We are often asked how the performance displayed in the app (return in %) is actually calculated. The VIAC app always shows the TWR (time-weighted rate of return). The TWR is easy to calculate and is generally regarded as an industry standard, but sometimes has its pitfalls in its interpretation.
First, a daily return rt is calculated for each day:
r1 = (P1 – P0 + D1) / P0
The portfolio value at the end of the day P1 and the portfolio value at the end of the previous day P0 are used. The difference corresponds to the development on the stock exchange. Any dividend payments D1 during the day are added to this. Conversely, any cash flows (incoming or outgoing payments) of the current day are not taken into account.
The TWR is then created by geometrically linking these daily returns – from the first r1 to the last rt day of the period under consideration:
TWR = (1 + r1) * (1 + r2) * … * (1 + rt) – 1
Advantages and disadvantages
The TWR is easy to calculate and makes strategies comparable since all deposits and withdrawals are ignored. Accordingly, the TWR reflects the actual return achieved as if the same amount had always been invested from the start. However, it is precisely this omission of incoming and outgoing payments that can make interpretation more difficult, as the following example illustrates:
We consider two equally long periods. CHF 100 is invested at the start of period 1. The return in period 1 is 50%; accordingly we achieve a profit of CHF 50. CHF 100 will be invested again at the start of period 2 – in other words, we start with a total of CHF 250 in period 2. The return in period 2 is then equal to -30%, which implies a loss of CHF 75. At the end of period 2, the portfolio value is CHF 175. Since we made deposits in total of CHF 200, we lost CHF 25 in absolute terms. However, the TWR is +5%, since
(1 + 50%) * ( 1+ (-30%)) – 1 = 5%
This means that we have a loss in CHF compared to the total of incoming payments with a simultaneously positive TWR performance. The discrepancy or “wrong” sign arises because the timing of the second payment at the start of period 2 was unfavourable – we increased our position exactly before the correction of 30%. This example illustrates the problems of the TWR, even if it is, of course, an extreme one. In practice, however, it will happen regularly that the displayed performance does not exactly correspond to one’s own intuition. Payments that are not immediately invested can also make the interpretation more difficult.