價值平均與定期定額績效比較：實證分析與蒙地卡羅模擬

本文探討加入技術指標之定期定額投資策略和價值平均投資策略應用在台灣50的績效。首先，以台灣50之歷史資料驗證過往的投資績效。其次，應用蒙地卡羅法模擬未來股價可能走勢進一步分析投資策略績效，比較歷史實證與模擬分析的差異。實證結果與模擬分析顯示，納入技術指標能提高投資策略績效。定期定額投資策略加入移動平均和布林通道指標後投資績效都獲得提升，價值平均投資策略納入布林通道指標能大幅提升績效，但不建議加入移動平均指標。長期價值平均投資策略模擬優勢次數明顯高於定期定額投資策略，短期價值平均投資策略加入布林通道指標及定期定額投資策略加入移動平均指標優勢次數較多。布林通道策略的內部報酬波動度普遍較高，移動平均策略波動度與原始策略無太大差異。長期價值平均投資策略每期投入金額的波動度大，因此投入價值平均投資策略時，需要有充足的資金，定期定額投資策略無論在長期或短期，每期投入金額波動度小。

關鍵字

價值平均；定期定額；布林通道；移動平均；蒙地卡羅

並列摘要

This study mainly evaluates the Taiwan 50 performance between the DCA strategy and the VA strategy with the technical analysis indicators. First, we examine the past investment performance with the historical data of Taiwan 50. Secondly, the Monte Carlo method is used to simulate the possible trend of future stock prices to further analyze the performance of investment strategies, and to compare the differences between historical evidence and simulation analysis. The strategy with the technical analysis indicators is able to improve the investment performance in both historical evidence and simulation analysis. It suggests that the investment performance will be much better when the DCA strategy with MA and Bollinger bands, so does the VA strategy with the Bollinger bands. However, the investment performance will diminish greatly when we apply the VA strategy with MA. The long-term VA investment strategy simulation dominance frequency is significantly higher than the DCA strategy. The dominance frequency also is higher on the short term VA strategy with the Bollinger bands and the short term DCA strategy with MA. The internal rate volatility of the Bollinger bands strategy is generally high, but the internal rate volatility of MA strategy is not much different from the original strategy. In addition, the long-term VA strategy has a large fluctuation in the amount of investment per period, so the sufficient investment fund is necessary for those who invest in the VA strategy, but for the DCA strategy, the amount of investment per period is stable.