Conditional Estimates of Diffusion Processes for Evaluating the Positive Feedback Trading

Positive feedback trading, which buys when prices rise and sells when prices fall, has long been criticized for being destabilizing as it moves prices away from the fundamentals. Motivated by the relationship between positive feedback trading and investors cognitive bias, this paper provides a quantitative measurement of the bias based on the conditional estimates of diffusion processes. We prove the asymptotic properties of the estimates, which helps to interpret the investment behaviors that if a feedback trader finds a security perform better than his expectation, he will expect the future return to be higher, while in the long term, this bias will converge to zero. Furthermore, the observed deviations between the return forecast and its realized value lead to adaptive expectations in reality, for which we raise an exponential smoothing model as an adjustment method. In the empirical study on the stock market in China, we show the effectiveness of the ES method in bringing the biased expectation closer to the fundamental level, and suggest that the feedback traders, who are often over-optimistic about the return, are likely to suffer from downside risk and aggravate the speculative bubbles in the market.