Abstract

In this paper the problem of the proper construction of the average rate of return (ARR) of pension (or investment) funds is considered, using a chain price index approach. Some known formulas of the ARR can be expressed by chain indices. The paper proposes and discusses a continuous-time formula. The prices and the number of the participating units are assumed to be continuous-time stochastic processes. Using the Ito theorem (Ito, 1951) it is proved that the relative change in net assets of funds equals a product of relative changes in unit prices and number of fund clients. Simulation study compares the discrete time formulas and the continuous formula in some illustrative case.

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