在不確定環境下，探討投資比率可變的投資組合分析

Adjusted Investment Proportions in Portfolio Analysis Under Uncertain Environment

黃茵茵(Yin-Yin Huang)

指導教授 ： 曹銳勤 ； 邱建良

淡江大學/商管學院/管理科學學系博士班/博士(2021年)

https://doi.org/10.6846/TKU.2021.00116

摘要

對於不斷變化的實際資產市場，投資者對於資產及其相關面象的變化只能以語意描述其模糊的信息。因此，想獲得報酬率的精確機率分佈並不容易，針對此類問題，相關學者建議使用模糊集理論作為替代方法，來求解最佳的投資組合。有鑑於此，本研究規劃兩個研究議題。
首先，對不穩定的、模糊報酬相關的最佳投資組合選擇方法，提出一個模糊投資組合模型。本文嘗試引介一種新的模糊報酬函數——基於報酬的選擇保證率，將某些證券放在超額投資的框架下來討論——來改善可能平均值與變異值，導向一種改良的模糊組合分析模型。本文驗證前述模型在不同的投資風險下，設定最低保證報酬率的期望投資報酬率，是大於較高保證報酬率的期望投資報酬率。這個投資組合分析可以提供一個更有貢獻的投資選擇。其次，在不穩定或模糊的報酬中，本文提出了另一個模糊的投資組合模型作為最佳投資組合選擇方法。
雖然許多論者已經戮力於研究模糊的投資組合模型，在模糊投資組合模型中，設定可調式證券比例以探討投資保證率的超額投資與缺額投資。為了處理這樣的投資，我們根據最低報酬保證率假設某些證券被考量超額投資而某些證券被考量為缺額投資。研究範例顯示在不同等級的投資風險下，較低的報酬保證率的期望報酬率是高於較高的報酬保證率的期望報酬率的，而在較高的投資風險下，投資報酬率低的證券的投資比率是幾近於零。

關鍵字

模糊投資組合模型 ； 最低保證報酬率 ； 期望投資報酬率 ； 超額投資 ； 缺額投資

並列摘要

For the changing asset market, investors can only use Linguistic description to describe the vague information of the changes in assets and related aspects. Therefore, it is not easy to obtain an accurate probability distribution of the rate of return. For such problems, relevant scholars suggest using fuzzy set theory as an alternative method to solve the best investment portfolio. Therefore, this research plans two research topics. First, a fuzzy investment portfolio model is proposed for the optimal portfolio selection related to unstable and fuzzy returns. This article attempts to introduce a new fuzzy return function based on the selection guarantee rate of return, some securities are discussed in the framework of excess investment to improve the possible average value and variance value, leading to an improved fuzzy combination analysis model. This article proves that under different investment risks, the proposed model sets the expected return on investment with a lower guaranteed rate of return, which is greater than the expected return on investment with a higher guaranteed rate of return. This portfolio analysis can provide a more contributory investment option. Secondly, in the unstable or fuzzy returns, this paper proposes another fuzzy portfolio model as the best investment portfolio selection method. Although many commentators have worked hard to study the fuzzy portfolio model, in the fuzzy portfolio model, the adjustable securities ratio is set to explore the excess investment and the short investment of the guarantee rate of return. In order to deal with such investments, we assume that certain securities are considered excess investment and certain securities are considered short investment based on the guaranteed rate of return. The illustration shows that under different levels of investment risk, the expected return rate of a lower guarantee rate of return is higher than the expected return rate of a higher guarantee rate of return. With higher investment risks, the ratio of securities investment with low return on investment is almost zero.

並列關鍵字

Fuzzy portfolio model ； guaranteed rate of return ； expected return ； excess investment ； short investment

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