Empirical distributions of daily equity index returns: A comparison

• We answer the question of which model to use to represent equity index returns.
• We compare performances of different distributions using KS and AD statistics.
• We also test the power of the models using Value-at-Risk failure rates.
• The generalized lambda distribution outperforms other models.

The normality assumption concerning the distribution of equity returns has long been challenged both empirically and theoretically. Alternative distributions have been proposed to better capture the characteristics of equity return data. This paper investigates the ability of five alternative distributions to represent the behavior of daily equity index returns over the period 1979–2014: the skewed Student-t distribution, the generalized lambda distribution, the Johnson system of distributions, the normal inverse Gaussian distribution, and the g-and-h distribution. We find that the generalized lambda distribution is a prominent alternative for modeling the behavior of daily equity index returns.