考量真實投資情形之線性回歸改善評估策略並結合量子啟發式禁忌搜尋演算法解決投資組合最佳化問題

Solving Portfolio Optimization Based on Quantum-inspired Tabu Search Algorithm and Novel Assessment Strategy Improved by Linear Regression Model with Initial Funds

羅翊慈(Yi-Tzu Lo)

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(2017年)

摘要

當投資者選擇股票做投資時，首要面對的問題就是要選擇投資哪些股票。因此，在股票研究中，選股問題是一個重要的議題。一般來說，在選擇股票時，投資者都會考量風險以及報酬。目前常見被廣泛使用的選股指標就是夏普值，其設計理念為當風險一樣時，選擇高報酬的投資組合；或是當報酬一樣時，選擇低風險的選股指標。然而，夏普值使用標準差來計算投資組合風險，所以處於上漲趨勢的投資組合就會具有高風險，而這將會違反一般投資者的投資心理。因此，本研究提出一個新穎的評估指標─趨勢值。在評估投資組合趨勢時，本研究使用線性回歸來輔助，並同時考量到投資組合的初始資金，因而自行推導從相同初始資金回歸的趨勢線。其趨勢線的斜率為每日預期報酬，背離趨勢線的差值是每日風險。本研究所提出的趨勢值完全改變傳統夏普值用報酬率和標準差評估投資組合的方式，因而不會懲罰上漲的股票，還能夠預測股票的趨勢和報酬，藉此達到在符合真實投資情形時，有效推薦一組穩定上漲的投資組合。在尋找最佳投資組合時，本研究沒有限制投資組的股票檔數，因此需要使用演化計算幫忙在廣大的解空間中找到最佳投資組合。但是，本研究在過程中發現量子啟發式禁忌搜尋演算法存在一些問題，因此提出利用有史以來最佳解及量子領域中的反閘來改進量子啟發式禁忌搜尋演算法。所以，本研究結合趨勢值、改進過的量子啟發式禁忌搜尋演算法及滑動視窗來解決選股的問題。實驗結果可以發現趨勢值找到的投資組合比夏普值所選的更具有穩定上漲趨勢，而且比政府所推薦的台灣50有更好的表現。此外，實驗結果也發現本研究所特別新增的隔年季對季滑動視窗能找到台灣股票的週期性，達到良好的投資效果。

關鍵字

選股 ； 投資組合 ； 夏普值 ； 線性回歸 ； 演算法 ； 趨勢 ； 滑動視窗

並列摘要

The first problem which investors face is stock selection when they invest in stock market. Therefore, stock selection is of paramount importance in stock investment. Generally, selecting stock considers return and risk simultaneously. The common assessment strategy is the Sharpe ratio. However, the Sharpe ratio uses the standard deviation as portfolio risk, so portfolio in uptrend has high risk. It defies investor psyche of most investors. Therefore, this paper proposes a novel assessment strategy, trend ratio. The trend ratio uses the simple linear regression which is improved with the initial funds to find the trend of portfolio. Slope of trend line is daily expected return, and difference between the trend line and the portfolio funds standardization is daily risk. It changes the way of the Sharpe ratio which assesses portfolio by return ratio and standard deviation. Hence, the trend ratio not only can find the portfolio which is in uptrend but also solves the problem of the Sharpe ratio. Besides, this paper does not limit stock number in a portfolio, so it uses the quantum-inspired tabu search algorithm which is improved by the current best-known solution and the quantum not gate (NQTS) to find the best portfolio. In the over-fitting problem, this paper uses the sliding window to avoid. Hence, this paper combines the trend ratio, NQTS and the sliding window to solve the problem of stock selection. The experiment results show our method can find the better portfolio than the Sharpe ratio, and it has better performance than Taiwan 50 ETF which is recommended by the government.

並列關鍵字

stock selection ； portfolio ； Sharpe ratio ； linear regression ； trend line ； evolutionary algorithm ； sliding windows

參考文獻

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