It is well documented in the finance literature that the empirical
distribution of daily stock
market returns has very specific shape which is far from normal. It may have very long left tail and specifically high peak. The fund managers require information about the shape of distribution for their portfolio diversification.
Skewness is a measure of length of tail while the
kurtosis measures are highly correlated, they together are usually used to measure the shape of distribution. Conventionally the skewness and kurtosis are estimated by first four central moments. But these estimates are usually biased and have large variances which increases further if the underlying distribution is not normal. In the present study several alternative and robust
methods of measuring skewness and kurtosis for the empirical distribution of Muscat Stock Market daily returns are investigated. These consist of the methods based on Central Moments, Standardized moments, Linear Combination of Order Statistics and percentiles. Estimates of skewness and kurtosis by each of these methods are compared in terms of their non parametric bootstrap standard errors and length of percentile confidence intervals.