Advertisement

Journal of Systems Science and Complexity

, Volume 22, Issue 3, pp 360–371 | Cite as

Skewness of return distribution and coefficient of risk premium

  • Fenghua Wen
  • Xiaoguang Yang
Article

Abstract

The skewness of the return distribution is one of the important features of the security price. In this paper, the authors try to explore the relationship between the skewness and the coefficient of risk premium. The coefficient of the risk premium is estimated by a GARCH-M model, and the robust measurement of skewness is calculated by Groeneveld-Meeden method. The empirical evidences for the composite indexes from 33 securities markets in the world indicate that the risk compensation requirement in the market where the return distribution is positively skewed is virtually zero, and the risk compensation requirement is positive in a significant level in the market where the return distribution is negative skewed. Moreover, the skewness is negatively correlated with the coefficient of the risk premium.

Key words

Coefficient of risk premium return distribution robust skewness speculation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. K. Kraus and R. H. Litzenberger, Skewness preference and the valuation of risky assets, Journal of Finance, 1976, 31: 1085–1185.CrossRefGoogle Scholar
  2. 2.
    I. Friend and R. Westerfield, Co-Skewness and capital asset pricing, Journal of Finance, 1980, 35: 897–913.CrossRefGoogle Scholar
  3. 3.
    J. C. Singleton and J. Wingender, Skewness persistence in common stock returns, Journal of Financial and Quantitative Analysis, 1986, 21: 335–341.CrossRefGoogle Scholar
  4. 4.
    K. G. Lim, A new test of the three-moment capital asset pricing model, Journal of Financial and Quantitative Analysis, 1989, 24: 205–216.CrossRefGoogle Scholar
  5. 5.
    R. Aggarwal, R. P. Rao, and T. Hiraki, Skewness and Kurtosis in Japanese equity returns: Empirical evidence, Journal of Financial Research, 1989, 12: 253–260.Google Scholar
  6. 6.
    M. Richardson and T. Smith, A test for multivariate normality in stock returns, Journal of Business, 1993, 66: 295–321.CrossRefGoogle Scholar
  7. 7.
    A. L. Alles and J. L. Kling, Regularities in the variation of skewness in asset returns, Journal of Financial Research, 1994, 17: 427–438.Google Scholar
  8. 8.
    C. R. Harvey and A. Siddique, Autoregressive conditional skewness, Journal of Financial and Quantitative Analysis, 1999, 34: 465–552.CrossRefGoogle Scholar
  9. 9.
    C. R. Harvey and A. Siddique, Conditional skewness in asset pricing tests, Journal of Finance, 2000a, 60: 1263–1287.CrossRefGoogle Scholar
  10. 10.
    Y. Ait-Sahalia and M. W. Brandt, Variable Selection for Portfolio Choice, Journal of Finance, 2001, 56: 1297–1355.CrossRefGoogle Scholar
  11. 11.
    A. Peiró, Skewness in financial returns, Journal of Banking and Finance, 1999, 23: 847–909.CrossRefGoogle Scholar
  12. 12.
    A. Peiró, Skewness in individual stocks at different investment horizons, Quantitative Finance, 2002, 2: 139–185.CrossRefGoogle Scholar
  13. 13.
    R. Cont, Empirical properties of asset returns: Stylized facts and statistical issues, Quantitative Finance, 2001, 1: 223–259.CrossRefGoogle Scholar
  14. 14.
    E. Jondeau and M. Rockinger, Testing for differences in the tails of stock market returns, Journal of Empirical Finance, 2003, (10): 559–581.Google Scholar
  15. 15.
    C. R. Harvey and A. Siddique, Time-Varying conditional skewness and the market risk premium, Research in Bank and Finance, 2000b, 1: 25–58.Google Scholar
  16. 16.
    F. D. Arditti, Risk and the required return on equity, Journal of Finance, 1967, 22: 19–36.CrossRefGoogle Scholar
  17. 17.
    F. D. Arditti, Another look at mutual fund performance, Journal of Financial and Quantitative Analysis, 1971, 6: 909–912.CrossRefGoogle Scholar
  18. 18.
    P. Samuelson, The fundamental approximation of theorem in portfolio analysis in terms of means, variances and higher moments, Review of Economic Studies, 1970, 37: 537–542.CrossRefGoogle Scholar
  19. 19.
    M. Rubinstein, The fundamental theorem of parameter preference security valuation, Journal of Financial and Quantitative Analysis, 1973, 8: 61–69.CrossRefGoogle Scholar
  20. 20.
    G. Tayi and P. Leonard, Bank balance sheet Management: An alternative multi-objective model, Operational Research Society, 1988, 39: 401–410.Google Scholar
  21. 21.
    T. Y. Lai, Portfolio selection with skewness: A multiple-objective approach, Review of Quantitative Finance and Accounting, 1991, 1: 293–305.CrossRefGoogle Scholar
  22. 22.
    P. Chunhachinda, K. Dandapani, S. Hamid, and A. J. Prakash, Portfolio selection and skewness: evidence from international stock markets, Journal of Banking and Finance, 1997, 21: 143–167.CrossRefGoogle Scholar
  23. 23.
    H. Fang and T. Lai, Co-Kurtosis and capital asset pricing, the Financial Review, 1997, 32(2): 293–307.CrossRefGoogle Scholar
  24. 24.
    A. J. Prakash, C. H. Chang, and T. E. Pactwa, Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets, Journal of Banking and Finance, 2003, 27: 1375–1390.CrossRefGoogle Scholar
  25. 25.
    Q. Sun and Y. X. Yan, Skewness persistence with optimal portfolio selection, Journal of Banking and Finance, 2003, 27: 1111–1121.CrossRefGoogle Scholar
  26. 26.
    Tae-Hwan Kim and Halbert White, On more robust estimation of skewness and kurtosis, Finance Research Letters, 2004, (1): 56–73.Google Scholar
  27. 27.
    M. A. Canela and E. P. Collazo, Portfolio selection with skewness in emerging markets, Working paper, 2004, IESE Business School.Google Scholar
  28. 28.
    J. M. Vanden, Portfolio insurance and volatility regime switching, Mathematical Finance, 2006, 16: 387–417.zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    R. C. Merton, On estimating the expected return on the market, Journal of Financial Economics, 1980, 8: 323–361.CrossRefGoogle Scholar
  30. 30.
    M. Rubinstein, Implied binomial trees, Journal of Finance, 1994, 49: 771–818.CrossRefGoogle Scholar
  31. 31.
    G. Bakshi, C. Cao, and Z. Chen, Do call prices and the underlying stock always move in the same direction? Review of Financial Studies, 2000, 13: 549–584.CrossRefGoogle Scholar
  32. 32.
    Y. Ait-Sahalia and A. W. Lo, Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices, Journal of Finance, 1998, 53: 499–547.CrossRefGoogle Scholar
  33. 33.
    D. B. Madan, P. P. Carr, and E. C. Chang, The variance gamma process and option pricing, European Finance Review, 1998, 2: 79–105.zbMATHCrossRefGoogle Scholar
  34. 34.
    D. Bates, Post-87 crash fears in S and P 500 futures options, Journal of Econometrics, 2000, 94: 181–238.zbMATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    D. Duffie, J. Pan, and K. Singleton, Transform analysis and asset pricing for affine Jump-Diffusions, Econometrica, 2000, 68: 1343–1376.zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    A. Ang, R. J. Hodrick, Y. Xing, and X. Zhang, The cross-section of volatility and expected returns, Journal of Finance, 2006, 61: 259–299.CrossRefGoogle Scholar
  37. 37.
    T. Bollerslev and H. Zhou, Estimating stochastic volatility diffusion using conditional moments of integrated volatility, Journal of Econometrics, 2002, 109(1): 33–65.zbMATHCrossRefMathSciNetGoogle Scholar
  38. 38.
    T. Adrian and J. Rosenberg, Stock returns and volatility: Pricing the short-run and long-run components of market risk, Staff Reports 254, 2006, Federal Reserve Bank of New York.Google Scholar
  39. 39.
    G. Bakshi, N. Kapadia, and D. Madan, Stock return characteristics, skewness law, and the differential pricing of individual equity option, the Review of Financial Studies, 2003, 16: 101–143.CrossRefGoogle Scholar
  40. 40.
    Anders Ekholm and Daniel Pasternack, The negative news thresholdan explanation for negative skewness in stock returns, the European Journal of Finance, 2005, 11(6): 512529.CrossRefGoogle Scholar
  41. 41.
    F. H. Wen, D. L. Huang, Q. J. Lan, and X. G. Yang, Numerical simulation for influence of overconfidence and regret aversion on return distribution (in Chinese), Systems Engineering Theory and Practice, 2007, 27(1): 1–10.zbMATHCrossRefGoogle Scholar
  42. 42.
    A. L. Bowley, Elements of Statistics, Charles Scribner's Sons, New York, 1920.Google Scholar
  43. 43.
    D. V. Hinkley, On Power Transformations to Symmetry, Biometrika, 1975, 62: 101–111.zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    R. A. Groeneveld and G. Meeden, Measuring skewness and kurtosis, the Statistician, 1984, 33: 391–399.CrossRefGoogle Scholar

Copyright information

© Academy of Mathematics & Systems Science, Beijing, China 2009

Authors and Affiliations

  1. 1.School of Economics and ManagementChangsha University of Science and TechnologyChangshaChina
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

Personalised recommendations