極值理論於風險控制下投資組合之研究

Safety-First Portfolio Selection Problem under Extreme Value Theory

林姿利(Tze-Li Lin)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600403

摘要

近年來，投資人在追求最大化報酬的同時，風險管理也逐漸被重視。本研究的目的主要在探討safety-first 投資組合最佳化之問題，其在追求期望報酬最大化的同時，也能將最大損失限制在風險值( VaR ) 內。為了避免在常態分配假設下低估了下方風險，我們應用極值理論中的一般柏拉圖分配(GPD) 在一給定顯著水準下估計其風險值。另外，由於資產間常存在尾部相關性，因此在模擬資產未來價格的同時，我們特別考慮Copulas 相關結構以更能精確地掌握資產尾部的變化。最後，在求得最佳資產配置的比例後，由於指數資產無法直接交易，我們建立線性規劃決定其指數投資組合，以接近各指數的變化。
在本研究中，為了分散風險，我們特別選取台灣電子類股、金融類股及債劵三資產為投資組合標的，並和大盤指數及債券組成的投資組合比較其績效。最後驗證結果證實，由三個資產組成的投資組合比兩資產的投資組合績效為佳；並且藉由safety-first 投資組合模型所選取的投資組合比市場大盤的利潤較為穩定且高於定存。

關鍵字

一般柏拉圖分配 ； Copulas 相關結構 ； 風險值 ； Safety-first 投資組合

並列摘要

The purpose of this thesis is to investigate the safety-first portfolio optimization problem to maximize expected return subject to the constraint that maximum loss should meet the Value-at-Risk limits. In order to avoid the underestimates of downside risk under normal distribution, we apply the tool of univariate extreme value theory (EVT) in the asset allocation problem. Therefore, it will be expected to get a better estimation of VaR under generalized Pareto distribution (GPD) with some
significant level. In addition, there often exists some tail dependence between assets. Thus, we specially consider the Copulas dependence structure when simulating the future returns of each asset with Brownian motion. Finally, although the proportion of allocated assets is determined, the market index cannot be purchased directly. Therefore, we need to find portfolios, called index portfolios, to mimic the role of index by a linear programming problem.
For diversifying risks, we choose the combination of electrical industry index, financial industry index, and bonds as our investment positions and compare its performance
with that of the combination of market index and bonds. We denote the two combinations as Strategy 1 and Strategy 2. The results verify that the performance of Strategy 1 is better than that of Strategy 2 since diversifying the investment positions can disperse the risks and raise the profits. And both strategies under the safety-first portfolio optimization models are steadier and more profitable than market.

並列關鍵字

Generalized Pareto distribution ； Safety-first portfolio selection ； Value-at-Risk ； Copulas dependence structure

參考文獻

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