A Novel Portfolio Optimization Based on Funds Allocation with Short Selling Using GNQTS Algorithm and Trend Ratio

[[abstract]]在股票市場投資時，投資者首先會遇到股票選擇的問題，所以選股對股票投資至關重要。因此，選擇潛在的股票組合是一個值得研究的問題。現在常見的一種計算風險–夏普值，是基於現代投資組合理論（MPT）衍生的指標。MPT使用標準差來評估投資組合風險，但這並不符合投資人想要的結果，因為即使在上升的趨勢下投資組合也存在高風險。因此，本文提出了一種有效的策略來表示趨勢比，以每日預期報酬來當趨勢線斜率，風險則是趨勢線與資金水位之間的差。這個方法改進了夏普值使用報酬率和標準差來評估投資組合的缺陷。此外，我們提出了同時進行正常交易與融券交易兩種交易手法以提高報酬與分散風險。我們利用趨勢值在正常交易下尋找穩定上漲的投資組合，同時在融券交易下尋找穩定下跌的投資組合。由於股票投資組合中並沒有限制股票數量，且MPT的計算複雜度會隨著股票的數量增加呈指數增長，所以我們利用量子演化禁忌搜尋演算法，並加入了量子領域中反閘(GNQTS)在龐大的解空間中找出一組最佳的投資組合。此外，爲了避免過度適應的問題，我們使用了滑動視窗，並應用在各種不同的訓練測試週期中。因為考慮到有些股票在股票市場上具有景氣循環的現象，我們使用了相較於傳統方法的近期區段爲訓練期不同的視窗，即使用測試期相同的前一年的時段做為訓練。由實驗結果可以表示，透過趨勢值來評估正常交易與融券交易的投資組合，搭配GNQTS演算法與滑動視窗，能有效率的分散風險增加報酬讓效果更好。[[abstract]]When investing in the stock market, investors first encounter the stock selection problem. Therefore, selecting a potential combination of stocks is a problem worth investigating. One commonly-used risk indicator is the Sharpe ratio. However, it defies the logic of investors because even an uptrend portfolio has a high risk. Thus, this paper proposes a strategy to improve the Sharpe ration denoted the trend ratio where the daily expected return is the slope of the trend line and the risk is the difference between the trend line and the fund standardization. Moreover, we propose doing normal trading and short selling simultaneously to increase the profit and spread the risk. We use the trend ratio to find a stable uptrend portfolio for normal trading and a stable downtrend portfolio for short selling. As there is no limitation to the amount of stocks in a portfolio, and because MPT’s computation complexity grows exponentially when the number of stocks increases, we utilize the quantum-inspired tabu search algorithm improved by the quantum-not-gate (GNQTS), to find an optimal portfolio in a large solution space. Besides, we use the sliding window to overcome overfitting problem. In addition of using the nearest time period as the training period, we use the same time period from the last year as the training period and tested it in the same period in current year, as some stocks have an economic cycle. Using the trend ratio while doing normal trading and short selling, with the GNQTS and sliding window, the experiment results show a promising result in which the risk is spread effectively and the profit is maximized.[[note]]碩