| Modern Portfolio Theory is mainly about the measurement of risk and the pricing of assets. Markowitz's remarkable research of《Portfolio Selection》has been the milestone of the Financial Pricing Model. Sharpe and Lintner etc. developed CAPM based on the work of Markowitz, and Ross etc. provided with APT. All of these have built the framework of the asset pricing theory of capital market.Non-arbitrage equilibrium analysis is a fundamental fashion of modern Finance, and it involves the assumptions of full rationality, risk neutrality, and risk-free arbitrage. Arbitrage uses the opportunities of mispricing of assets, abnormal relationship between stocks'prices, and market's inefficiency to buy the under-valued assets and short-sell the over-valued assets, which means that earning is free of risk.However, there has been found a lot of anomalies in the security market, including calendar effect, momentum and reversal, and size effect etc. And this means that spread is still there with the existence of arbitrage. In fact, there have been lots of arbitrage opportunities not utilized which is contrary to the fundamental of non-arbitrage equilibrium.Studies about Statistical Arbitrage are mainly focused in securities market index and index future, which test Statistical Arbitrage opportunities in constituent shares and follow the index with Statistical Arbitrage strategy. In recent years, scholars concentrate on the dynamic characteristic of security'price and test of market efficiency.The participants in security market, especially fund companies, mainly focused on the realization and application of Statistical Arbitrage strategy, but the results of studying were kept only inside the industry. Along with the development of computational modeling technique and the success of Statistical Arbitrage strategy, Statistical Arbitrage model became more and more important to the scholars and investors.In this thesis, we think the generalized concept of Statistical Arbitrage is an investment strategy that seeks to identify the relative mispricing relationship between stocks. The investment strategy entails buying the undervalued stocks or portfolio while short-selling the overvalued stocks or portfolio, and the mispricing of the whole portfolio is expected to be corrected in the future. And we consider Pairs Trading a special case of Statistical Arbitrage which is involved with only two stocks.Market neutrality is the core concept of Statistical Arbitrage and Mean-Reversion is its key characteristic. In general, one single portfolio can not be strictly market neutral, but many Statistical Arbitrage portfolios together could be perfectly market neutral. And Statistical Arbitrage strategy which is irrelevant with market has the feature of mean-reversion. This means that if time series is stationary, asset price will revert back to its mean. So we can design the trading signal system to find whether the price is significantly away from the long-term mean.Statistical Arbitrage can be based on Fundamental Analysis, Technical Analysis, Finance, Econometrics, Time Series Analysis, and other Mathematical or modeling methods. In this thesis, we use Cointegration to measure the spread between the long and short equities of the Statistical Arbitrage portfolio. Of course, it's a parametric method.Since 1970s, the empirical studies about Asset Pricing and Efficient Market Hypothesis have found the phenomena that are contradictory with CAPM and EMH, called Anomalies. In the past 30 years, scholars have been trying to explain the origin the Anomalies through the investors'rationality and the limitation of arbitrage. But there is still not accordant view towards the origin of the Anomalies among the scholars.No arbitrage opportunity and equilibrium analysis is a basic fashion of modern Finance, which involves the assumptions of full rationality, risk neutrality, and risk-free arbitrage. But market anomalies have been constantly found and spread doesn't vanish fast with the existence of arbitrage. In fact, there have a lot of arbitrage opportunities which have not been utilized by the investors. Absolutely this is contradictory with the assumptions.Efficient Market Hypotheses argues that rational arbitrageurs take advantage of the wrong views of non-rational speculators. And the strategies of buying undervalued and short-selling overvalued could make the security'price move to its value. So the result of the arbitrage is a market with better efficiency without anomalies.Behavioral Finance considers that rational arbitrageurs are not full rational, they are limited rational with imperfect information and knowledge. Behavioral Finance divides the investors into rational arbitrageurs and noise traders. The existence of noise traders makes the rational arbitrageurs ignore the fundamental information and make use of noise traders'reaction to earn smart money. At some extent risk arbitrageurs became the noise traders, and this could weaken the market efficiency. The behavioral inclination is the main reason of the limited arbitrage.In sum, Asset Pricing theory, EMH and Behavioral Finance would keep on arguing about the anomalies. But in some meaning, no matter what the arguing would be in the future, the market anomalies would always be there in the security market.We find that existence of security market anomalies is Statistical Arbitrage opportunity's necessary condition.In general, the anomalies reflect the difference between the market price and the equilibrium price. And we consider the difference as mispricing. Statistical Arbitrage captures the anomalies by depicting the relationship of mispricing and through this way the expectation earning can be achieved. So Existence of security market anomalies is Statistical Arbitrage opportunity's necessary condition, and Statistical Arbitrage opportunity comes from the short-term market difference between market price and asset pricing model or market euqulibrium price, which is caused by the problems of the market friction and information asymmetry and market participants'rationality.By Cointegration, we know that the short-term difference will be corrected in the long run and recover to its long-term equilibrium relationship. And mean-reversion is an important feature of Statistical Arbitrage which means volatility will move to 0. So from the point of long-term view, Cointegration and Statistical Arbitrage strategy are consistent. We can build equities portfolios by the method of Cointegration, and the short-term difference of can be viewed as profitable Statistical Arbitrage opportunities.In the empirical part of the thesis, we concentrate on the test of the effectiveness of the Statistical Arbitrage strategy based on Cointegration.First, based on the relationship of Cointegration we build portfolios which involves 2, 3, and 4 equities from the 30 constituent shares of DJIA 30. Second, we choose 1, 2, and 3 years as in-sample term.Third, we design the trading standard as 0.75σ, 1σ, 1.5σ, and 2σ(σis in-sample unconditional standard deviation).At last, out-sample test of performance can be applied.The results of out-sample performance of the Statistical Arbitrage strategy show that the strategy is effective, which is also compared with DJIA 30. At the same time, stable Sharpe ratios tell us the effectiveness of the strategy, while the trading standards and the holding duration need to be determined by the cost and risk preference of the investors. |
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