How to Calculate Time-Weighted Rate of Return

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Alex Frank

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In the complex world of investments, understanding the performance of your portfolio is key. That’s where the Time-Weighted Rate of Return (TWRR or TWR) comes into play. It’s a specialized tool used by investors and portfolio managers to measure the compound growth rate of their investments, irrespective of external cash flows like deposits or withdrawals. This article aims to provide a comprehensive understanding of what it is, how it’s calculated, and its importance in investment decision-making.

What is the Time-Weighted Rate of Return?

TWRR is a method used to gauge the performance of investment portfolios. It essentially eliminates the effect of cash flow timings on the return. This approach breaks down the investment period into smaller intervals, typically at points when cash flows occur, and calculates the return for each period separately. These individual returns are then geometrically linked to represent the investment’s overall performance.

Why the Time-Weighted Return Matters

TWRR is important because it provides a level playing field for comparing the performance of different investment strategies or fund managers. It focuses solely on the investment’s growth, excluding the impact of external cash flows. This unique feature makes it a preferred choice for evaluating the performance of managed funds, particularly those experiencing frequent cash inflows and outflows.

Calculating the Time-Weighted Rate of Return: A Step-by-Step Guide

Calculating TWRR involves several steps:

  1. Identify Valuation Points: These include the start and end of the investment period and any dates when cash flows occur.
  2. Calculate Returns for Each Sub-Period: Determine the portfolio’s return for each interval between valuation points.
  3. Geometrically Link Returns: Multiply the returns of each sub-period together to find the overall return.

The formula for TWRR is:

TWRR = (1 + R_1) \times (1 + R_2) \times \cdots \times (1 + R_n) - 1

Where R_1, R_2, \ldots, R_n are the returns for each sub-period. Each R_n can be calculated using this formula:

R_n = \frac{\text{End Value}_{n}\; -\; \text{Deposits}_n\; +\; \text{Withdrawals}_n -\; \text{Initial Value}_n\;}{\text{Initial Value}_n}

Practical Example

Let’s take a practical example to understand TWRR:

  • Initial Investment: $1,000,000 on 1 January 2023.
  • First Period End: Portfolio grows to $1,110,000 by 31 December 2023.
  • Cash Flow: You add $25,000 on 31 December 2023.
  • Second Period End: Portfolio is worth $1,335,000 by 31 December 2024.
  • Cash Flow: You pay $1,250 in fees on 31 December 2024

Here, you’ll calculate the return for January to December 2023 and December 2023 to December 2024 separately and then multiply them to find the overall performance. I’ve plugged these details into an online TWRR calculator as shown below:

Time-weighted rate of return calculator

The Limitations of Time-Weighted Rate of Return

While TWRR is a powerful tool but it’s not without limitations. It may not reflect the experience of an individual investor, especially in cases of significant cash inflows or outflows. In such scenarios, the Money-Weighted Rate of Return could be more applicable.

Money-Weighted Rate of Return (MWRR) and Time-Weighted Rate of Return (TWRR) differ significantly in how they account for the timing and size of cash flows:

Focus on Cash Flows

  • Money-Weighted Rate of Return: It focuses on the investor’s actual experience by considering the size and timing of cash flows. MWRR calculates the internal rate of return (IRR) on an investment, taking into account when and how much money is added or withdrawn from the portfolio. This means the MWRR can be higher or lower depending on whether contributions are made when the market is down (benefiting from subsequent rises) or up (suffering from subsequent falls).
  • Time-Weighted Rate of Return: It removes the impact of cash flows on investment performance. By breaking the investment period into smaller intervals at each cash flow point, TWRR calculates the growth of $1 initially invested, irrespective of subsequent deposits or withdrawals. This method provides a measure of the portfolio manager’s performance, independent of the investor’s actions.

Suitability

  • Money-Weighted Rate of Return: It is more suitable for individual investors, as it reflects the actual return they have achieved based on their specific investment and withdrawal timings.
  • Time-Weighted Rate of Return: It is more appropriate for evaluating the performance of fund managers or comparing different investment strategies, as it is not influenced by the individual investor’s cash flow decisions.

Calculation Complexity

  • Money-Weighted Rate of Return: The calculation can be more complex as it involves solving for the rate of return that sets the present value of all cash inflows and outflows equal to the value of the initial investment.
  • Time-Weighted Rate of Return: It involves calculating the returns of several sub-periods and geometrically linking them, which is relatively straightforward.

In summary, MWRR is influenced by the investor’s behavior and cash flow timing, reflecting personal investment performance, while TWRR provides a standardized measure of a portfolio’s returns, making it ideal for comparing the performance of fund managers or investment strategies without the bias of cash flow timings.

Conclusion

The Time-Weighted Rate of Return is an invaluable tool for evaluating the performance of investment portfolios. It offers a fair method for comparison and helps investors and fund managers make informed decisions. By understanding TWRR, you can better assess the effectiveness of your investment strategies.

Additional Resources

For further reading on TWRR and other financial metrics, check out:

  1. The Time-Weighted Rate of Return write-up and calculator at TheCalculatorKing.com
  2. What is the time weight rate of return? https://freetrade.io

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