On the basis of the above mentioned and by the group sampling from the nomal overall,the paper discusses the sampling distribution question where there is a constant correlation within a group and independence between the different groups .

In this paper,the sampling distribution theory based on simple random sample is extended to the case for heteroscedasticity and constant correlation sample, which has set up the basis for studying the statistical inference theory and application of non simple random sample.

Secondly we discuss the optimal portfolios in terms of whether there are riskless assets, we also get the optimal portfolios on the assumption that the risk assets are constant correlated.

Following the characteristic of the open found,the paper used the single-index method to analysis the optimum investment combination of the open found under the assumption that the risk assets are constant correlated,also discussed the optimum investment combination of the open found while it can not be short selling.