Reference Price Updating, Adaptation, and Trading Volume

Abstract

Trading an individual stock in mental accounting, crowd’s traders usually buy and sell in terms of narrowly defined gain and loss relative to a reference price about a behavioral value rather than a fundamental value on a trading day. A reference price is the price where trading volume or trading weight is the maximal across different prices on a trading day. The trading action generates a limited number of patterns about cumulative trading volume distribution over a price range because of mental accounting, loss aversion, trading weight, and coherence or agreement in trading. However, a reference price is updated to realize a significant gain and loss from time to time after a large imbalance on a trading day. We study how a past gain or loss elicits people to trade more or less frequently in a time series. We examine their adaptive behaviors to gain or loss in trading by analyzing correlation between realized gain or loss and change in total trading volume in any two consecutive trading days. Crowd’s traders update a reference price about the value of an individual stock via learning and generate a significant realized gain or loss. They adapt to the gain and loss realized by the updating via trading volume increase or decrease significantly in any two consecutive trading days. Our study makes distinction on two types of a reference price in multiple reference prices in trading: a reference price about a value in a time interval and a reference price about realized gain or loss in a time series. It also captures the coexistence of apparently contrary attitudes to risk from crowd’s traders in stock market: risk aversion from sellers and risk seeking from buyers in the gains of high probability; and risk seeking from sellers and risk aversion from buyers for the losses of high probability.