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The big block of problems is connected with process of mathematical modeling and management of portfolios of securities. The portfolio of financial assets is the difficult financial object having own theoretical base. Thus, when forecasting there are problems of modeling and use of mathematical apparatus, in particular, of the statistical. Of course, in some cases, when it is possible to speak not about a portfolio, and about some elements of "portfolio approach", it is possible to manage simpler receptions, but before everyone who is engaged in this perspective, there are serious settlement and research problems sooner or later. And universal approach to the solution of all arising tasks does not exist, and specifics of a concrete case demand modification of basic models.

The first and one of the most expensive, labor-consuming elements of management, is the monitoring representing the continuous detailed analysis of stock market, tendencies of its development, sectors of stock market, investment qualities of securities. An ultimate goal of monitoring is the choice of the securities possessing the investment properties corresponding to this type of a portfolio. Monitoring is a basis of both an active, and passive way of management.

Thus two approaches are possible: the heuristic - based on the approximate forecast of dynamics of each type of assets and the analysis of structure of a portfolio, and statistical - based on creation of distribution of probability of profitability of each tool separately and all portfolio in general.

Also such way of passive management as a method of index fund is hardly applicable. The index fund — is the portfolio reflecting the movement of the chosen market index characterizing a condition of all securities market. If the investor wishes that the portfolio reflected a condition of the market, it has to have such share of securities what these papers make at calculation of an index in a portfolio. In general the securities market is ineffective now therefore application of such method can yield losses instead of desirable positive result.

Costs for management of excessively diversified portfolio will not yield desirable result as profitability of a portfolio will hardly increase higher rates, than costs in connection with excessive diversification.

Diversification of investments - the basic principle of portfolio investment. The idea of this principle is well shown in an ancient English saying: do not put all eggs in one basket - "do not put all eggs in one basket".