Axiomatic Characterization of the Time-Weighted Rate of Return

In a recently published banking industry study [Fisher, Lawrence. 1968. Measuring rates of return. Chapter 2 in James H. Lorie et al., Measuring the Investment Performance of Pension Funds for the Purpose of Inter-Fund Comparison, Bank Administration Institute, Park Ridge, Illinois.], it was pointed out that the venerable internal rate of return is inappropriate for measuring the performance of pension fund managers. It is suggested that a measure of management performance should depend solely on the way in which the manager proportions the fund's resources and not on fund contributions and withdrawals. Unfortunately, the internal rate depends on this contribution and withdrawal pattern.

The banking industry study proposed a new measure, the time-weighted rate of return, which is not dependent on the contribution and withdrawal pattern. The study, however, was incomplete in that it did not state or show that the time-weighted rate is the only well-behaved rate of return that is not influenced by contributions or withdrawals.

The latter result is developed in this paper.