# How can I interpret the displayed return?

We are often asked how the performance (return in %) displayed in the app is calculated. In the VIAC app you can choose between two return measures, which are explained in the following article. These are the TWR (Time-Weighted Return) and the MWR (Money-Weighted Return).

### TWR – Time-Weighted Return

The TWR is easy to calculate and generally considered to be the industry standard, but it can sometimes be tricky to interpret.

#### Calculation

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

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.

### MWR – Money-Weighted Return

The MWR is a money-weighted return measure that takes into account cash inflows and outflows. In contrast to the TWR, the MWR is therefore also suitable for measuring investment decisions and accordingly includes a personal timing component. This often makes the MWR more intuitive in a portfolio with frequent cash flows and facilitates interpretation. At the same time, however, the MWR % value is no longer comparable with other strategies or funds.

#### Calculation

An optimization procedure is used to calculate the MWR, which is best explained using a simple example:

Date Comment Value
31.12.2020 Deposit 1 CHF 80
31.12.2021 Deposit 2 CHF 20
31.12.2022 Current portfolio value CHF 105
31.12.2022 MWR (p.a.) 2.74%

In simple terms, the optimization procedure calculates the annual interest rate that must be applied to the deposits in order to obtain the indicated portfolio value as of 31 December 2022. The MWR is therefore an annual rate of return that exactly solves the optimization problem – that is, the deposits bearing interest at the MWR yield exactly the current portfolio value. In the VIAC app, this annual MWR is then scaled to the customer-specific period, i.e. the % return since start is displayed analogously to TWR. In the example above, the money-weighted return since start is 5.56%.

In general, the MWR is intuitive and easier to interpret, since the personal timing component in the form of deposits and withdrawals is taken into account and the % value is therefore often close to the effective profit/loss in CHF. Since personal investment decisions are included in the %-value, the MWR loses the possibility to compare the personal portfolio return with other portfolios or other providers. In addition, the MWR can also take on values that are not intuitive at first glance, as the following example shows:

Date Comment Value
31.12.2018 Deposit 3a CHF 7’000
31.12.2019 Deposit 3a CHF 7’000
31.12.2020 Deposit 3a CHF 7’000
31.12.2021 Transfer VB and deposit 3a CHF 1’007’000
31.12.2022 Current portfolio value CHF 1’060’000
31.12.2022 MWR (p.a.) 2.98%

The VIAC app shows the return since start over the whole 4 years. The MWR p.a. of 2.98% is thus scaled up and the displayed money-weighted return is 12.48%. At first sight it looks like a return of 12.48% is too high if the current portfolio value of CHF 1’060’000 is compared with total payments of CHF 1’028’000.

The reason is that the MWR is dominated by relatively large cash flows. The large and late incoming vested benefits transfer is therefore decisive for the % return here – and this also applies to the displayed % return since start, although the vested benefits transfer has actually only been invested for one year.