本文探討波動度的波動度對於台灣股價指數期貨報酬的影響，在考慮市場風險、統計量偏鋒態、未平倉量之後，發現波動度的波動度影響報酬的現象不受其他變數因子干擾而且現象顯著。實證結果得到波動度的波動度增加報酬會遞減；偏態與峰態甚至未平倉量對於報酬也呈現出特定關係。將上述提到的所有變數執行OLS迴歸產生的估計係數同樣和報酬與因子的關係吻合。
波動度的波動度對於報酬的負向影響原因基於兩種概念，第一種:喜愛風險不確定性高的投資人願意付出風險貼水來獲得高度風險不確定性；第二種:投資人對於風險不確定性偏好程度異質性越紛歧也會降低風險貼水帶來的報酬。其餘變數對於報酬的影響有特定關係而且顯著只有報酬偏態。

This study discusses the relationship between the volatility-of-volatility and the monthly return of Taiwan index futures. After considering market risk, skewness, kurtosis, and open-interest, the phenomenon that volatility-of-volatility affects the return of Taiwan index futures still exists. Base on empirical research when the volatility-of-volatility increases, the monthly return decreases simultaneously. Moreover, there is a specific relation between the monthly return of Taiwan index futures and skewness or kurtosis, even open-interest. The OLS regression estimate also coincides with the relation for all factors between return.
The reason for volatility-of-volatility leading the return to decreases could be based on two concepts. First, investors who prefer uncertainty of risk might pay some premium in order to gain higher uncertainty of risk. Second, the higher the heterogeneity for preference in the uncertainty of risk, the greater decreases in premium. Among other variables that have effects on monthly return only return skewness has a significant effect.

1.Bossaerts, Ghirardato,Guarnaschelli,Zame(2010),Ambiguity in asset markets: theory and experiment, Review of Financial Studies,vol.2, Issue.4,pp.1325-1359.

2.Chip(1991), Preference and Belief: Ambiguity and competence in choice under uncertainty, Journal of Risk and Uncertainty,vol.4,Issue.1,pp.5-28.

3.Changyu¬-Wang,Min-Yu(2004), Trading activity and price reversals in futures markets, Journal of Banking & Finance,vol.28,Issue.6,pp.1337-1361.

4.Chapman, Polkovnichenko(2009),First order risk aversion, heterogeneity, and asset market outcomes, Journal of Finance,vol.64,Issue.4,pp.1863-1887.

5.Debais-Bagchi(2012),Cross-section analysis of emerging market volatility index(India VIX) with portfolio returns, International Journal of Emerging Markets,vol.7,Issue.4,pp.383-396.

6.Eugene F. Fama, Kennth R.French(1993),common risk factor in the returns on stocks and bonds, Journal of Financial Economics , vol. XLVII ,No 2.

7.Guido,Sjoerd,Bart(2014) , unknow unknows: uncertainty about risk and stock returns,working paper,New York University.

8.Health,Tversky(1991),Preference and belief: Ambiguity and competence in choice under certainty, Journal of Risk and Uncertainty,vol.4,Issue.1,pp.5-28.

9.Jian-yang(2004),The informational role of open interest in futures market, Applied Economics Letters,vol.11,pp.569-573.

10.Juho(2006), Rothschild – Stiglitz's definition of increasing risk and the relationship between volatility and risk premium, Review of Financial Ecomonics,vol.16 pp.363-374.

11.Jai-Jen Wang ,Yin-Rou Wang,Jin-Ping Lee(2015),Volatility Skew Measures and TAIFEX Return,2015 the Conference of CTFA_journal of Futures and Options.

12.Kin,Lean(2006),mean-variance-skewness-kurtosis based portfolio optimization, IEEE Computer Society ,vol.2.

13.Larry-martin(2008),ambiguity information quality and assest pricing,The Journal of Finance,vol LXIII,NO.1.

14.Nengjiu-ju(2012),Ambiguity, Learing, and Asset Return, Journal of Econometric Society,vol.80,NO.2,pp.559-591.

15.Pomchai-Chunhachinda(1997), Portfolio selection and skewness Evidence from intemational stock markets, Journal of Banking & Finance,vol.21,Issue.2,pp.143-167.

16.Prithviraj,james,David(2006),Impiled volatility and future portfolio returns,Journal of Banking and Finance,vol.31,Issue.10,pp.3183-3199.

17.Tsong-Yue Lai(1991), Portfolio selection with skewness: s multiple-objective approach, Review of Quantitative Finance and Accounting,July 1991,pp.293-305.

18.Uzi-segal(1987),the Ellsberg paradox and risk aversion: anticipated utility approach, International Economic Review,vol.28,NO.1,pp.175-202.