- 學位論文
風險趨避與持有期間對產業VaR模型之比較—以加權股價指數與分類指數為例—
The Effect of Risk Aversion and Holding Period on VaR - An Empirical Study in Taiwan Weighted Stock Index and Sub-index
摘要
在一般的風險值評估中，若只估計單日風險值，未必能符合假設期間內可平倉的事實，故計算多天期的風險值是必要的 (Beder,1995) 。此外，不同的信賴水準代表廠商或投資者的風險態度，愈趨避風險者，其設定信賴水準愈高。因此，持有期間與風險態度影響風險值估計甚鉅。本研究將考慮產業別、持有期間、風險態度與模型方法，對風險值進行評估，以決定最適的風險值評估模型。 本研究使用歷史模擬法、蒙地卡羅模擬法與極值理論來衡量VaR，其中極值理論是使用超越門檻值模型進行估計，而門檻值分別依下列兩種方法選擇：一、Mcneil and Frey (2000) 使用總樣本數的第10分位數當門檻值，二、陳佩君 (2005) 使用總樣本數的第15分位數當門檻值。另外，使用天數平方根與Daníelsson et al. (1997) 的 根規模法則來推算多天期風險值。最後，利用誤差均方根及回溯測試的失敗率與Kupiec (1995) 的概似比檢定來評估各組合的最佳預測方法。實證上使用台灣加權股價指數、塑膠化工類、電子類與金融類股價指數為對象。樣本內資料共計1000筆，樣本外資料共20筆。 實證結果得知，使用不同門檻值來估計極值理論，將其與歷史模擬法、蒙地卡羅模擬法做比較，使用所有樣本的第10分位數會比使用所有樣本第15分位數有較佳之預測結果。其次，不論在何種股價指數上，歷史模擬法低估最大損失的機率相當高，蒙地卡羅法大都適用於二十日VaR之估計，極值理論則較適用為單日VaR之估計。再者，以不同股價指數來看，塑化類股價指數較適合使用歷史模擬法來進行VaR之估計；金融類股價指數較適合使用蒙地卡羅模擬法來估計VaR。最後，以不同投資者的風險態度來看，對風險趨避程度相當高的投資者而言，蒙地卡羅法的資金運用效率為最佳方法；而對一般投資者而言，歷史模擬法的資金運用效率為最佳方法。
並列摘要
In evaluating value at risk (VaR) the confidence level, holding-day of portfolio and portfolio scale all play important role. This study employs different methods to estimate the VaR by considering different asset holding days and risk attitude. This study attempts to consider various confidence levels, holding-day of portfolio and assets to find out the best method to measure asset’s VaR. In empirical study this article uses the Taiwan Weighted Stock Index, Plastics & Chemical Sub-index, Electrical Sub-index and Banking Sub-index as sample objects to evaluate their VaRs, based on three approaches, including historical simulation, Monte Carlo simulation and extreme value theory. To judge the threshold value in the extreme value theory, we use the 10 percentile or 15 percentile of sample data as proxy. In addition, we use the square-root-of-time rule and α-root scaling law to calculate the VaRs of different holding days. Finally, we use back-testing and RMSE to evaluate the forecasting performance of different estimation models of VaR. Empirical study shows that the extreme value theory with 10 percentile has better forecast results than other risk evaluation models. Historical simulation has high probability to underestimate the VaR no matter which stock index is chosen. For a 20-day (1-day) holding of asset, Monte Carlo simulation (the extreme value theory) has the best evaluation performance in VaR. The optimal VaR evaluation method for Plastics & Chemical Sub-index (Banking Sub-index) is to adopt historical simulation (Monte Carlo simulation). With regard to the effect of risk attitude on VaR, Monte Carlo simulation (historical simulation) is more appropriate for the discreet (general) investor.