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

@inproceedings{Vovk2011TheCA,
  title={The Capital Asset Pricing Model as a corollary of the Black – Scholes model},
  author={Vladimir Vovk},
  year={2011}
}
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… CONTINUE READING