A non linear generalization of arbritage pricing theory

Arbitrage Pricing Theory (APT) leads good estimates of expected utility stock returns by means of k factors. Notwithstanding initial skepticism the idea of using multiple risk factors to explain the relationship between expected return and asset risk has been winning. In literature the APT has been seen as a generalization of single risk factor approach of Capital Asset Pricing Model (CAPM). The APT provides a better indication of asset risk and a better estimate of expected return than CAPM does. In this paper we propose a generalization of APT to non-linear case. In order to study the relationships which occur between return and multiple risk factors, we propose non-linear principal components. To find justifications for embracing a more complicated model than traditional APT we evaluate the consistency of results by known real data