When teaching our Fundamentals of Investment Performance course, when writing my books, and often when simply having conversations with clients, I am often faced with the task of explaining, in as clear a manner as possible, the differences between time and money weighting. This topic is one of the most confusing in our industry. I’ve heard, on several occasions, performance measurement veterans misspeak when it comes to these matters.
At the core it all boils down to cash flows: whether to include them in the process, or eliminate (or at least reduce) their impact on the resulting return. And while a few folks suggest that their implementation has nothing to do with who controls the cash flows, the reality is that this is definitely the main reason behind deciding upon which to use (though there are times when we actually ignore this, in favor of the insights provided).
And it also boils down to linking. That is, the geometric linking of returns.
Time weighting comes in two forms: exact and approximate. Exact methods revalue the portfolio for all cash flows, and calculate returns between each of these revaluations. Approximation methods may revalue for large flows, but not all flows (or they’d be exact). And linking occurs at any point when the portfolio is revalued (either when large flows occur, or at month-ends).
We typically use either the Modified Dietz or Internal Rate of Return (IRR) formula in our approximation methods. Both of these formulas, by themselves, are actually money-weighted methods. We transform them into time-weighting when we employ geometric linking!
The following graphic contrasts money and time weighting:
As you can see, we are calculating returns in two ways: by time and money weighting. The essential difference is that with time-weighting, we value the portfolio multiple times during the period, and link the intermediate results, while for money weighting, we only value at the end points.
Can more be said on this topic? Yes! And more will be, so stay tuned.