台美主流指數股票型基金之最適投資組合 – 合併計算匯率與台灣個人稅率後之效率前緣分析

Abstract

指數股票型基金 (ETF，另譯交易所交易基金) 是一個簡單高效的投資方式。台灣投資人常購買台灣ETF、美國ETF或是台灣上市投資美國標的的ETF。然在以上三種基金中選擇時，投資人需綜合考慮匯率、跨國投資可能隱含的效率損失、不同所得造成的股利稅率及資本利得稅率對投資結果造成的影響。 本研究以17檔台美主流指數ETF過去7年之歷史資料為參考，假設股利再投資、並設計模型計算匯率與五個台灣常見的稅率條件以衡量投資績效，發現各ETF單獨比較時，美國ETF之平均報酬率一般較高，但台灣ETF的風險則較低。以夏普比率與索提諾比率衡量，兩國的本土基金互有優劣。在不同稅務條件下，可觀察到夏普比率之排序略為消長，然沒有大幅變動。本研究以效率前緣模型合併匯率與五組常見稅率計算最適投資組合，在不同稅率下，上述三大類ETF均出現在最適投資組合中，且其投資組合之成分基金改變不大，惟持股比例需依稅率做調整。探討其原因之一為三者彼此之相關係數低於與同類型基金之相關係數。除上述三種基金外，相對保守的投資組合可增加債券ETF以進一步降低風險。 本研究亦發現台灣上市，投資美國之基金報酬雖落後追蹤相同指數的美國基金，但因與匯率之負相關，其避險效益可補償部分報酬損失。另因此類基金預先支付美國股利稅；而台灣人直接投資美國ETF，亦需要支付股利稅，惟此稅負較為投資者知曉。本研究建議評估此類基金時，應以投資人的稅後報酬作為比較模型較為適當。 整體而言，本研究認為台灣ETF，美國ETF，台灣投資美國之ETF，與債券ETF四者均為具有價值之投資組合成分基金，且此結論在本研究中設定的五種稅率條件下均成立。

Exchange-Traded Funds (ETFs) present a comprehensive yet effective financial instrument to investors. Taiwan Investors often consider Taiwan ETFs, U.S. ETFs, or Taiwan-listed ETFs investing in U.S. assets. However, when choosing among these three types of funds, investors would need to evaluate the variation of exchange rates, potential efficiency losses due to cross-nation investments, and the potential liabilities of income-dependent dividend / capital gain tax rates on the investment outcomes. This study references the historical data of 17 mainstream Taiwan and American ETFs over the past seven years, assumes dividend reinvest and created investment return models including exchange rates and five common Taiwanese tax rate conditions. It was found that, when comparing each ETF individually, U.S. ETFs generally have a higher average return, whereas Taiwanese ETFs exhibit lower risk. Measured by the Sharpe ratio and the Sortino ratio, domestic funds of both countries present attractive investment choices. Under the five tax conditions forementioned, the Sharpe ratios vary, though only minor changes occur in the Sharpe ratio rankings. The conclusions were reached by utilizing Markowitz’s Efficient Frontier model, combining exchange rates and tax rates to calculate the optimal investment portfolios. It was further observed that, under different tax rates, all three ETF categories – U.S. ETFs, Taiwan ETFs and Taiwan-listed ETFs investing in the U.S., are contributing elements to the optimal investment portfolios, with the composition percentages changing slightly due to different tax rates. One reason for the presence of all three ETF categories is the low correlation coefficient between the three fund types compared to the correlation coefficient within the same type of fund. Relatively conservative investors would need to include an additional bond ETFs to further reduce risk to their desired level. The study also discovered that Taiwan-listed funds investing in the U.S., although trailing behind U.S. domestic funds tracking the same index in terms of average returns, can compensate some return losses through hedging benefits due to their negative correlation with exchange rates. Furthermore, these funds pay U.S. dividend taxes in advance, while Taiwanese investing directly in U.S. ETFs are also subject to dividend taxes, which is far more aware by investors than the hidden tax burden of the prior one. This study suggests that it is more appropriate to compare such funds based on the investor's after-tax returns. Overall, this research concludes that Taiwanese ETFs, U.S. ETFs, Taiwan-listed ETFs investing in the U.S., and bond ETFs are all attractive components composing an optimal investment portfolio, and this conclusion holds under the five tax rate conditions established in this study.