The Linear Relationship Between Expected Returns and Price of Risk

The linear relationship between assets' expected returns and price of risk as defined by the Arbitrage Pricing Theory does not depend on the number of the non-pervasive risk factors included in the relationship. The linear relationship is decided solely on the grounds that assets expected reurns are linear when conditioned on the risk factors and that there is no arbitrage. However, as investors neglect relevant non-pervasive risk factors, the linear relationship becomes less accurate and has an accuracy flaw linked to the relevance of the neglected factor, that is to say, to its factor loading and standard deviation.