It is well known that index fund selections are important for the risk hedge of investment in a stock market. The ‘selection’ means that for ‘futures’, n companies of all ones in the market are selected. Suppose that we invest in c stocks of each selected company. The total return rate of a group of n companies, then, has to follow well the increasing rate of the stock price index in the market. We adopt the coefficient of determination (CDP) as the measure of fitness between the total return and increasing rates. The main purpose of this paper is to propose a simple method for the selections. The method consists of two steps. One is to select N companies in the market with heuristic approach. The other is to construct a group of n companies, say In,N, by applying genetic algorithms to the set of N companies. The method is applied to the 1st and 2nd Sections of Tokyo Stock Exchange. The results show: the method gives a near optimal solution for the case of selecting n companies from all ones in the market. There is a set of N0 companies such that the CDP of In,N depends a little on the N when N>N0. This means that it is possible to construct an efficient In,N even when N is relatively small and hence n is small. The method especially works well when the increasing rate of stock price index over a period can be viewed as a linear time series data.
