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The Capital Asset Pricing Model as a corollary of the Black-Scholes model

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  • Vladimir Vovk

Abstract

We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is efficient, in the following sense: we do not expect a prespecified self-financing trading strategy whose wealth is almost surely nonnegative at all times to outperform the index greatly. We show that, for a long investment horizon, the appreciation rate of the stock has to be close to the interest rate (assumed constant) plus the covariance between the volatility vectors of the stock and the index. This contains both a version of the Capital Asset Pricing Model and our earlier result that the equity premium is close to the squared volatility of the index.

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  • Vladimir Vovk, 2011. "The Capital Asset Pricing Model as a corollary of the Black-Scholes model," Papers 1109.5144, arXiv.org.
    • Handle: RePEc:arx:papers:1109.5144
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    References listed on IDEAS

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    1. Vladimir Vovk, 2011. "The efficient index hypothesis and its implications in the BSM model," Papers 1109.2327, arXiv.org.
    2. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
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    Cited by:

    1. Vladimir Vovk & Glenn Shafer, 2016. "A probability-free and continuous-time explanation of the equity premium and CAPM," Papers 1607.00830, arXiv.org.
    2. Vladimir Vovk, 2011. "A simplified Capital Asset Pricing Model," Papers 1111.2846, arXiv.org.

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