The link between asymmetric and symmetric optimal portfolios in fads models

Abstract

We study a financial market where asymmetric information, mispricing and jumps exist, and link the random optimal portfolios of informed and uninformed investors to the deterministic optimal portfolio of the symmetric market, where no mispricing exists. In particular, we show that under quadratic approximation, the expectation of the random optimal portfolio in the asymmetric market is equal to the optimal deterministic portfolio in the symmetric market. We also compute variance bounds of the optimal portfolios for investors having logarithmic preferences, and prove that the variance of optimal portfolios are bounded above by a simple function of the mean–reversion speed, level of mispricing, and the variance of the continuous component of the return process of the asset.