Porfolio Model Improvement Based On Statistics

This paper introduces modern portfolio theories and discusses the possibility to use statistics for the improvement of portfolio models, especially for the optimization of security portfolio.When considering portfolio, we focus on the correlations among assets and the individual return rate. Since latest information does not always spread timely among different capital markets, we have to consider the hysteresis when calculating the correlations. However, the classic portfolio models don't present this phenomenon very well. Meanwhile, the "efficient markets" hypothesis does not exist in a real market environment. Therefore, in the calculation of return rate it is inappropriate that price is the only indicator taken into account in disregard of others. In this article, we will try to improve portfolio model from both the correlation side and the return rate side.During this article, we will use the latest data of HS300 in China market, the global exchange rate market, future & spot market and option & object market to illustrate the existence of hysteresis and the impact to future return rate brought by high turnover.Besides, we will introduce the methodology how to calculate the efficient frontier curve of portfolio model. And a series of mathematical proofs will be given.Based on experiments, we find out that under certain hypothesis, the improved model can uncover the relationship between portfolio's risk and return more exactly. And it better reflects the hysteresis level between securities and the real return rates of them.Finally we choose 20 securities from China stock market to undergo a 2-year, 8-period simulated investment. Based on the result we can see that the improved model is more stable to the old one. Due to the consideration of hysteresis, it has a quick response time which makes it adjust its strategy much faster when the market tendency changes. And also the investments it makes are more reasonable because of high-accurate return rate. Although sometimes this model is too cautious to miss some opportunities when the market is going up, it has good defense when the market is declining. And we believe the improved portfolio model can be applied to the complex market environment nowadays.