| Summary: | 碩士 === 國立臺灣大學 === 財務金融學研究所 === 89 === This article uses several approaches to evaluate Value at Risk (VaR) of mutual funds in Taiwan, and presents an application of VaR to asset allocation on mutual funds portfolio. We use three main approaches to evaluate VaR of mutual funds; they are Variance-Covariance approach, Historical Simulation approach, and Monte Carlo Simulation approach. The result shows that the best approach is NAV (Net Asset Value) method of Historical Simulation approach and the second best approach is EWMA (Exponential Weighted Moving Average) method of Variance-Covariance approach.
As far as different applying periods are concerned, for the long horizon we should choose fund NAVs as inputs and use NAV method to compute VaR since NAV represents real historical performance of one mutual fund. On the other hand, for the short horizon we should use portfolio compositions of mutual fund and use EWMA method to compute VaR. From the outcome of sensitivity analysis of the portfolio compositions, in order to maintain accuracy of VaR, we suggest the risk manager must dynamically adjust the weight of each security in the portfolio.
In the aspect of VaR‘s application, we replace standard deviation with VaR to establish efficient frontier called MVaR (Mean-Value-at-Risk) efficient frontier on which is the optimal portfolio that minimizes the VaR at a given level of expected return. After depicting MV (Mean-Variance) and MVaR efficient frontier on the same picture, we find MVaR efficient frontier is better in terms of downside risk than MV efficient frontier. The reason is MVaR efficient frontier take lower risk than MV efficient frontier at the same expected return. By using several indexes to measure the real performance of ten portfolios under both MVaR and MV efficient frontiers, we find that MVaR efficient frontier is better than MV efficient frontier in the bear market. Therefore, an investor who is risk avert or anticipates the stock market will be downward in the future can use MVaR efficient frontier model to set up his investment portfolio.
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