneouly riskfree. Second, we show explicitly that CAPM is not, as economists claim, an equilibrium theory.

Suggested Citation

  • McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "On CAPM and Black–Scholes differing risk-return strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 170-177.
    • Handle: RePEc:eee:phsmap:v:329:y:2003:i:1:p:170-177
    DOI: 10.1016/S0378-4371(03)00588-0
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    References listed on IDEAS

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    1. B. Rosenow & V. Plerou & P. Gopikrishnan & H. E. Stanley, 2001. "Portfolio Optimization and the Random Magnet Problem," Papers cond-mat/0111537, arXiv.org.
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    Cited by:

    1. Chargoy-Corona, Jesús & Ibarra-Valdez, Carlos, 2006. "A note on Black–Scholes implied volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 681-688.

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    2. McCauley, Joseph L. & Gunaratne, Gemunu H., 2003. "On CAPM and Black-Scholes, differing risk-return strategies," MPRA Paper 2162, University Library of Munich, Germany.

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