臺灣博碩士論文加值系統

研究指出不確定性包含了模糊性和風險性，也有其他研究發現模糊性測度捕捉了未來股票報酬的分配的變異程度。Ehsani、Krause和Lien在2013年提出了一個新的模糊性測度(MD)。Brenner和Izhakian在2012年提出了一個新的模糊性測度(℧)關於四倍的損失機率的變異數。Baltussen、Bekkum和Grient在2013年也提出了一個模糊性測度(VOV)關於波動度的標準差。而這三個側度都是建立在常態分配上，但許多研究指出股票報酬並不服從常態分配，所以本研究把常態分配延伸至厚尾T分配和指數常態分配。接著我們使用這三個模糊性測度去預測S&P 500指數的報酬和比較之間的預測能力。
傳統的財務模型注重風險與報酬的關係，但在本研究中，我們發現模糊性會影響資產價格和報酬，且發現報酬與模糊性之間存在著負的相關性。本文結果發現，模糊性測度使用T分配和指數常態分配在預測報酬中優於標準常態分配。除此之外，本研究S&P 500指數報酬的預測能力優於個股報酬的預測能力。

Previous study found that uncertainty include risk and ambiguity. Researchers found that ambiguous measure can capture the variation of investor expectations regarding the underlying probability distribution of future stock returns. Ehsani, Krause and Lien (2013) proposed mean distance (MD) and Brenner and Izhakian (2012) provided four times the variance of the probability of loss during the month as omega. Baltussen, Bekkum and Grient (2013) proposed standard deviation of implied volatility during the month as VOV. These three measures are calculated based on normal distribution assumption. Many papers pointed out that return is not normal distributed, so our study extends normal distribution to fat-tailed t and lognormal distribution. Furthermore, we use the three ambiguous measures to predict the S&P 500 index returns and evaluate the prediction ability among them.
Modern portfolio theory focuses on the relationship between risk and return. This paper assumes that ambiguity can affect asset prices and test relationship between risk, ambiguity and return. We found that ambiguity has negative effect on return and risk mostly has negative effect on return. Ambiguity measure use t distribution or lognormal distribution on predicting return is better than normal distribution. Omega has the best prediction ability for S&P 500 index return. Additionally, the prediction ability for S&P 500 index return in this study is better than those for predicting individual stock returns in the studies of Brenner & Izhakian (2012) and Ehsani, Krause & Lien (2013).

1 Introduction 4
2 Ambiguous measure and predictive variable 8
2.1 MD(Mean Distance) 8
2.2 Omega(℧) 10
2.3 VOV (Volatility of Volatility) 12
2.4 Predictive variable 13
3 Data and Description 15
3.1 Raw data 15
3.2 Ambiguity index time trend 16
3.3 Ambiguity index distribution 19
3.4 Correlations among Variables 21
3.4.1 Return and ambiguity index 21
3.4.2 Return and Predictive variable 23
4 Empirical evidence 25
4.1 Contingency tables by ambiguity measure 25
4.2 Contemporaneous Regression Tests 30
4.3 Predictive Regression Tests 34
5 Conclusion 39

Reference 41
Appendix A：Contemporaneous Regression 43
Appendix B：Predictive Regression 65


List of Figures
Figure 3 1: Excess return and MD from 2005/1-2015/1 17
Figure 3 2: Excess return and ℧(ave) from 2005/1-2015/1 17
Figure 3 3: Excess return and ℧(mid) from 2005/1-2015/1 17
Figure 3 4: Excess return and VOV(ave) from 2005/1-2015/1 18
Figure 3 5: Excess return and VOV(mid) from 2005/1-2015/1 18
Figure 3 6: The distribution of MD 19
Figure 3 7: The distribution of ℧(ave) 19
Figure 3 8: The distribution of ℧(mid) 20
Figure 3 9: The distribution of VOV(ave) 20
Figure 3 10: The distribution of VOV(mid) 20

List of Tables
Table 3 1: (A) Cross correlations between excess return and ambiguous index 21
Table 3 2: (B) Cross correlations between excess return and ambiguous index 22
Table 3 3: Cross correlations between excess return and control variable 23
Table 4 1: Control variable sorts by MD 26
Table 4 2: Control variable sorts by ℧(ave) 27
Table 4 3 : Control variable sorts by ℧(med) 28
Table 4 4: Control variable sorts by VOV(ave) 28
Table 4 5 : Control variable sorts by VOV(med) 29
Table 4 6: Ambiguity using normal distribution on contemporaneous regression 31
Table 4 7: Ambiguity using lognormal distribution on contemporaneous regression 32
Table 4 8: Ambiguity using T distribution on contemporaneous regression 33
Table 4 9: Ambiguity using normal distribution on predictive regression 35
Table 4 10 : Ambiguity using lognormal distribution on predictive regression 36
Table 4 11 : Ambiguity using fat-tailed t distribution on predictive regression 37

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