Aribitrage Research Under Noise Trading

The efficient market theory suggests that price spread will always be corrected and noise traders will always be eliminated by rational arbitrageurs. But the noise trading theory and limited arbitrage theory questioned this view. The noise trading theory demonstrated that noise traders can get positive returns in the market and can survive long-term. And limited arbitrage theory argues noise trading risk and fundamental risk will limited arbitrage. In such circumstances, this article attempts to analysis noise trade and its impact on the arbitrage,and then under the influence of noise trading ,conduct a study on the arbitrage-related problems(portfolio allocation in arbitrage and pair trading etc). The essay divided into four parts:(1)We start with the long-term survival of noise traders , market performance of noise trading ,and then empirical calculate discount and excess volatility in close-end fund in China. After that we advocates a noise trading measurement methods, and uses daily data to description noise trade features in Chinese stock market. Next, a correlation analysis and Granger causality test between noise trading and price behavior is examined.The result show that: the same period of noise trading ,volatility, liquidity were significantly positive correlation. And noise trade can raises the level of trading activity, but extended the price volatility.(2)Under the margin trading framework, we build a model in which noise trading led to limited arbitrage. In this model, uncertainty noise trading makes the no risk asset be riskly, arbitrageurs arbitrage behavior will change, arbitrageurs will not take fully ability to correct the price deviations. We also obtain the arbitrage traders's optimal investment strategy, and have a simulation analysis of this strategy.( 3)Considering noise trading risk, we derive the optimal dynamic strategy for arbitrageurs with a finite horizon and log utility facing a mean-reverting arbitrage opportunity. The optimal dynamic strategy is a function of mean-reversion coefficient, spread deviation, correlation coefficient between the assets, volatility, remaining time. Following this strategies, when mispricing divergence, the arbitrageur first increases his positions to bet more, but if mispricing goes on divergence beyond a critical value, the arbitrageur begin to cut off some positions. In the arbitrage process, the mean return is higher than or equal to risk-free return at every time, even so arbitrageur typically experiences losses in some cases, but the probability of these situations become smaller as the arbitrage horizon longer. At last we find spread path with smaller mean and variance have the bigger return under the optimal strategy.(4)Considering the impact of noise trading on arbitrage, we build dynamic adjust pair trading strategies. Introduced the dynamic portfolio adjustment strategies and dynamic positions adjustment strategies ,we canculate the return of these pair tradeing strategy use Chinese securities market date, and compared return, transaction characteristics with pair trading strategies not introducing dynamic adjust strategies.