**The Capital Asset Pricing Model as a corollary of the Black-Scholes model.** / Vovk, Vladimir.

Research output: Working paper

Published

**The Capital Asset Pricing Model as a corollary of the Black-Scholes model.** / Vovk, Vladimir.

Research output: Working paper

@techreport{48f346d135fe4f60bdf7c90b6849211e,

title = "The Capital Asset Pricing Model as a corollary of the Black-Scholes model",

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.",

keywords = "Black-Scholes model, efficient market hypothesis, efficient index, CAPM",

author = "Vladimir Vovk",

note = "arXiv report",

year = "2011",

month = sep,

day = "23",

language = "English",

type = "WorkingPaper",

}

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AU - Vovk, Vladimir

N1 - arXiv report

PY - 2011/9/23

Y1 - 2011/9/23

N2 - 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.

AB - 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.

KW - Black-Scholes model

KW - efficient market hypothesis

KW - efficient index

KW - CAPM

M3 - Working paper

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

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