Time-Weighted Rate of Return (TWR)
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What is the Time-Weighted Rate of Return (TWR)?
The time-weighted rate of return (TWR) measures the compound growth rate of a portfolio. Growth rates can be distorted by cash inflows and outflows. By calculating the TWR, this distortion is removed. For this purpose, the returns are grouped into intervals, always at the time when money is flowing in or out. As a result, these adjusted returns are more suitable for comparing the returns of different portfolios of securities.
Calculation of the TWR
A new period is created for each interval in which cash inflows or outflows have taken place. The yield is calculated separately for each of these periods. The returns for each individual period are then multiplied together.
Example: Time Weighted Rate of Return (TWR) vs. Simple Return
Example 1
Over the course of three years, an investor invests CHF 10,000 in a securities portfolio each year. Suppose that the securities portfolio grows by 10% in its first year. By the end of the year, the portfolio had a value of CHF 11,000. A further CHF 10'000 has been invested. Therefore, at the beginning of the second year, the portfolio would have a value of CHF 21'000. The value of the portfolio declined by 5% in the second year to CHF 19'950. Following the third investment of CHF 10'000, the portfolio earned a profit of 15% in the third year. After three years, the portfolio has a value of approximately CHF 34'443. The profit is approximately CHF 4'443. There is a simple return of 14.8% (4'443/30'000). However, the TWR is 20.2%.
Example 2
For three years, an investor invests CHF 30,000 in the same securities portfolio as in example 1. Similarly to example 1, the value of the portfolio increases by 10% in the first year (CHF 33,000), decreases by 5% in the second year (CHF 31,350), and increases again by 15% in the third year (CHF 36,053). Due to the fact that no money was added or subtracted in this example, the time-weighted rate of return is the same as the simple return. This profit amounts to CHF 6'053. Both the TWR and the simple return yield 20.2% (6'053/30'000).
Comparison Example 1 and Example 2
Comparing simple returns from examples 1 and 2, the securities portfolio from example 2 appears to be more profitable. As a matter of fact, this is not the case. The portfolio used in the examples is the same. Investors who invested the full amount at the beginning (example 2) earned more money. However, this may not always be the case. In certain circumstances, it may be more advantageous to invest according to a savings plan, as in example 1. Consider, for example, a scenario in which the value of the securities portfolio fell by 5% in the first year, then increased by 10% in the second year, and then increased by 15% in the third year. After three years, the portfolio of the investor from example 1 would have been worth CHF 36,168. Wealth managers may be responsible for selecting investments for portfolios, but they are limited in their influence on how much money is invested and when. A comparison of securities portfolios cannot be made based on simple returns alone. In assessing the performance of wealth managers, it is advisable to consider the TWR.
The example illustrates the difficulty of determining how much money can be earned from a securities portfolio if deposits and withdrawals are made over time. In this case, the TWR calculation is beneficial. The TWR should not, however, be confused with the investor's actual return.
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