Hi everyone,
The question about calculating returns may seem simple, but in my opinion it's really not easy to understand, so I'll try to shed some light on the topic of returns in more detail. Have fun!
The return is the linchpin of every investment. Yield objects such as capital investments or investments in tangible & financial assets can be compared with each other in terms of their earnings situation.
However, there are different methods for calculating the return. Depending on the time period and whether there is a lot of trading in the portfolio and thus strong fluctuations in value, one or the other may make more sense.
I. Simple return
II. time-weighted return
III. value-weighted return
IV. Calculation principles
V. Positive relative return - negative absolute return
VI Which calculation makes sense for me?
I. The simple return
This is the simplest method of calculating returns. Here, the profit/loss of an investment is set in relation to the invested capital for any given period. This form is therefore particularly useful for a one-off investment, without further deposits or withdrawals. As soon as further account movements take place, the simple percentage is no longer an ideal indicator for the growth of your portfolio. Cash flows dilute the return, as the net investment amount increases by leaps and bounds, but the profit/loss remains constant at this point.☝️
Example 1.1
01.01.2021: €1,000 with 20% p.a.
01.01.2022: €1,200 with 20% p.a.
01.01.2023: 1.440€
_________________________
Simple return:
p.a. = 20.0%; total = 44.0%
Time-weighted return:
p.a. = 20.0%; total = 44.0%
Value-weighted return:
p.a. = 20.0%; total = 44.0%
Trade Republic, for example, uses exactly this calculation method in its display & this is also the default setting for Getquin (which is also OK). You can change the calculation here in the app under > Settings > Investment settings > Yield calculation 🤝. Getquin has also created an article on this. 👉 https://app.getquin.com/learn/getquin-depot-performance-berechnung
II The time-weighted return
The time-weighted rate of return (TWROR), on the other hand, is ideal for comparing portfolios with regular cash flows, e.g. in the form of executed savings plans. How is this calculated? Basically, the return is divided into partial periods. Each time a deposit or withdrawal is made, a return calculation based on the new capital is started! This results in several different return values within a large period, which then together form the total return. This individual consideration of the sub-periods means that the payment flows and their amount, as well as the timing, are disregarded. Nevertheless, it is advisable to show the total profit/loss in addition to the time-weighted return. Why? We will come to this in section V.
Simply put, in the time-weighted return, the return factors are multiplied together based on the simple return (see above).
This form of calculation is also the standard method used by professional investors and investment companies or is used when comparing the performance of ETFs. [1]
Example 2.1
01.01.2021: €1,000 with 20% p.a.
01.01.2022: €1,200 + €1,000* with 20% p.a.
01.01.2023: 2.640€
_________________________
*Savings plan execution as of 01.01.22
Simple return:
p.a. = 14.9%; total = 32.0%
Time-weighted return:
p.a. = 20.0%; total = 44.0%
Value-weighted return:
p.a. = 20.0%; total = 44.0%
As in example 1.1, the time-weighted return here still shows 44%, as the performance is considered independently of the execution of the savings plan, which is 20% p.a. as in example 1.1.
III The value-weighted return
In comparison to the time-weighted return, which only considers the relative performance, the timing and amount of the investments are now taken into account. Market timing can thus be measured. This is because it obviously makes a difference whether a profit/loss is generated with a small or large amount. Behind this return calculation is the internal rate of return (IRR) of the investment. In other words, the rate of return that has been earned at the end of the respective investment period on each previously invested monetary unit and thus also equates the individual cash flows with the final value. The IZF is determined by a kind of "trial & error" procedure. There is a complicated formula for the calculation, some programs such as Portfolio Performance or Excel can map this.
Example 3.1
01.01.2021: €1,000 with 5% p.a.
01.01.2022: €1,050 + €1,000* at 35% p.a.
01.01.2023: 2.767,50€
_________________________
*Investment on 01.01.22
simple return
p.a. = 17.6%; total = 38.4%
Time-weighted return:
p.a. = 19.1%; total = 41.8%
Value-weighted return:
p.a. = 23.7%; total = 53.0%
Reverse return over the years:
Example 3.2
01.01.2021: €1,000 with 35% p.a.
01.01.2022: €1,350 + €1,000* at 5% p.a.
01.01.2023: 2.467,50€
_________________________
*Investment on 01.01.22
simple yield:
p.a. = 11.1%; total = 23.4%
Time-weighted return:
p.a. = 19.1%; total = 41.8%
Value-weighted return:
p.a. = 14.8%; total = 31.9%
As you can see here, the simple return changes and the value-weighted return also changes, as the investor in example 3.1 achieved a return of 35% after investing €1,000 and therefore had "better timing" than in example 3.2, where "only" 5% was achieved after the investment. The time-weighted return, however, remains constant at 41.8% because, as we have learned, cash flows and the timing of the investment are disregarded here.
What exactly does the IZF tell us here? 23.7% p.a. from example 3.1 is the interest rate at which you would have to invest 1000 euros for two years and another 1000 euros for one year in order to achieve a simple return of 38.4%. It therefore determines the average interest rate per year.
IV. Calculation principles according to Example 2.1:
Simple: (2640/2000)^0.5 -1 = 14.9% p.a.; (2640/2000) -1 = 32% total
Time-weighted: 1.44^0.5 = 1.2 = 20% p.a.; 1.2 x 1.2 = 1.44 = 44% total
Value-weighted: (1000 x (1 + rw)^2 + 1000 x (1 + rw)^1) - 2640 = 0 ⇔ rw = 20% p.a.
V. Positive relative return - negative absolute return
As the time-weighted return calculation is shown independently of the cash flows and their amounts, in some cases there may be a positive return in % and a negative return in € and vice versa.
01.01.2021: €1,000 with 50% p.a.
01.01.2022: €1,500 + €10,000* with -20% p.a.
01.01.2023: 9.200€
_________________________
*Investment on 01.01.22
simple return:
p.a. = -8.5%; total = -16.4%
Time-weighted return:
p.a. = 9.5%; total = 20%
The simple return would therefore indicate the absolute loss of €1,800 (€11,000 to €9,200), whereas the time-weighted return, which ignores the inflows and their amount, only takes into account the +50% & -20% return and therefore comes to +9.5% p.a.
VI Which of the return calculations is the best?
It depends on what you want to analyze. The simple return is often used because it is immediately comprehensible and obvious to everyone. The time-weighted return, on the other hand, calculates the increase in value, adjusted for cash inflows and outflows, regardless of the time period. The value-weighted return allows the portfolio to be compared with a fixed interest rate, as the average interest rate p.a. is calculated.
If the capital invested in the period under review changes little, the internal rate of return is a recognized method for evaluating personal investment decisions. However, if there is a lot of trading or the portfolio value fluctuates greatly, the assumption of a fixed interest rate is incorrect and the values should be treated with caution.
In conclusion, it can be said that the time-weighted return measures the investment success of the strategy, whereas the money-weighted return measures the investment success of the investor.
Since I invest my available monthly savings installments directly without waiting for "the" time, only the time-weighted return makes sense for me. At the same time, the absolute values are also displayed here on Getquin.
Do you use the simple or time-weighted return on Getquin?
[1]
Further information on TWROR & IRR:
https://blog.rentablo.de/rendite-berechnen-interner-zinsfuss-irr/
