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博碩士論文 etd-0708111-165843 詳細資訊
Title page for etd-0708111-165843
What is the optimal leverage of ETF?
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槓桿ETF、標準普爾 500 指數、大崩盤、動態槓桿預測模型、ARMA-GARCH模型
Leveraged ETF, ARMA-GARCH, S&P 500 index, dynamic leverage model
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最近,有越來越多的文獻討論有關問題的槓桿 ETF的投資策略。在文章中,我們主要探討標準普爾500指數是否存在最佳的槓桿使得報酬率最大化。跟據 ARMA- GARCH模型的假設,我們發現預測最佳槓桿的模型可以由報酬率和殘差所服從分配的特徵函數所組成。在本文中我們使用MA(1)- GARCH(1,1)作為預測報酬率和波動性的模型,根據過去1008天的日報酬率資料預測下一天的報酬率和波動性,並依此數據計算下一天的投資槓桿,而我們的估計時間是從1954年到2011年3月。在本文中我們使用四個動態槓桿預測模型(Normal,Student T,VG和最佳模型的槓桿),來找出預測日的最佳槓桿。在我們的模型預測的準確性約55%,這是略高於 SPX上漲的機率。但在長期的複利效果下,動態槓桿模型的報酬率遠高於固定槓桿模型。其中可能存在非常多的因素但是其中一個重要的因素是預測股市大跌的能力。 SPX在1980年道2011年有14次日跌幅大於6%的記錄,然後動態槓桿模型可以有效地避免10的大崩盤。最後,在短期投資期限並不存在最佳的模型,然而在過去的六十年中,當投資期限為2400天時,根據最佳模型策略選出的槓桿進行投資可以永遠獲得正報酬率。
Recently, there are more and more literatures discuss on the issues of investment strategies of leveraged ETFs. In our works, we concentrate our issues on optimal leverage of ETF of S&P 500 index. Based on ARMA-GARCH model’s assumption, we find out that the forecasting optimal leverage can be shown in a formula which contains return and characteristic function. In this paper, we use MA(1)-GARCH(1,1) to forecast volatility based on 1008 rolling window to forecast one day ahead’s volatility; and our estimation time is start from 1954 to March 2011. In this paper, we present four dynamic leverage models (Normal, Student T, VG, and Best model’s leverage) to find out the payoffs under these models. In our model, the forecasting accuracy is just about 55% which is slightly higher than SPX raise probability. But during long-term compound effect, the dynamic leverage models can out-perform than constant leverage. There may exist some important factors in these results, one of them is the crash forecasting ability. During 1980 to 2011 SPX has 14 big crashes and these models can effectively avoid 10 big crashes. In short-term investment horizon none of these five models are always outperform than others but in long-term investment horizon the strategy of best model’s leverage can always earn money when investment horizon is 2400 days.
目次 Table of Contents
論文審定書 i
Abstract (in Chinese) ii
Abstract iii
1. Introduction 1
2. Methodology 6
3. Data 11
4. Empirical Results 17
5. Conclusion 34
Reference 36
參考文獻 References
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Trainor, W. J. and E. Baryla (2008). "Leveraged ETFs: A Risky Double that doesn’t multiply by Two." Journal of Financial Planning 21(5): 48-55.

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