Measuring Average Rate of Return of Pensions: A Discrete, Stochastic and Continuous Price Index Approaches

摘要

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.