Fractional return and fractional CAPM

Abstract

The explanatory power of the capital assets pricing model (CAPM) is low because, it uses parsimonious modelling and differenced data. Overdifferenced asset prices show lower R 2 values than the data with I(1) property (i.e. first difference of them give ADF-test–statistics near to the critical level). The CAPM of fractionally differenced series has a higher R 2 than the traditional CAPM. Fractional return, or generalized return, is a long-run concept that is consistent with long-run CAPM. Various estimation methods, such as robust estimators, or alternative models, such as arbitrage pricing theory (APT), cannot handle the loss of information that occurs when data are transformed to the stationary series.