Time weighted rate of return

The time-weighted rate of return (TWR) is a crucial metric in portfolio performance measurement that evaluates an investment's compound growth rate, neutralizing the impact of external cash flows such as deposits or withdrawals. By effectively removing the influence of investor timing decisions, the time-weighted rate of return provides a clear picture of the portfolio's underlying performance due to its investment selections and market movements. It is widely regarded as a standardized measure for comparing the efficiency of different portfolio managers or funds. The time-weighted rate of return, also known as the geometric mean return, fragments the overall investment period into sub-periods, with new sub-periods commencing whenever there is a capital inflow or outflow.¹³

History and Origin

The concept of the time-weighted rate of return gained prominence with the development of standardized performance reporting in the investment industry. As the financial markets grew more complex and global, there was an increasing need for consistent and transparent methods to evaluate investment performance. This led to the creation of the Global Investment Performance Standards (GIPS), which largely mandate the use of time-weighted returns.¹²,¹¹ The GIPS standards, developed by the CFA Institute (formerly the Association for Investment Management and Research, AIMR), began their development in 1995, building upon earlier North American standards. The first edition of the GIPS standards was formally endorsed in February 1999, providing a voluntary yet widely adopted ethical framework for calculating and presenting investment performance.¹⁰ This standardization was critical for promoting fair competition and instilling investor confidence by allowing for comparable performance evaluations across different firms globally.⁹

Key Takeaways

• The time-weighted rate of return (TWR) measures the compound growth of an investment, isolating the impact of investment decisions from the timing of cash flows.
• It is the standard metric used by professional fund managers because they do not control investor deposits or withdrawals.
• TWR is calculated by geometrically linking the returns of individual sub-periods, each defined by an external cash flow.
• This method allows for fair comparisons between different mutual funds and other managed portfolios.
• The Global Investment Performance Standards (GIPS) strongly advocate for the use of time-weighted returns for performance reporting.

Formula and Calculation

The time-weighted rate of return is calculated by breaking the total investment period into sub-periods based on the dates of external cash flows (deposits or withdrawals). The return for each sub-period is calculated, and these sub-period returns are then geometrically linked to determine the overall time-weighted rate of return.⁸

The formula for the time-weighted rate of return (TWR) is:

Where:

• (HP_n) = Holding Period Return for sub-period n
• (HP = \frac{Ending\ Value - (Beginning\ Value + Cash\ Flow)}{Beginning\ Value + Cash\ Flow})⁷
• n = Number of sub-periods

Each (HP_n) accounts for the change in net asset value within that specific sub-period, adjusting for any new money invested or withdrawn only at the beginning of the subsequent sub-period. This effectively isolates the impact of market fluctuations and investment choices from the timing of money movements.

Interpreting the Time-Weighted Rate of Return

The time-weighted rate of return indicates the return generated by the investment strategy itself, independent of the size and timing of additions or withdrawals made by the investor. For instance, if two investment horizon periods had identical market performance, but an investor added significant capital just before a downturn in the second period, the money-weighted return (which considers cash flows) would appear lower. However, the time-weighted rate of return for both periods would reflect the same underlying investment strategy's performance. This makes it particularly useful for assessing the skill of professional asset allocation and security selection. It enables prospective investors to compare a fund's past performance against its peers or relevant benchmarks without the distortion caused by varying cash flow patterns.

Hypothetical Example

Consider an investment portfolio with the following activity over a year:

• January 1: Initial investment of $10,000.
• June 30: Portfolio value grows to $12,000. An additional deposit of $5,000 is made.
• December 31: Portfolio value ends at $16,000.

To calculate the time-weighted rate of return:

Sub-period 1 (January 1 to June 30):

• Beginning Value = $10,000
• Ending Value (before deposit) = $12,000
• Cash Flow = $0
• (HP_1 = \frac{$12,000 - ($10,000 + $0)}{$10,000 + $0} = \frac{$2,000}{$10,000} = 0.20 \text{ or } 20%)

Sub-period 2 (July 1 to December 31):

• Beginning Value (after deposit) = $12,000 + $5,000 = $17,000
• Ending Value = $16,000
• Cash Flow = $0 (the $5,000 was accounted for at the start of the period)
• (HP_2 = \frac{$16,000 - ($17,000 + $0)}{$17,000 + $0} = \frac{-$1,000}{$17,000} \approx -0.0588 \text{ or } -5.88%)

Now, geometrically link the sub-period returns:

• (TWR = (1 + 0.20) \times (1 - 0.0588) - 1)
• (TWR = 1.20 \times 0.9412 - 1)
• (TWR = 1.12944 - 1)
• (TWR = 0.12944 \text{ or } 12.94%)

The time-weighted rate of return for the year is approximately 12.94%, reflecting the performance of the investment decisions, distinct from the impact of the mid-year cash injection. This method ensures that the calculation of capital gains and income, such as dividends, is accurately captured without being skewed by external flows.

Practical Applications

The time-weighted rate of return is the industry standard for performance measurement, particularly among professional financial reporting entities. Its primary application is in evaluating the performance of investment managers who do not have control over the timing or size of client deposits and withdrawals. This includes managers of mutual funds, pension funds, and endowment funds.

Regulators and industry bodies, such as the SEC, often refer to performance advertising standards which implicitly or explicitly rely on methodologies like the time-weighted rate of return to ensure fair representation of investment results.⁶ The Global Investment Performance Standards (GIPS), which are widely adopted ethical standards, generally require firms to use time-weighted returns when presenting their performance.⁵,⁴ This ensures that investors can make informed decisions by comparing different investment products on a level playing field, focusing on the manager's skill rather than the coincidental timing of client contributions. For example, Morningstar, a global investment research firm, emphasizes compliance with GIPS for model portfolios, further highlighting the practical relevance of time-weighted returns in promoting transparency in performance reporting.³

Limitations and Criticisms

While highly effective for evaluating manager performance, the time-weighted rate of return does have limitations. One primary criticism is that it may not accurately reflect the actual return experienced by an individual investor, especially those who make significant deposits or withdrawals at opportune or inopportune times.² Because the time-weighted rate of return neutralizes the effect of cash flows, an investor who made a large deposit just before a substantial market decline might see a positive time-weighted return for the period, even if their personal account value decreased due to the timing of their contribution.

Another limitation arises in situations where the investment manager does control the timing of cash flows, such as in private equity or venture capital funds. In these cases, a money-weighted rate of return, like the internal rate of return, might be more appropriate as it considers the investor's perspective and the actual dollars invested over time. Critics also point out that the calculation can become complex and data-intensive for portfolios with frequent cash flows, requiring precise valuations at each transaction point.¹ Despite its widespread use, understanding when and why to apply the time-weighted rate of return is crucial for accurate investment analysis and avoiding misinterpretations of portfolio performance.

Time-Weighted Rate of Return vs. Money-Weighted Rate of Return

The time-weighted rate of return (TWR) and the money-weighted rate of return (MWRR) are two distinct methods for calculating investment returns, each serving a different purpose and providing unique insights. The core difference lies in how they account for external cash flows into and out of a portfolio.

The time-weighted rate of return is ideal for evaluating investment managers because it isolates the return generated purely from their investment decisions, removing any bias from when investors chose to add or remove funds. In contrast, the money-weighted rate of return, also often referred to as the internal rate of return, considers the specific timing and amount of each cash flow, making it a better measure of the actual return experienced by an individual investor who has discretion over their contributions and withdrawals. Confusion often arises because both metrics measure "return," but they answer different questions: TWR answers "How did the investments perform?" while MWRR answers "How did my money perform?"

FAQs

What does time-weighted return tell me?

The time-weighted rate of return tells you how well the underlying investments in a portfolio performed, independent of any money you added or withdrew. It's a measure of the investment manager's skill and the market's impact on the assets. It essentially shows the compound annual growth rate of a single dollar invested in the portfolio over the period.

Why do fund managers use time-weighted return?

Fund managers use the time-weighted rate of return because they do not control when investors deposit or withdraw money. By removing the influence of these cash flows, the time-weighted rate of return provides a fair and comparable measure of their investment decisions, allowing investors to assess the manager's abilities across different funds.

Is time-weighted return always the best measure of performance?

No, the time-weighted rate of return is not always the best measure for every situation. While it's excellent for evaluating the performance of professional investment managers, it may not reflect the actual return an individual investor experiences, especially if their personal contributions or withdrawals significantly impact their overall portfolio value. For personal returns or situations where the manager controls cash flows (like private equity), the money-weighted rate of return might be more suitable.

How often is time-weighted return calculated?

The time-weighted rate of return is calculated whenever there is an external cash flow into or out of the portfolio, or at least monthly, according to Global Investment Performance Standards (GIPS). This creates sub-periods, and the returns of these sub-periods are then linked together to find the total time-weighted return over a longer period.

Can I calculate my own time-weighted return?

Yes, you can calculate your own time-weighted rate of return, though it can be complex if you have many transactions. It requires valuing your portfolio immediately before and after every deposit or withdrawal. Many online brokerage platforms and portfolio tracking tools now provide time-weighted return calculations, making it easier for individual investors to track their investment performance.