استراتژی مقیاس زمانی ترکیبی در مدیریت پرتفوی

The fluctuation in the prices in a stock market can be separated into two time scales: a long term trend guided by financial principles and a short term trend governed by the specific trading mechanisms used. We proposed a mixed strategy for managing stock portfolios in which the long term trend is tracked by Markowitz's theory of mean variance analysis, and the short term fluctuation in stock price is monitored by a trading threshold. This strategy is tested in a two-stock portfolio formed from twenty four selected stocks in the Hang Seng Index from July 10 2007 to July 21 2009, which covers the financial Tsunami in 2008. In our mixed strategy, the test is based on a periodic trading with a period of ten trading days. At the beginning of each trading period, a two-stock portfolio that has the optimal Sharpe ratio among all the possible combination of 24 chosen stocks from the Hang Seng Index is selected using mean variance analysis. This is accomplished through a two steps process that involves a maximization of the Sharpe ratio for each pair with an implementation of the worst scenario hypothesis and a threshold that control the activation of trading. Then we examine the price fluctuation of the chosen stocks to determine the trading action. A trading threshold is proposed to facilitate the trading decision so as to ensure that the price of the selected portfolio will likely follow a rising trend on the decision day. The yield of the portfolio based on this mixed strategy is compared to the Hang Seng Index and the averaged price of the 24 stocks over the same period. The results show that this strategy of portfolio management yields a factor of 1.6 of the initial value, whereas the corresponding yield of the Hang Seng Index is a decrease in value by a factor of 0.8. Over the period of two years for the comparison, the investment using our mixed strategy in portfolio management maintains a positive return for a wide range of trading threshold, from a few days to one month. Our choice of a trading period of 10 days reduces the transaction frequency in order to avoid the penalty of transaction fee. Our strategy therefore allows higher flexibility in the trading scheme for investors of different trading habits. An important observation of our strategy is that it preserves the assets over the Tsunami in 2008, which is important to conservative investors who prefer protection in the worst situation.

The problem of financial resource allocation in portfolio management has been of research interest since the seminal work on the mean variance analysis by Markowitz, 1952 and Markowitz, 1959. The mean variance analysis, which is a mathematical formation of the concept of diversification, suggests that the selection of two or more assets for investment can lower the risk involved in the investment of any individual asset, thereby providing a guideline in risk control in portfolio management. Markowitz's theory provides a simple and elegant solution for resource allocation, such as in the fraction of money invested in each constituent stock in the two-stock portfolios by specifying the investment frontier and the risk tolerable by the investor. In practice, however, one does not have a static picture of the mean nor the variance as they are time dependent. To handle this problem, pattern recognition (Fukunaga, 1990 and Zemke, 1999), genetic algorithm (Szeto et al., 1997, Szeto and Cheung, 1997 and Szeto and Cheung, 1998), neural network (Froehlinghaus & Szeto, 1996), and fuzzy rule (Fong and Szeto, 2001 and Szeto and Fong, 2000) are some of the approaches that have been applied in real application. In this paper, we introduce two different time scales into the mean variance analysis. First of all, we assume that the long term behavior provides guidance to the trend of the stock in the near future. This point of view on the importance of long term behavior in resource allocation is very different from the point of view on time series forecasting, where the predictive power of a forecast relies heavily on an intelligent data-mining algorithm, applied not on the long or medium term data, but on the news and fluctuation of the market in the past few days. In order to accommodate the fluctuation in stock price in the short term, it will be desirable to incorporate these two points of view, so that we have a general platform to construct a resource allocation algorithm, with the definition of the long time scale and short time scale given by the user. Recently, we have investigated a multi-agent system of stock traders, each making a two-stock portfolio using the mean variance analysis (Chen et al., 2008). The results of this work show that there exists portfolio with low risk and high return, in spite of the random nature of the stock price and the unknown mechanism between the price variations of individual stock. Indeed, in all the works on portfolio management involving stocks, a common goal is to pursue high return, low risk and consistent performance. On the other hand, we are also aware of the short term nature of the correlation of the stock price, which can be as short as 1–2 days (Chen & Szeto, 2011). Therefore, it is desirable to extend our previous works by considering both the long term and short term conditions for portfolio management. Furthermore, we perform the portfolio selection and trading over a fixed period, thereby reducing the frequency of trading in order to avoid the penalty of the transaction fees. This constraint on the trading period also provides more flexibility in the trading scheme for investors of different trading habits in practical application. The final result should produce an algorithm that avoid frequent trading, while providing a good guidance for selecting stock combination that yield good profit with low risks. Such algorithm is ideal for conservative investors who can regularly enjoy consistent yield with low risk.

We have proposed a rather conservative strategy of investment using the time dependent mean variance analysis on a two-stock portfolio. The time dependence covers both the long term aspect of the pair of stocks, as well as the short term fluctuation of the stock prices. The long term aspect is determined by computing the “Sharpe ratio” at time t, while the short term stock price return provides a risk control through a trading threshold. By setting a critical value for the trading threshold, we can avoid loss caused by the transaction fees incurred by frequent trading. Numerical simulation of this mixed time scale strategy with real data on a set of blue chips in the Hang Seng Index indicates good return on the bull market and small loss on the bear market. The overall performance of our strategy beats the performance of the average performance of the chosen set of stocks, as well as the Hang Seng Index. This strategy should therefore be suitable for conservative investors. Moreover, mean variance analysis is quite general. Therefore, the portfolio selected by the mean variance analysis should perform well universally for different stock markets. Since the stock purchase criteria incorporating the short term stock price fluctuation do not rely on information of particular stock markets, we expect our analysis works also well on stock data outside Hong Kong market and the American market.