It is well known that an index fund portfolio is useful for the risk hedge of investment. The portfolio consists of M-company (called brand) stocks and its price as a function of time traces the stock price index in the market. From a practical viewpoint, it is desired that M-company is smaller and the correlation between the portfolio price and stock price index, included in the portfolio is higher. The correlation is called the contribution rate. Suppose that there are some portfolios where the contribution rate is greater than a fixed level. We then select the portfolio that minimizes its own risk in the portfolio. The main purpose of the paper is to find such a portfolio by using a genetic algorithm (GA). We present some numerical examples that demonstrate the usefulness of GA. We show that GA works well for finding such portfolios.
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