使用模擬尾端分配資料以考慮單邊風險上界指標之數理規劃求解最佳化投資組合

Safety-First Optimal Portfolio with Approximated Bound on One-Sided Risk Using Simulated Tail Distribution

王政鈞(Cheng-Chun Wang)

指導教授 ： 張國華

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2012年)

https://doi.org/10.6840/cycu201201022

摘要

近年來，美國次級房貸造成美國多家銀行陸續爆發財務危機，連鎖效應下使得信貸緊縮加劇，通貨膨脹問題在世界各地上演，儼然形成一起全球性的金融危機，又歐洲幾個國家的債務問題也持續導致全球股市低迷不振。諸如此類的金融問題不斷陸續在我們的生活中上演，甚至越演越烈，許多投資人漸漸將眼光從高獲利轉移至低風險，學者們也投注更多心力於鑽研風險管理的議題；過去的風險管理中，常常以常態假設進行問題之分析，但卻容易發生了低估極端風險的缺陷，故要以更精確的下端分配來正視風險發生的問題。
為了能夠精確估計尾端分配，我們透過極值理論(Extreme Value Theory)對尾端資料進行參數估計以符合投資組合之厚尾性質，但唯一的缺陷是樣本的大小將決定極值理論的精確度，故我們以Copula相關結構進行資料量之模擬與擴充。有了充足且符合尾端相關性質的資料與樣本，我們更進一步採取單邊下端風險估計的風險指標取代以往的平均絕對離差(Mean-Absolute Deviation)進行對風險值的衡量。最後，我們以Safety-First投資組合選取理論限制下端風險發生之機率，並透過線性規劃的模式求取最佳化之投資組合。
本研究中，以摩根台灣股價指數(MSCI Taiwan Index)中的前二十大成分股作為觀察對象，並以之進行Pair-copula的蒙地卡羅法(Monte Carlo simulation)模擬極值理論所估計之符合尾端相關性的模擬資料，最後由Safety-First限制單邊下端風險上界求得最佳化投資組合。且經實驗驗證，本研究將對下端風險估計與風險下求解最佳化投資組合提供正面幫助。

關鍵字

單尾下端風險 ； Copula相關結構 ； 極值理論 ； Safety-First投資組合

並列摘要

As the increasing of complexity of financial product, it’s more and more difficult to handle the risk in recent years. In order to make sure that the securities do not fail us, we concern about the probability of extreme cases called downside risk, and it can be calculate with mathematical programming since Markowitz and Roy purposed their portfolio selection models. It’s not that hard to make a portfolio selection today, savants are working on finding further methods to improve the invest strategy by a more accuracy distribution estimation of the return such as data simulation with tail dependency or some more efficiency programming skill like.
In this study, we estimated downside risk with a one-sided estimator instead two-sided one, such as MAD, because the symmetry of the variance was leading us into an underestimated risk. On the other hand, we simulated heavy-tail return with EVT and pair-copula, where EVT provide an accuracy tail distribution of asset, and pair-copula describe the tail dependency of multi-assets, so that we could estimate downside risk with sufficient data set, and finally optimized portfolio with safety-first portfolio selection model.

並列關鍵字

one-sided risk measure ； Pair-Copula ； Extreme Value Theory (EVT) ； Safety-First Portfolio

參考文獻

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