投資組合之風險值評估—以台灣五十成分股為例

Evaluation of Value-at-Risk in Investment Portfolio: Evidence from Component Stocks of Taiwan 50 Index.

吳文仁(Wen-Jen Wu)

指導教授 ： 吳博欽

中原大學/商學院/國際經營與貿易研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200775

摘要

經歷2008年金融海嘯，一間百年歷史的公司倒閉及一些國家發生債務違約，更加確定不能把全部的雞蛋，都放在同一個籃子裡。因此，投資人需要利用投資組合方式以避免投資單一商品的風險，且在風險與報酬抉擇中，將風險列為優先考量。
本本研究的目的在於，使用調整除權息後的日報酬資料，以及股票型基金經理人投資限制下，利用Markowitz 的平均數－變異數分析法對台灣 50 成份股進行篩選，並以有無限制條件及不同期間選出近半年、一年與三年最佳的股票投資組合標的。再利用變異數-共變異數法、歷史模擬法、蒙地卡羅模擬法等三種風險值評估方法，衡量該不同狀況下，各種最佳投資組合的風險值，以及找出有無限制的狀況下，最佳的評估區間及方法。
台灣的股市屬於淺碟式市場，常常因為各種國際因素而造成大幅波動，這種波動有時甚至會使得公司面臨倒閉。以股票型基金經理人而言，這種風險是不被允許的。本研究以台灣五十成分股為研究對象，因為這些成分股是台灣市值前五十大的股票，相較於其他投資標的，有較好的流通性，且包含各種台灣的重要產業，故利用此成分股來做投資組合的篩選標的，是相當合適的。
本研究結論為以風險預測能力來看，在有限制的狀況下，以歷史模擬法為最佳，而以區間來看，則是以三年期區間為最佳。在無限制的狀況下，則是以蒙地卡羅模擬法為佳，以區間來看，則是以半年期區間為最佳。綜合上述，在有無限制的狀態下，不管是最佳方法或區間都不相同，本研究結果供投資人依身分不同，可以選擇最佳的區間及方法。

關鍵字

變異數-共變異數法 ； 風險值 ； 歷史模擬法 ； 蒙地卡羅模擬法

並列摘要

Experienced the financial tsunami of 2008, a century-old company closed down and some countries defaulted on its debt. Thus, we really cannot put all eggs in one basket, and need to employ the concept of portfolio selection to engage in investment and avoid the risk of single one investment goods.
The aim of this study is decide the optimal investment portfolios and their value at risk (VaRs) by considering the adjustment of daily returns with the payment of dividend, and the constraint of the holding ratio of a specific stock in mutual fund. The optimal portfolio is determined by Markowitz’s Mean-Variance method and the VaRs are measured by the variance-covariance approach, historical simulation method, and Monte Carlo simulation method. The sample objects are Taiwan's 50 constituent stocks and holding periods are half-year, one-year, and three-year, respectively. We further compare the conclusions of different holding periods, different measurement methods of VaR, and different conditions of holding ratio constraint.
Taiwan’s stock market belongs to a shallow dish one; therefore, it is easily disturbed by a variety of international factors, which in turn result in sharp fluctuations of stock prices or the bankruptcy of companies. From the viewpoint of equity fund managers, this risk is not allowed. This study to selects the constituent stocks of Taiwan 50 as sample objects, because these constituent stocks represent the top fifty market values in Taiwan’s stock market. Compared to other investment targets, they have better liquidity and contain a variety of important industry in Taiwan; therefore, they are proper target companies for constructing optimal portfolio.
Empirical results show that, in the case of having the constraint of holding ratio of a specific stock, historical simulation method is the best approach for evaluating the VaRs of portfolio. In addition, the longer the holding period is, the more forecasting performance historical simulation method would be. On the contrary, in the situation of no holding ratio constraint, Monte Carlo simulation has the optimal forecasting ability on the VaRs of portfolio. However, the shorter the holding period is, the more forecasting performance Monte Carlo simulation method would be. According to above conclusions, the forecasting performance of VaRs depend on the holding period, the constraint of holding ratio, and measurement methods of VaR. Thus, to select optimal method to evaluate the VaR of a specific portfolio, the managers of mutual fund need to consider these factors.

並列關鍵字

Variance-Covariance approach ； Value at Risk (VaR) ； Historical Simulation ； Monte Carlo Simulation

參考文獻

劉美纓（2006），研究銀行投資組合風險模型之測試與應用，金融風險管理季刊，第二卷第一期。

謝旻瑜（2008），國內股票投資組合之風險值評估－以台灣50指數成份股為例，中原大學國際貿易學研究所碩士論文。

Beder, T. S. (1995), “VaR: Seductive but Dangerous,” Financial Analysis, 51, 12-14.

Duffien, D. and J. Pan (1997), “Overview of Value at Risk”, Journal of Derivatives, 4, 7-49.

Markowitz, H. M. (1952) ,“Portfolio Selection,” Journal of Finance, 7, 70-91.