When we speak of "asymmetric" or "asymmetry" we are mainly referring to the imbalance between profits and losses in tactical asset allocation or active portfolio management decisions. This paper discusses asymmetric response as a human behavior when we respond differently and the persistance of beliefs that is a cause of price drift (trend/momentum).

...asymmetric bias may help explain empirical patterns such as loser momentum and suggests modifications to models of belief persistence in markets

Our second hypothesis is related to motivated reasoning, which should cause
people to scrutinize and distort undesirable information more than desirable information. Hence, biases should be asymmetric such that they are greater for losses than gains. If confirmatory bias were symmetric, reported news for the favored stock (nonfavored) would be positively (negatively) biased for both losses and gains equally.

Abstract

A number of behavioral finance theories posit that investors adhere to prior beliefs in spite of new information. This paper reports the results of an investment experiment which shows that subjects’ inferences are biased by their prior beliefs in a manner that depends on investment outcomes. Specifically, their perception of new information was more positively biased for their prior favored assets when incurring losses than gains. This asymmetric bias may help explain empirical patterns such as loser momentum and suggests modifications to models of belief persistence in markets.

 

Source: http://www.personal.psu.edu/faculty/k/j/kjk14/Info_Proc.pdf