Is the Distribution of Returns Symmetric?—Empirical Evidence from Agricultural Futures Market of China


The presence of asymmetry in the distribution of financial returns is not only an important factor which should be considered in the process of optimal portfolio allocation, but also one of the variables having close relationship with the recognition and measurement of financial risk. This paper adopts a method based on bootstrap to measure asymmetry in the distribution of financial returns, as proposed by Lisi (2007). Results of asymmetry test on the distribution of four representative price index series coming from agricultural futures market in China are presented, and the four indexes are hard wheat index, cotton index, sugar index and soybean oil index. The results indicate that, except for the distribution of soybean oil index return which has an evident asymmetry characteristic, the other three ones all can be considered symmetric at a high confidence level. This paper contributes to asymmetry evaluation in the marginal distribution of financial returns, as well as the study of distribution characteristics in agricultural futures index returns of China, in the way of providing new empirical evidence.

Share and Cite:

Wang, P. and Xiong, T. (2014) Is the Distribution of Returns Symmetric?—Empirical Evidence from Agricultural Futures Market of China. Journal of Financial Risk Management, 3, 29-39. doi: 10.4236/jfrm.2014.32004.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Bai, J., & Ng, S. (2005). Test for Skewness, Kurtosis and Normality for Time Series Data. Journal of Business and Economics Statistics, 23, 49-60.
[2] Bali, T., & Theodossiou, P. (2007). A Conditional-SGT-VaR Approach with Alternative GARCH Models. Annals of Operations Research, 151, 241-267.
[3] Bera, A., & Premaratne, G. (2001). Adjusting the Tests for Skewness and Kurtosis for Distributional Misspecifications (Working Paper). Champaign, IL: University of Illinois.
[4] Christofferson, P. F. (2003). Elements of Financial Risk Management. San Diego, CA: Academic Press.
[5] Christoffersen, P. F., Heston, S., & Jacobs, K. (2006). Option Valuation with Conditional Skewness. Journal of Econometrics, 131, 253-284.
[6] Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 987-1007.
[7] Harvey, C. R., Liechty, J. C., Liechty, M. W., & Muller, P. (2010). Portfolio Selection with Higher Moments. Quantitative Finance, 10, 469-485.
[8] Karoglou, M. (2009). Breaking Down the Non-Normality of Stock Returns. European Journal of Finance, 16, 79-95.
[9] Kendall, M., & Stuart, A. (1969). The Advanced Theory of Statistics. New York: McGraw-Hill Press.
[10] Khalifa, A., Miao, H., & Ramchander, S. (2011). Return Distribution and Volatility Forecasting in Metal Futures Market: Evidence from Gold, Silver and Copper. Journal of Futures Markets, 31, 55-80.
[11] Lisi, F. (2007). Testing Asymmetry in Financial Time Series. Quantitative Finance, 7, 687-696.
[12] Mcneil, A. J., & Frey, R. (2000). Estimation of Tail Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance, 7, 271-300.
[13] Peiro, A. (2004). Asymmetries and Tails in Stock Index Returns: Are Their Distributions Really Asymmetric? Quantitative Finance, 4, 37-44.
[14] Premaratne, G., & Bera, A. (2005). A Test for Symmetry with Leptokurtic Financial Data. Journal of Financial Econometrics, 3, 169-187.
[15] Rosenberg, J. V., & Schuermann, T. (2006). A General Approach to Integrated Risk Management with Skewed, Fat-Tails Risks. Journal of Financial Economics, 79, 569-614.
[16] Sabiruzzaman, M., Huq, M., Beg, R. A., & Anwar, S. (2010). Modeling and Forecasting Trading Volume Index: GARCH versus TGARCH Approach. Quarterly Review of Economics and Finance, 50, 141-145.
[17] Samuelson, P. (1970). The Fundamental Approximation of Theorem of Portfolio Analysis in Terms of Means, Variance and Higher Moments. Review of Economic Studies, 37, 537-542.
[18] Shi, L. M., Wen, B., & Hu, W. X. (2009). The Study on the Relationships of Exchage and Agricultural Products Futures Prices. Journal of Central University of Finance & Economics, 33, 37-42.
[19] Tang, Y. W., Chen, G., & Zhang, C. H. (2005). An Empirical Research on the Long-Term Correlation of the Price Volatility of the Agricultural Products Futures Markets. Systems Engineering, 23, 79-84.
[20] Terasvirta, T., & Zhao, Z. (2011). Stylized Facts of Return Series, Robust Estimates and Three Popular Models of Volatility. Applied Financial Economics, 21, 67-94.
[21] Wang, J., & Zhang, Z. C. (2006). Study of Price Discovery of China’s Farm Produce Futures Based on VAR Model. Chinese Journal of Management, 2, 680-684.
[22] Yi, R., Zhang, W., Chen, C., & Wang, S. Y. (2010). Agricultural Futures Basis Behaviors Basing on Expectations Theory. Systems Engineering—Theory & Practice, 30, 1954-1959.
[23] Zhang, S. Z., Li, T. Z., & Ding, T. (2006). An Empirical Study of the Relationship between Agricultural Futures Price Index and CPI. Journal of Financial Research, 34, 103-115.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.