A test of the stable and mixture of normals hypotheses for international stock returns

الملخص EN

This paper uses the stability under addition and the Generalized Central Limit Theorem (GCLT) properties of the stable Paretian distribution to test two alternate hypotheses, the stable and mixture of normal’s distributions.

The study uses stock market indices of ten countries.

The ten countries are U.

K,.

Germany, France, Italy, Holland, Japan, Hong Kong, Singapore, U.

S.

A.

and Canada to compare the extent to which the distribution characteristics of returns varies much between countries.

The results indicate that the returns of U.

K,.

Germany, France, Holland, and U.

S.

A.

correspond well to the mixture of normal’s distribution, while the returns of Italy, Canada, Japan, Hong Kong, and Singapore correspond better to the stable Paretian distribution.

The results suggest that the three Asian markets of Japan, Hong Kong and Singapore have the highest probability of large losses.

Italy and Canada have the second highest probability while UK, Germany, France, Holland and USA have lower probabilities of large losses.

The returns distributions of all countries were found to be negatively skewed indicating a larger probability of losses than that expected under the normal distribution.

The results do not mean that international diversification has no benefit.

Recent studies have shown that a global portfolio has always outperformed a local portfolio in the worst case events in Japan, Germany, U.

K,.

France, and U.

S.

A1.

The results only question the underlying assumptions that are used in modern portfolio management techniques, namely stocks returns in long run can be approximated by the normal distribution.

This could lead to suboptimal portfolio weightings.