基於線性回歸改良報酬與風險的評估策略並結合演化計算解決投資組合最佳化問題

Portfolio Optimization Problem Based on Novel Return and Risk Assessment Strategy Improved by Linear Regression Model with Evolutionary Algorithm

劉懿誼(I-I Liu)

指導教授 ： 周耀新

國立暨南國際大學/科技學院/資訊工程學系/碩士(2016年)

摘要

在股票市場中投資，首要面對的就是選股問題，而如何挑選出兼顧低風險且高報酬的投資組合是個值得探討的問題。夏普值是目前被廣泛使用的選股指標，用以計算每單位風險的報酬，設計理念是在固定報酬中選擇低風險或是在固定風險中選擇高報酬。夏普值對於風險的定義是標準差，也就是每日資金水位對於平均線計算波動大小，因此能避免投資大跌的投資組合，但缺點是會將趨勢穩定上漲的投資組合也視為風險大而不選擇，因此錯失投資機會。而且在報酬率為負時，夏普值的算法會使投資人認為風險大的投資組合才是較好的。

因此本研究提出一個新的選股指標「趨勢值」，延續夏普值選擇低風險且高報酬的理念，且利用投資組合的趨勢改良報酬與風險的定義。以一次線性回歸的趨勢線代表投資組合的趨勢，趨勢線的斜率為報酬，而風險則是每日資金水位對於趨勢線計算波動大小，並在報酬為負時調整公式算法。這種評估方式不僅找到投資組合整體的趨勢，更改良了夏普值對於風險的定義，更加符合投資人的心情波動，趨勢值比起夏普值更能評估一組投資組合的品質，將趨勢穩定上漲且風險小(低風險且高報酬)的投資組合推薦給投資人。本研究利用基因演算法且編碼不限制投資組合的檔數，實作於臺灣股票市場，在臺灣50 ETF成分股中找出一組趨勢值最高的投資組合。此外，利用滑動視窗的訓練和測試方式，定期更換投資組合，避免股票領域常見的過度適應問題。

實驗結果發現投資組合比起只投資單檔更能降低風險，而且本篇方法提出的趨勢值的表現會比買進持有臺灣50 ETF策略還要好，也比傳統所使用的夏普值更能夠找到趨勢穩定上漲且風險小的投資組合。

關鍵字

選股 ； 投資組合 ； 夏普值 ； 資金水位 ； 一次線性回歸 ； 趨勢 ； 演化計算 ； 滑動視窗

並列摘要

Stock selection is an important and primary issue while investing in the stock market. However, it is worth investigating in the problem of considering not only low risk but also high return on investment while selecting portfolio. From all researches, the Sharpe ratio is the most common criterion of stock selection, and its core idea is that investors would choose and hold portfolios that maximize returns under the given risk or minimize investment risks with the same amount of returns. The standard deviation is used to indicate the risk of portfolio, which is the funds standardization with the average line. From the advantages above, the Sharpe ratio makes investors avoid investing the portfolio with a fallen trend, but also considers the trend that rises stably with high risk. However, the Sharpe ratio considers the portfolio is better with high risk when return is negative.

We proposed a new criterion of stock selection, called trend value. With the same core idea as Sharpe ratio, the system consults the trend of portfolio to improve return and risk assessment strategy. The trend line, found by linear regression model, presents the trend of portfolio. The slope of the trend line presented as return, and the risk is the funds standardization of the line. Besides, we revise the formula when return is negative. This assessment finds a portfolio that rises stably with lower risk. An Evolutionary Algorithm is used to compose the portfolio with the low risk and stable returns in component stocks of Taiwan 50 ETF, and the portfolio is without number constraint. Moreover, Over-fitting is a common problem in the stock market, and this paper uses sliding windows to replace portfolio periodically to avoid the problem. The experiment results show that the proposed method, compared with the Sharpe ratio, is able to identify the optimal portfolio and performs efficiently and outstandingly.

並列關鍵字

stock selection ； portfolio ； Sharpe ratio ； funds standardization ； linear regression model ； trend line ； Evolutionary Algorithm ； sliding windows

參考文獻

[1] William Sharpe, “Investors and Markets: Portfolio Choices, Asset Prices, and Investment Advice,” Princeton University Press, 2011.

[2] Harry Markowitz, “Portfolio Selection,” The Journal of Finance, vol. 7, no. 1, pp. 77-91, 1952.

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