From Pair Trading To The Momentum Test

With the fast development of Computational Finance and the successful application of statistical arbitrage methods,statistical arbitrage methods and models are receiving more and more attention from both scholars and investors.This paper aims to learn and study statistical arbitrage from the demonstration point of view.On the basis of the theory knowledge,we will explain the ways and means of statistical arbitrage by the demonstration of the pair trading in the stock market and the momentum test in Shanghai stock market.In the demonstration of the pair trading in the stock market,we choose Shanghai Pudong Development Bank(600000) and China Merchants Bank(600036) 2006-2007 two years daily closing quotations.On the basis of the old method,we introduce the time-relative variance which is calculated from the GARCH model to the trade-start condition and stop lose boundary.Mark strategy 1 and strategy 2 respectively for different use of simple standard deviation and time-relative standard deviation.The demonstration results display that the two strategies have small volatilities,explaining the receipts are both steady;at the same time,small betas accord with the market neutral orientation of statistical arbitrage.Besides,the trade chances of strategy 2(16) is much more than that of strategy 1(3),and the receipt of strategy 2 is 28.69%,which is bigger than that of strategy 1(3.36%).The result illuminates that the effect of strategy 2 with the time-relative standard deviation based on GARCH model overmatches that of strategy 1 with simple standard deviation.In the demonstration of the momentum test in Shanghai stock market,we introduce the market neutral property of statistical arbitrage to the investment portfolio.On the assumption that the portfolio can create statistical arbitrage opportunity,we establish the investment portfolio. Then,we test the payoff of the momentum strategy in the holding periods.In the end,we judge whether the market has momentum effect and its size.The main contribution of our approach is that we consider statistical arbitrage models as constrained optimization problems.The constraints include zero beta of the portfolio with respect to market and zero cost of the strategy.We are considering portfolio's variance,the measure of risk.The demonstration results show that①short-term momentum effect of Shanghai stock market is not clear,but contrarian effect is visible;②medium-term momentum effect corresponding the 26 weeks holding periods is obvious;③ besides,the momentum effect in bull market is more distinct,and the contrarian effect in bear market is more distinct.