Whether “simple”, “time-weighted” or “money-weighted”, not all returns are the same: why we calculate different metrics for our customers and how they differ.
You pay in €1,000, you get €1,100 back, you make a profit of €100 – so a positive return of ten percent: that seems to follow pretty simply and logically. Return is what comes out as “more” or “less” at the end when you invest. But often what at first seems plausible and simple turns out, on closer inspection, to be a little more complicated after all. And returns on investments are one such case.
With the simple return calculation, you merely subtract the amount paid in from the current value and work out the growth rate. But this simple approach can sometimes lead to distorted information. Because a lot is in flux over the course of an investment. You have to take into account different performance across different time periods as well as deposits and withdrawals during the investment period.
How did the strategy I invested in perform? Where do I personally stand with my total assets at quirion? Depending on which question you are looking to answer, the calculation works out a little differently – and often so does the result.
How successful was the strategy?
Prices don't move uniformly; the returns of different investment periods differ from one another. A few percent up one moment, then down again the next: if you want to know how successful one strategy was compared to another, you need to look at the time-weighted returns (TWR). When calculating these, the amount of capital invested is disregarded. That's because it differs from one investor to another and is not itself part of the investment strategy.
For our customers, we calculate this metric for each strategy and for the period in which they were invested in it. To do so, we evaluate the returns of the individual trading days and use them to calculate the time-weighted total returns.
Where do I stand with my assets?
The money-weighted return (MWR) takes individual cash flows into account. In every portfolio there are both deposits and withdrawals over the course of an investment. With savings plans as well as top-ups or withdrawals, this is quite obvious. In addition, there are, for example, income such as dividends. Fees, for instance, are debited.
Because cash flows differ from one investor to another, money-weighted returns cannot be compared with each other or with time-weighted ones. That would be like the proverbial apples and oranges. As a rule: the longer you invest, the more time-weighted and money-weighted returns can diverge.
A simplified, schematic example with just three deposits illustrates the difference:
| Vermögenswert zum Jahresbeginn | Einzahlung zum Jahresbeginn | Angenommene Rendite p. a. |
|---|---|---|
| 0 | 10.000 € | + 10 % |
| 11.000 € | 10.000 € | - 5 % |
| 19.950 € | 10.000 € | + 15 % |
Assets reached at the end of the period: €34,443.
Simple return calculation:
€4,443 ÷ €30,000 = 14.8% total return, equivalent to 4.93% p.a.
Time-weighted return calculation:
((1+0.1) × (1-0.05) × (1+0.15)) – 1 = 20.2% total return, equivalent to 6.32% p.a.
Money-weighted return calculation:
€10,000 × (1+return p.a.)3 + €10,000 × (1+return p.a.)2 + €10,000 × (1+return p.a.) = €34,443
Solving the equation gives a return of 7.06% p.a..
In your personal area after logging in, we also make money-weighted return metrics available to you. In the quarterly reporting in your inbox, you will also find time-weighted return metrics for various periods. Because we want to be as transparent as possible.
But what's important is this: all return metrics during an investment are always only a snapshot in time. Our investment strategy is designed for a long-term investment horizon. That is the basis for systematically harnessing the return opportunities of the capital markets and the compound interest effect.
