This paper aims to deduce the composition of a portfolio of investment funds when the investor wishes a periodic subscription of the shares belonging to the said portfolio. To do this, starting from the historical series of the selling values and using the model of Roy, we have deduced the profitabilities of each one of the funds in the case of a systematic subscription and so we have calculated the proportion of each fund in the portfolio. These results have been compared using the profitabilities obtained when the investor carries out a simple operation. Finally, this approach can be presented either when the investor can place his contributions according to an arithmetic succession or a geometric one.