報酬率為厚尾分配與極值相關最佳化投資組合之研究

The Study of Safety-First Portfolio Optimization Under Heavy Tail Distribution

連利翔(Li-Hsiang Lien)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2009年)

https://doi.org/10.6840/cycu200901040

摘要

隨著衍生性金融商品如雨後春筍般出現，投資者在追求最大化報酬的同時，需要一套有系統的計量方法來分析，因此風險管理也越來越被投資人所重視。傳統上利用常態分配分析整體分配，越來越多文獻證明這樣容易低估下端風險。因此我們利用極值理論估計下端風險，但是將極值理論應用在投資組合時，目前僅能以窮舉法求得最佳解，是非常沒有效率。因此在本研究中，我們利用極值理論來估計下端風險並利用Pair-Copula 找出資產報酬率分佈的相關性並模擬資產未來報酬，藉由篩選後近似尾端分佈的資料和傳統safety-first模式以及平衡機制模式建立我們的投資組合模式。
本研究中，我們自摩根台灣股價指數（MSCI Taiwan Index）成份股之中選取二十支股票以及定存作為投資標的，並和大盤指數以及傳統safety-first模式比較其績效，經實證結果顯示，我們的研究優於市場以及傳統safety-first模式。

關鍵字

極值理論 ； 下端風險 ； Safety-First投資組合 ； Pair-Copula

並列摘要

More and more financial derivatives are born as bamboo shoots after a spring rain. The investors indeed need a systematic method to analyze the risk of portfolio. Most of investors are usually more concern about the loss to a threshold return. More evidence shows that the rate of return is not normally distributed, but fat-tailed. Due to There are rare data in the tail from historical returns which is easily to underestimate the downside risks. So we use extreme value theory (EVT) to calculate the downside risks. But it is inefficient to use EVT to calculate the portfolio problem.
In this thesis, we simulate the future rate of return by combination the EVT and pair-copula dependence structure, and then we screened the scenarios which all the stocks’ return below zero and put them into our safety-first model. In addition, we proposed our rebalancing model based on safety-first model. The results verified that the performances of these models are more stable than the Taiwan-Weighted Stock Index.

並列關鍵字

Downside Risk ； Pair-Copula ； Safety-First ； Extreme Value Theory( EVT)

參考文獻

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