The game-theoretic capital asset pricing model

Using Shafer and Vovk’s game-theoretic framework, we derive a capital asset pricing model from an efficient market hypothesis, with no assumptions about the beliefs or preferences of investors. Our efficient market hypothesis says that a speculator with limited means cannot beat a particular index by a substantial factor. The model we derive says that the difference between the average returns of a portfolio and the index should approximate, with high lower probability, the difference between the portfolio’s covariance with the index and the index’s variance. This leads to interesting new ways to evaluate the past performance of portfolios and funds.