Returns with Contributions
Simple returns can only be calculated if the amount invested does not change over the the time period measured. If contributions (withdrawals are contributions with a negative sign) take place during the time period measures, then the amount invested changes and the ending market value is not only the result of capital gains, but also of additional contributions that took place after the initial investment was made.
Calculating returns as the percent change of market value in the presence of contributions will lead to distortions: In the case of positive (negative) contributions, positive returns would be overestimated (underestimated) and negative returns would be underestimated (overestimated).
When contributions take place, other calculation methods are needed. All these methods have in common that they address the issue of a time-variable amount invested. But the methods differ in how they deal with this issue and will lead to different return figures will differ too.
This difference in results has important implications: For example, an observed difference in returns between portfolio A and portfolio B could simply be the result of a difference in calculation methodologies used and not be the result of differences in risk or investment process and its implementation.
So-called Money-Weighted Returns (MWR) or 'Dollar-Weighted Returns' as they are called in Northern America) express returns on investment including the timing decision about net contributions. So called Time-Weighted Returns (TWR) and the Unit-Value Method express returns on investment excluding the impact of the timing of net contributions. It can be shown that certain convergence relationships exist between TWR and MWR. Also, various approximations exist so that TWR and MWR can be expressed with a multitude of formulas.
This seeming complexity has resulted in the creation of something like a "performance measurement industry" offering a wide range of software products and consulting services. Theoretically, this industry should serve clients to better understand their returns on their investments. Practically, this industry can also create a lot of smoke to distract from the obvious. On the other hand, whenever there is smoke there's a fire, so smoke alone can be an interesting indicator.
A great deal of confusion regarding TWR and MWR can be found in the literature as well as in practical applications. A lof of the consfusion is the result of confuse terminology. The best thing would be to dispose the established terminology altogether and distinguish returns on unit-basis and returns on dollar-basis: returns on unit-basis do not include the effect of a changing amount invested over time and returns on dollar-basis do report results including the timing effect of net contributions. Any further discussions are about detail differences between calculation methodologies and the fact that returns on unit-basis and returns on dollar-basis converge, the smaller the impact (=size and timing) of net contributions. Please keep this in mind when getting lost in the details of the following discussion of return formulas.
Submenu
|
