Time-Weighted vs. Money-Weighted Returns Examples

Explore practical examples of Time-Weighted vs. Money-Weighted Returns for better investment performance measurement.
By Jamie

Understanding Time-Weighted vs. Money-Weighted Returns

When evaluating investment performance, two primary methods come into play: Time-Weighted Returns (TWR) and Money-Weighted Returns (MWR). Both methods serve to measure how an investment has performed over time, but they differ significantly in their approach to cash flows. TWR focuses on the investment’s performance independent of cash inflows and outflows, while MWR considers the timing and amount of cash flows, reflecting the actual investor experience. Below are three practical examples that illustrate the differences between these two measurement methods.

Example 1: A Steady Investment with No Cash Flows

Context

This example demonstrates a straightforward investment scenario where an investor does not make any additional contributions or withdrawals.

An investor places \(10,000 in a mutual fund at the beginning of the year. At the end of the year, the fund’s value has increased to \)12,000.

For TWR, we calculate the annual return:

  • Beginning Value = $10,000
  • Ending Value = $12,000
  • Return = (Ending Value - Beginning Value) / Beginning Value = (\(12,000 - \)10,000) / $10,000 = 0.20 or 20%.

For MWR, since there were no cash flows, the calculation is the same:

  • MWR = TWR = 20%.

Notes

In this case, both TWR and MWR yield the same result because there were no additional cash flows during the investment period. This scenario is ideal for understanding the basic calculations involved in both methods.

Example 2: An Investment with Multiple Cash Flows

Context

This example illustrates how cash inflows and outflows can affect MWR compared to TWR. Here, an investor makes an additional contribution mid-year.

An investor starts with \(10,000 in an investment. After six months, the investment grows to \)12,000. At that point, the investor adds another \(5,000, bringing the total to \)17,000. By the end of the year, the investment value is $20,000.

For TWR:

  1. First half-year return = (12,000 - 10,000) / 10,000 = 0.20 or 20%.
  2. The second half-year return = (20,000 - 17,000) / 17,000 = 0.1765 or 17.65%.
  3. To calculate TWR, we compound these returns:
  • TWR = (1 + 0.20) * (1 + 0.1765) - 1 = 0.3558 or 35.58%.

For MWR:

  1. Calculate the time-weighted cash flows. The initial cash flow is \(10,000, the additional cash flow is \)5,000 made halfway through the year, and the final value is $20,000.
  2. MWR calculation considers the timing of cash flows:
  • MWR = (Ending Value - Cash Flows) / (Beginning Value + Cash Flows) = (20,000 - 5,000) / (10,000 + 5,000) = 0.5333 or 53.33%.

Notes

In this scenario, MWR is significantly higher than TWR due to the additional investment made at a time of strong performance. This demonstrates how the timing and amount of cash flows can influence MWR, highlighting the importance of considering cash flows when assessing performance.

Example 3: A Decline Followed by Recovery

Context

This example showcases an investment that initially declines in value before recovering, affecting TWR and MWR differently.

An investor starts with \(15,000. At the end of the first quarter, the investment value drops to \)10,000. In the second quarter, the investor adds \(5,000, raising the total investment to \)15,000. By the end of the year, the investment has rebounded to $20,000.

For TWR:

  1. First quarter return = (10,000 - 15,000) / 15,000 = -0.3333 or -33.33%.
  2. Second quarter return = (15,000 - 15,000) / 15,000 = 0 or 0%.
  3. Final return = (20,000 - 15,000) / 15,000 = 0.3333 or 33.33%.
  4. TWR = (1 - 0.3333) * (1 + 0) * (1 + 0.3333) - 1 = -0.1111 or -11.11%.

For MWR:

  1. Calculate cash flows: \(15,000 initial investment, \)5,000 additional investment midway, and $20,000 ending value.
  2. MWR = (Ending Value - Cash Flows) / (Beginning Value + Cash Flows) = (20,000 - 5,000) / (15,000 + 5,000) = 0.25 or 25%.

Notes

In this case, MWR reflects a positive return despite the initial downturn due to the additional investment during the low point, while TWR reflects a negative return due to performance throughout the period. This emphasizes the importance of understanding both metrics for informed investment decisions.

By analyzing these examples of Time-Weighted vs. Money-Weighted Returns, investors can gain insights into how different situations affect their overall investment performance and make more informed decisions moving forward.