Arbitrage and leverage strategies in bubbles under synchronization risks and noise-trader risks

This paper develops a model that explains the causation of persistent bubbles when arbitrageurs have noticed the overpricing. It has been claimed that a sufficient proportion of arbitrageurs needs to sell over-priced stocks to correct the mis-pricing. However, because each arbitrageur tends to choose his optimal time of entering or exiting the market, there exists a lack of coordination in selling out. Thus, the bubble will continue growing for a considerable period. Moreover, our work incorporates trend followers' impacts on stock prices into the analysis of the duration of bubbles. The derived equilibrium trading strategy suggests that each arbitrageur will wait for a longer period before selling out, compared with the optimal strategy obtained from previous models where only arbitrageurs' coordination risks are considered. This paper presents defects in the Efficient Market Hypothesis. Further, having shown that the duration of mis-pricing is increasing in arbitrageur's leverage ratio, the model provides rationales for regulations on individual use of leverage. This is compatible with the findings in previous literature that macro-prudential policy tools, such as limiting the use of leverages can be more effective than traditional monetary and fiscal policies in taming asset overpricing.