Return on investment is not the same as return on investment!? 📈💸
Hi Everyone,
the question about yield calculation may seem simple, but in my eyes it is really not easy to understand, so I'll try to shed some more light on the topic around yield. Have fun!😌
The return is the linchpin in any investment. Return objects such as capital investments or investments in tangible & financial assets can thus be compared with each other in terms of their earnings situation.
Now, however, there are different methods of calculating the rate of return. Depending on the period of time and the question, if there is a lot of trading in the portfolio and therefore strong fluctuations in value, e.g. 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 return calculation. Here, for any period of time, the profit/loss of an investment is set in relation to the invested capital. Thus, this form is particularly useful for a one-time investment, with no further deposits or withdrawals. As soon as further account movements take place, the simple percentage is no longer an ideal metric for the growth of your portfolio. Cash flows dilute the return, as the net investment amount jumps, but the gain/loss at that point remains constant.☝️
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 their display & also at Getquin this is the default setting (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 about 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 ideally suited for comparing portfolios in which regular payment flows take place, e.g., in the form of executed savings plans. So how is this calculated? Basically, the return is divided into partial periods. With each deposit & withdrawal starts a yield calculation based on the new capital! Thus, several different yield values are formed within a large period, which then together form the total return. By this single consideration of the partial periods the payment flows and also their height, as well as the timing are disregarded. Nevertheless, it is advisable to display the amount of the total profit/loss in addition to the time-weighted return. Why? We will come to this in section V.
Simply put, the time-weighted return is a multiplicative combination of the return factors based on the simple return (see above).
This form of calculation is also considered a standard method 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€ + 1000€* 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%
The time-weighted return now continues to show 44% here, as in example 1.1, because regardless of the savings plan execution, the performance is considered, which is exactly as in example 1.1 at 20% p.a..
III. the value-weighted return
Compared to the time-weighted return, which only considers the relative performance, the timing and the amount of investments are now taken into account. Thus, market timing can be measured. Because obviously it makes a difference if a profit/loss is generated with a low or high amount. Behind this return calculation is the internal rate of return (IRR) of the investment. In other words, the rate of return that is attributable to each previously invested monetary unit at the end of the respective investment period 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 like e.g. Portfolio Performance or Excel can show it.
Example 3.1
01.01.2021: 1.000€ with 5% p.a.
01.01.2022: 1.050€ + 1000€* with 35% p.a.
01.01.2023: 2.767,50€
_________________________
*Investment at 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%
inverse return in years:
Example 3.2
01.01.2021: 1.000€ with 35% p.a.
01.01.2022: 1.350€ + 1000€* with 5% p.a.
01.01.2023: 2.467,50€
_________________________
*Investment at 01.01.22
simple return:
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 changes as well, since the investor in example 3.1 earns a return of 35% after investing 1,000€ and thus had a "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 & 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 arithmetically the interest rate at which one would have to invest 1000 Euro for two years and another 1000 Euro for one year to achieve 38.4% simple return. It thus determines the average interest per year.
IV. Calculation principles according to Ex. 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
Since the time-weighted return calculation is presented independently of the cash flows and their levels, 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 at 01.01.22
simple return:
p.a. = -8.5%; total = -16.4%
time-weighted return:
p.a. = 9.5%; total = 20%.
Thus, the simple return would indicate the absolute loss of 1,800€ (11,000€ on 9,200€), whereas the time-weighted return, which ignores the inflows and their amount, only takes into account the +50% & -20% returns and thus 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 first of all directly comprehensible and obvious for everyone. The time-weighted return, on the other hand, calculates the increase in value, adjusted for inflows & outflows of funds, regardless of the time period. The value-weighted return makes it possible to compare the portfolio with a fixed interest rate, since the average interest rate p.a. is calculated.
Thus, if the invested capital of the period under study 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 if the portfolio value fluctuates strongly, the fixed interest rate assumption is incorrect and the values should be treated with caution.
In conclusion, 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 monthly savings, which are available directly, without waiting for "the" time, only the time-weighted return makes sense for me. In parallel, the absolute values are also displayed here on Getquin.
Do you use the simple or time-weighted return on Getquin?
[1]
More on TWROR & IRR:
https://blog.rentablo.de/rendite-berechnen-interner-zinsfuss-irr/
