開放型基金風險值應用與績效評估指標之探討

On the Application of Value at Risk and Performance Evaluation of Mutual Funds

林青瑤(Ching-Yao Lin)

指導教授 ： 陳思寬

國立臺灣大學/管理學院/國際企業學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.10389

摘要

本研究將風險值的觀念導入基金評比的工具中，強調的不只是投資標的物波動性，而是在設定之信賴水準下，求算出標的物報酬率之風險值。本研究重點著重於風險值估計方法的使用，在確定樣本的分配符合方法的假設後，才會採用；如發現樣本不符合分配假設，經試誤法後，仍無法找出符合分配之最佳自由度與樣本數，本研究即不採用此法估計風險值。
關於基金績效評比中，使用Sharpe指標，除傳統模式外，還將標準差以風險值代替、無風險報酬率以市場大盤代替，求算出指標。且本研究將研究標的物分為三組：區域或單一國家型、全球型和台灣區，進行組內評比，並且以相關係數比較不同方法是否會造成排名的改變。
本研究在風險值估計模型上使用：歷史模擬法、變異數—共變異數法(variance-covariance approach)和混合常態模擬(mixed normal simulation)法。經過回溯測試(Back test)後發現，在歷史模擬法中，短天期之估計能力較長天期為佳。至於變異數—共變異數法和混合常態模擬法在波動性估計上又使用了標準差法和GARCH(1,1)，結果發現不論是變異數—共變異數法或是混合常態模擬法，標準差法在風險值估計上較GARCH(1,1)精準，所以使用變異數—共變異數法或是混合常態模擬法並不是影響估計風險值的主因，而是在於估計波動性時，是否能找到能精確描述樣本狀況的方法。
本研究將風險值取代標準差後，進行基金排名，並且求算使用不同方法估算Sharpe對排名的影響，結果發現使用變異數—共變異數法和混合常態模擬法並不是造成基金排名變動的主因，而是標準差法&GARCH法和Sharpe1&Sharpe2較能造成排名變動。

關鍵字

風險值 ； 開放型基金 ； 夏普指標 ； 歷史模擬法 ； 變異數—共變異數

並列摘要

This study introduces the concept of Value at Risk (VaR) into fund performance evaluation tool. It stresses that the calculation of rate of return for underlying assets is not based on target volatility but on confidential level setting. The appropriate VAR calculation method is determined only after sample distribution meets the method’s assumption. In other words, if samples fail to meet the distribution assumptions, and trial and error is still unable to identify the best distribution with degree of freedom and sample size, such estimation method will not be adopted.
In the mutual fund evaluation, Sharpe Ratio will not only be used under the traditional model. The standard deviation will be replaced by risk, while the riskfree rate replaces the market rate. In this way, a new Sharpe Ratio is calculated. In addition, the research will divide the underlying assets into three groups: regional versus individual country type, global type and Taiwan type. The mutual funds are evaluated and ranked, using the Spearman coefficient , different methods are compared to see if they will cause changes on ranking.
This study estimates the VaR model with historical simulation, variance–covariance and mixed normal simulation. After Back test, it is found that the historical simulation is more accurate in short-term period estimation than in long-term period estimation. The variance-covariance method and mixed normal simulation also use the standard deviation approach and GARCH (1,1). The results from both variance-covariance method and mixed normal simulation showed that the standard deviation method in estimating the value of risk is more accurate than GARCH (1,1). Therefore, the use of variance-covariance method or mixed simulation does not affect the value of risk. Instead, finding a method that precisely describes samples is more important in the calculation of volatility. I replaced standard deviation with risk ratio to rank the funds, investigating the influences of different Sharpe estimation methods on rankings. The results showed that variance-covariance method and mixed simulation method do not cause major changes in the rankings, but standard deviation method &GARCH and Sharpe1&Sharpe2 cause more changes in the rankings.

並列關鍵字

VaR ； Mutual Fund ； Sharpe Ratio ； Historical Simulation Method ； Variance-Covariance

參考文獻

陳俞臻，風險調整後共同基金績效評估，淡江大學財務金學系碩士班，民國94年

古永嘉、康健廷、洪儒瑤，ARMA-GARCH風險值模型預測績效實證，Journal of China Institute of Technology Vol. 34-2006, pp.13-35

林楚雄、高子荃、邱瓊儀，結合GARCH模型與極值理論的風險模型，Journal of Management 2005, Vol.22, No. 1, 133-154

張有若，全球共同基金群組風險與績效評估—以修正夏普指標之應用—，中原大學企業管理學系，民國91年

Angelidis, Timotheos & Benos, Alexandros & Stavros Degiannakis “ The Use of GARCH Models in VaR Estimation” June 2003