An Exact Pricing Error of the APT within the Arbitrage Framework

We derive an exact deviation for an individual asset from APT Pricing in a finite economy within the arbitrage framework. This deviation is the product of a tradeoff between mean and variance of the efficient arbitrage portfolio, the asset's idiosyncratic variance and the proportion of this arbitrage portfolio represented by the asset. We show that the deviation becomes negligible in an infinite economy if the efficient portfolio is well diversified