Quantitative Investment:From Behavioral Finance To High Frequency Trading

Quantitative investment has history of more than thirty years in the oversea market and its market occupancy is still increasing because of its stable investment performance. In the domestic market, it gains quick development and more attention than other invest-ment techniques, although it is still at the primary stage. Trading strategy is the core of quantitative investment. And whether the investment will gain profits depends on the trading strategy mainly. Because of the importance of the trading strategy, this paper studies several trading strategies under behavioral finance and high frequency trading and we discuss the application of them.In behavioral finance, we mainly discuss the momentum strategy(Wang,S. and Zheng, W.A.[93]). In real financial market, lots of stylized facts can not be explained by classical finance. And these phenomena are called financial anomalies. Among these anomalies, momentum effect and reversal effect are two important facts. And there has been lots of research about the existence and source of them. Among the research about source of momentum effect, Hong-Stein model is the typically unified theory of momentum effect and reversal effect. Under Hong-Stein model, the equilibrium price function can generate momentum and reversal effect. However, this model tends to reach two extremes while it can generate momentum and reversal effect. On the one hand, the autocorrelation in the return sequence of basic equilibrium price functions is so distinct that the price change direction can be forecasted on the basis of the nearest price change direction. On the other hand, the autocorrelation in extended equilibrium price functions is so faint that the elements in the resulted return sequence are close to be independent of each other. About the two extremes, we design the corresponding test statistics and do the test in data of several countries indices. The test result shows that the two extremes will be rejected. In addition, we test the classical momentum strategy in A share market and the commodity futures market. The test result shows that there is no significantly positive profit from the momentum strategy in A share market while it can generate significantly positive profit in commodity futures market. Based on the discussion of Hong-Stein model, we construct the momentum strategy with stochastic holding period and we also test its profitability in A share market and commodity futures market. From the test results we can find that that the momentum strategy with stochastic holding period can generate significantly positive profit both in A share market and commodity futures market. And we can find that the returns of the strategy can not be explained by the related risk factors after the risk analysis, which also means that China market is not weak efficient.In the discussion of momentum strategy, we find that, although as a kind of low frequency trading strategy momentum strategy can absorb large volume of capital to invest in large amounts of assets and it can also generate significantly positive returns, it has some shortcomings. There are several main shortcomings. The position is open for long time and the cost of capital is high. During the position holding period, the book returns will be easy to fluctuate and the large return drawdown will impose high pressure to the investors. The longer position holding period will also increase the volatility of the return sequence, which will reduce the Sharpe Ratio of the strategy. Additionally, the exchange has provided more and more detailed data and the high frequency data can provide information that can not be revealed in low frequency data, such as information of market microstructure. The low frequency strategy has ignored these information. And this inspires us to develop high frequency trading strategy to overcome the problems in low frequency trading strategies.In high frequency trading, we construct the strategy based on a kind of technical indicator (Parabolic Stop and Reversal, Parabolic SAR) and study its application(Wang,S. and Zheng,W.A.[94]). Technical analysis is an important component in high frequency trading and technical indicator is the foundation of technical analysis. Since technical indicator are mainly the statistics of price and the pricing theory is the main question in mathematical finance, it is appropriate for us to discuss the trading strategy based on technical indicator in mathematical finance framework. Parabolic SAR is an important trending indicator and different from other trending indicators because of the property of tracing price accelerated. According to the definition of SAR, the value of SAR at each time depends on the initial value, which is complicate to the calculation of SAR. In this paper, we discuss the definition of new indicator based on truncated SAR. And we also define the new indicator of Xt as the difference between price and new SAR, since the new SAR also traces around the price sequence. We prove the stationary of Xt under Black Scholes model and the simulation data and the test based on this data support the stationary of Xt. According to Xu we design the trading strategy in this paper. And we test the profitability of the strategy on the high frequency data of China A share market. In the test of profitability of the trading strategy, we do the standard t test of the significance of the strategy returns. And we apply the residual bootstrap analysis to do the test of profitability of the trading strategy under GARCH classes models. The test results show that the strategy can generate significant buy return and sell return. Since high frequency trading is still in the rapid development and it can bring huge amount of profits to the institutional investors, lots of strategies are kept secret and the outside can not know the detailed information of the strategies. In this we discuss a kind of specific strategy and the profitability of this strategy has also been tested in the real application of investment. As a result, on basis of real investment application and the theory development, this paper is of much importance to the research of high frequency trading.