避險是風險管理重要的一環，因此如何決定避險比例是投資人所需面對的重要課題。本文利用Aumann and Serrano (2008)、Foster and Hart (2009)、Bali, Cakici and Chabi-Yo (2011)三個風險指標計算現貨–期貨的最適避險比例，有別於過去文獻使用的風險衡量方法，本文使用的風險指標有較良好的經濟意涵也符合隨機優越法則。為了與傳統風險指標做比較，本文加入被廣泛使用來當作風險指標–變異數作為本文風險衡量方法之一，以此檢測不同風險指標對於避險比例的影響。此外選取多個國家股價指數作為研究標的以檢驗不同國家避險比例的差異。
本文實證結果發現在動態避險時使用變異數所求的避險比例較穩定且各國避險比例差異最小，而使用Bali, Cakici and Chabi-Yo (2011)風險指標避險比例波動較劇烈且各國避險比例差異程度最大。Aumann and Serrano (2008)、Foster and Hart(2009)兩個風險指標所計算的避險比例較相近。

Hedge is an important part of risk management. It comes up with a critical problem to be addressed in determine hedge ratio. In this paper, we propose three spot-futures hedging methods that determines the optimal hedge ratio by minimizing the riskiness of hedged portfolio returns, where the riskiness is measured by the index of Aumann and Serrano (2008), Foster and Hart (2009) and Bali, Cakici and Chabi-Yo (2011). Unlike the risk measurements widely used in the literature, the riskiness indexes employed in our methods not only have better economic interpretation but also satisfy monotonicity with respect to stochastic dominance. We add variance which is widely used to measure the risk of portfolio returns as one of our methods in order to compare with traditional risk measurements. Moreover, we examine the hedge ratio between different countries.
Our empirical result shows that when we take dynamic hedging strategy, variance is the most stable hedge ratio method and the difference between countries is the smallest. Bali, Cakici and Chabi-Yo (2011) is the most unstable method and the difference between countries is the biggest. Hedge ratio measure by Aumann and Serrano (2008)and Foster and Hart (2009) are closed.

Anand, A., Liy T., Kurosaki T., Kim Y. S., 2016. Foster–Hart optimal portfolios. Journal of Banking & Finance 68, 117–130.
Artzner, P., Delbaen, F., Eber, J.-M., Heath, D., 1999. Coherent Measures of Risk. Mathematical Finance 9(3), 203-228.
Aumann, R.J., Serrano, R., 2008. An Economic Index of Riskiness. Journal of Political Economy 116(5), 810–836.
Bali, T., Cakici, N., Chabi-Yo, F., 2011. A Generalized Measure of Riskiness. MANAGEMENT SCIENCE 57(8), 1406-1423.
Bali, T. G., Cakici, N., and Chabi-Yo, F., 2012. Does aggregate riskiness predict future economic downturns? Fisher College of Business 29, 3-9.
Brooks C, Henry OT, Persand G., 2001. The Effect of Asymmetries on Optimal Hedge Ratios. The Journal of Business 75(2), 333-352.
Cecchetti, Robert E. Cumby, Stephen Figlewski., 1988 Estimation of the Optimal Futures Hedge. The Review of Economics and Statistics 70(4), 623-630.
Chen, S.S., Lee, C.F., Shrestha, K., 2003. Futures hedge ratios: a review. Quarterly Review of Economics and Finance 43, 433–465.
Chen, Y.T., Ho, K.Y., Tzeng, L.Y., 2014. Riskiness-minimizing spot-futures hedge ratio. Journal of Banking & Finance 40, 154-164.
Chen, Y.T., Huang R. J., Shih, P. T., Tzengy, L. Y., 2016. Capital Asset Pricing Model Based on a Generalized Economic Index of Riskiness.
De Jong, A., de Roon, F., & Veld, C., 1997. Out-of-sample hedging effectiveness of currency futures for alternative models and hedging strategies. Journal of Futures Markets 17(7), 817-837.
Ederington, L. H., 1979. The Hedging Performance of the New Futures Markets. The Journal of Finance 34(1), 157-170.
Foster, Dean P., and Sergiu Hart., 2009. An Operational Measure of Riskiness. Journal of Political Economy 117(5), 785-814.
Homm, U., Pigorsch, C., 2012. Beyond the Sharpe ratio: An application of the Aumann–Serrano index to performance measurement. Journal of Banking & Finance 36(8), 2274-2284.
Howard, C.T., & D’Antonio, L.J., 1984. A Risk-Return Measure of Hedging Effectiveness. Journal of Financial and Quantitative Analysis 19(1), 101-112.
Hsin, C.W., Kuo, J., & Lee, C.F., 1994. A new measure to compare the hedging effectiveness of foreign currency futures versus options. Journal of Futures Markets 14(6), 685-707.
Johansen, S., Juselius, K., 1990. Maximum likelihood estimation and inference on cointegration—with applications to the demand for money. Oxford Bulletin of Economics and Statistics 52, 169–210.
Kadan, O., Liu, F., 2014. Performance evaluation with high moments and disaster risk. Journal of Financial Economics 113(1), 131–155.
Leiss, M. and Nax, H. H., 2015. Option-implied objective measures of market risk. Working Paper 29.
Lence, S. H., 1995. On the optimal hedge under unbiased futures prices. Economics Letters. 47(3-4), 385-388.
Lence, S. H., 1996. Relaxing the Assumptions of Minimum-Variance Hedging. Journal of Agricultural and Resource Economics 21(1), 39-55
Lien, D., Tse, Y. K., 1998. Hedging time-varying downside risk. Journal of Futures Markets 18(6), 705-722.
Myers, R. J., Thompson, S. R., 1989. Generalized Optimal Hedge Ratio Estimation. American Journal of Agricultural Economics 71(4), 858-868.
Riedel, Frank, Hellmann. Tobias, 2015. The Foster–Hart measure of riskiness for general gambles. Theoretical Economics 10(1), 1–9.
Schreiber, A., 2012. An Economic Index of Relative Riskiness. Working Paper, Hebrew University of Jerusalem.
Schulze, K., 2014. Existence and computation of the Aumann–Serrano index of riskiness and its extension. Journal of Mathematical Economics 50, 219–224.
Taboga, M., 2014. The Riskiness of Corporate Bonds. The Journal Money, Credit and Banking 46(4), 693–713.