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Investment management on the capital market is a complex and multifarious process and the accuracy of decisions is an indispensable condition that an investor needs to fulfill if the expected economic results are to be achieved. The paper presents the concept of the optimization of investment portfolio on the capital market of shares. The maximum value of portfolio quality measure was used as an optimization criterion. It is expressed by the index of variability R/σ of the rate of return for each share in the portfolio. The cumulation of values of R/σ index in the successive years of the investigated period allowed for an econometric estimation of the continuous functions and their maximum. The indexes of asymmetry of rate of return for particular shares in the portfolio were introduced into the functions, which enabled to increase the efficiency of the selection of shares for the portfolio. This, in turn, allowed to achieve the optimum structure of shares in the portfolio

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A concept of using a dynamic programming method to optimize an investment portfolio allowing for asymmetric rates of return and a minimum risk portfolio