| Along with the constant development of China's securities investment fund and the constant improvement in the system of stock market index. Index funds have also begun to be familiar with by more and more investors. The development of indexing investment and the continual emergence of new products of indexing investment, also provide a wide variety of choices for investors. In typical portfolio delegation, the investor assigns the management of assets to a portfolio manager who is given the task of beating a benchmark. When the investor observes out performance by the active portfolio, the issue is whether the added value is in line with the risks undertaken. This issue is particularly important when performance fees are involved. Performance fees induce an option-like pattern in the compensation of the manager, who may have an incentive to take on more risk to increase the value of the option. To control this behavior, institutional investors commonly impose a limit on the volatility of the deviation of the active portfolio from the benchmark, which is also known as tracking-error volatility (TEV).From Roll.Richard (1992) bringing forward the tracking error to Jorion (2003) making the improvement of the model. As an effective management theory in the modern portfolio, tracking error by now has been widely applied in the financial services industry. And it become a good method to solve the agency problem, which is that it induces the manager to optimize in only excess-return space while totally ignoring the investor's overall portfolio risk. By comparison, the domestic research about tracking error still lags behind the abroad, so further research on the tracking error is very important. This has important practical significance for index fund evaluation mechanism and solving the agency problem in the investment portfolio.The review of existing research results at home and abroad in the tracking error shows the implication of the indexing investment, which leads to the definition of tracking error, causes and factors which can influence it. Through summarizing the use of tracking error in the indexing investment, we make out that tracking error play an important of the indexing investment. And in this part, we summarize the methods of performance evaluation of the investment portfolio, including tracking error. Then after comparing several foreign classical models on the tracking error, we explain the advantages of the Constant-TEV optimization model, which will use our financial market data in order to empirically test whether the results can be as good as the nature of foreign data. We point out that the Constant-TEV optimization model is not only in the form of an improved method, but also a risk management mechanism in I the indexing investment, that is, while focusing on the local risk, we should pay attention to control the overall risk.When comes to the selection of models, in addition to recalling the traditional Markowitz mean-variance model, we mainly compare the TEV optimization model put forward by Roll and the Constant-TEV optimization model gave by Jorion, and the calculus of the model is given in more detail too, explaining that the latter is more advantageous in terms of risk control, which is further described in the empirical analysis of the data of our financial market. In the process of empirical research, we mainly use Eviews and Matlab software.We select the data according to the principles, which should be followed when to select or build a good benchmark, such as: broad representative of the market, having the investable and reproductive qualities, and having a reasonable and transparent way and maintaining rules. What's more, the broad market's identity is also needed, and the actual situation of China's securities market must be taken into account too. In this paper, we evaluate the performance of the investment portfolio by the choice of benchmark consisted of stock market index and the bond market index in Shanghai Stock Exchange. From the stock market index, as a contrast, we choose A Stock Index, 180 Index, 50 Index, and the Public Index, Industrial Index, Business Index, Tract Property Index in the Shanghai Stock Index. And we choose Public Debt Index in the bond market in Shanghai Stock Exchange.Based on the review of development and the theoretics of tracking error, by using Constant-TEV optimization model integrated with actual situation in China, involving China's Shanghai Stock Exchange stock index data and bond index data, this passage do the empirical analysis of optimization problems of indexing investment and get the following conclusions: 1. Throughout the whole indexing investment process, tracking error is an important conception of indexing investment. It is not only an important risk controlling tool during the indexing investment process,but also an important indicator measure of investment performance. Tracking error is the result of a variety of factors working together: Among them, the number of stocks involved in the indexing investment, value ofβ, volatility of benchmark, and the different styles of benchmark portfolio investment constitute the main factors affecting tracking error.2. This paper also examined the effects of Constant-TEV optimization model with the domestic data. And by the empirical study which is based on the feasibility of the investing strategy of tracking error optimization model in China's securities market, specially when constant-TEV optimization's control of total risk played an important role in resolving agency problem, we get the conclusions: during the sample period, simulated delegation combinational index invest when it was kept on a less tracking error can gain the target index yield by most approximately, and at the same time with the smaller payment for risk we can get a maximize benefit.3. Constant TEV optimization improved the defects of the original optimization TEV which only focus on local risk, and by the controlling total risk we also can bound the Fund Manager's relative behavior. In fact, by using this method which presents a risk prevention mechanism, we also can get a solution to the authorized agent problem between the owner and founder of the found. Focusing on the local risk, we should also pay attention to the risks of total control, and present on how to calculate the total risk. This is also for our future in addressing other risks that may be encountered in providing the ideas for solving the problems and guidance.From the time of the theory's origin, the tracking error as a new theory of the risk control and performance evaluation in the indexing investment, is still in the development stage, and there are many issues worthy of further study. We believe that with the continuous development of China's securities market and improving theoretical studies much further, tracking error theory will give a better service to investors. |
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