Money Vs Time Weighted Return

Money-Weighted vs. Time-Weighted Return: Understanding the Differences and Choosing the Right Metric

Understanding investment performance is crucial for both individual investors and professional fund managers. However, accurately measuring that performance can be more complex than it initially seems. Two key metrics frequently used are money-weighted return (MWR) and time-weighted return (TWR). While both aim to quantify investment success, they do so using different approaches and yield different results, particularly when dealing with variable cash flows. This article will delve deep into the nuances of MWR and TWR, explaining their calculations, applications, and helping you determine which metric is most appropriate for your specific needs.

Introduction: Why Two Different Metrics?

The core difference between MWR and TWR lies in how they handle cash inflows and outflows. Time-weighted return isolates the impact of investment decisions from the effects of deposits and withdrawals, providing a measure of the investment manager's skill in selecting and managing assets. Money-weighted return, on the other hand, accounts for the timing and size of cash flows, reflecting the overall return experienced by the investor, including the impact of their own deposit and withdrawal activity.

Choosing between MWR and TWR depends on the specific context. Fund managers often prefer TWR to showcase their investment management prowess, eliminating the influence of investor behavior. In contrast, individual investors may find MWR more relevant as it reflects their actual experience, considering both their investment choices and their contribution patterns.

Understanding Time-Weighted Return (TWR)

TWR measures the compound growth rate of $1 invested over a specific period, irrespective of external cash flows. It effectively "breaks" the investment period into sub-periods, each with a distinct return. These sub-period returns are then geometrically linked to calculate the overall TWR. This methodology ensures that the manager's performance is evaluated independently of the investor's contribution or withdrawal activity.

How is TWR Calculated?

The calculation involves several steps:

Sub-period Returns: Divide the investment period into sub-periods based on significant cash flows (deposits or withdrawals).
Holding Period Return (HPR) for each sub-period: Calculate the HPR for each sub-period using the formula: HPR = (Ending Value - Beginning Value + Cash Flows) / Beginning Value. Note that cash flows are included only in the sub-period they occur.
Geometric Linking: Calculate the overall TWR by geometrically linking the HPRs of each sub-period. This means multiplying each (1 + HPR) and then taking the nth root, where n is the number of sub-periods. The final result is then expressed as a percentage. The formula is:

TWR = [(1 + HPR1) * (1 + HPR2) * ... * (1 + HPRn)]^(1/n) - 1

Example:

Let's say an investment has the following history:

Beginning Value: $10,000
Month 1: +$2,000 deposit; Ending Value: $11,500
Month 2: -$1,000 withdrawal; Ending Value: $10,000
Month 3: Ending Value: $10,500

Calculation:

Sub-period 1: HPR = ($11,500 - $10,000 + $0) / $10,000 = 0.15 (15%)
Sub-period 2: HPR = ($10,000 - $11,500 + $1,000) / $11,500 = -0.043 (approximately -4.3%)
Sub-period 3: HPR = ($10,500 - $10,000 + $0) / $10,000 = 0.05 (5%)

TWR = [(1 + 0.15) * (1 + (-0.043)) * (1 + 0.05)]^(1/3) - 1 TWR ≈ 0.0516 or 5.16%

Advantages of TWR:

Objective Performance Measure: It isolates the manager's skill from the impact of investor cash flows.
Industry Standard: Widely accepted and used in the investment management industry.
Consistent Comparison: Allows for fair comparison of investment performance across different funds or managers.

Disadvantages of TWR:

Ignores Investor Behavior: It doesn't reflect the actual return experienced by the investor due to their cash flows.
Complex Calculation: Can be more challenging to calculate compared to MWR, especially with frequent cash flows.

Understanding Money-Weighted Return (MWR)

MWR, also known as the dollar-weighted return, considers the timing and size of cash flows. It calculates the rate of return that equates the present value of all cash flows to the initial investment value. In essence, it answers the question: What is the overall return on my investment, considering all my deposits and withdrawals?

How is MWR Calculated?

MWR is calculated using the Internal Rate of Return (IRR) method. This requires solving a complex equation, often done using iterative calculations or financial calculators/software. The equation equates the present value of all cash flows (including the final value) to zero.

The general formula is:

0 = -Initial Investment + Σ [CFt / (1 + MWR)^t] + Final Value / (1 + MWR)^n

Where:

CFt = Cash flow at time t
t = Time period
n = Total number of periods
MWR = Money-Weighted Return

Example:

Using the same investment example from the TWR section:

Initial Investment: -$10,000
Month 1: -$2,000 (deposit is negative cash outflow from the investor's perspective)
Month 2: +$1,000 (withdrawal is positive cash inflow)
Month 3: +$10,500 (final value)

To find the MWR, we need to solve the following equation:

0 = -10000 - 2000/(1+MWR) + 1000/(1+MWR)^2 + 10500/(1+MWR)^3

This equation needs to be solved iteratively using a financial calculator or software. The solution provides the MWR.

Advantages of MWR:

Reflects Investor Experience: Directly reflects the actual return experienced by the investor, considering their contribution and withdrawal patterns.
Personalized Return: Provides a personalized performance measure tailored to each investor's specific cash flow activity.

Disadvantages of MWR:

Sensitive to Cash Flow Timing: The timing of deposits and withdrawals significantly impacts the calculated MWR. A large deposit just before a market downturn can artificially lower the MWR, even if the investment manager’s skill is high.
Difficult to Compare: MWRs are difficult to compare across different investors or funds due to the variations in cash flow patterns.
Less Useful for Fund Managers: Not an ideal metric for evaluating fund manager performance as it is influenced by factors outside their control.

Choosing Between MWR and TWR: Which Metric is Right for You?

The choice between MWR and TWR depends heavily on the context:

For Fund Managers: TWR is the preferred metric. It provides a more objective and consistent measure of investment management skill, removing the influence of investor cash flows. This allows for fair comparisons across different funds and investment strategies.
For Individual Investors: MWR is generally more relevant. It reflects the actual return achieved on their investments, considering their personal investment decisions and the timing of their contributions and withdrawals.
For Performance Attribution: While TWR is useful for overall performance, both MWR and TWR can be used to conduct a more detailed analysis. By breaking down the performance into different components (e.g., stock selection, sector allocation), one can dissect and understand the various elements contributing to the overall return.

Frequently Asked Questions (FAQ)

Can I use both MWR and TWR simultaneously? Yes, using both metrics provides a more comprehensive view of investment performance. TWR shows the manager's skill while MWR shows the investor's actual experience.
Which metric is better for benchmarking against a market index? TWR is generally preferred for benchmarking as it isolates the manager's skill, making it a fairer comparison against an index that doesn't experience cash flows.
How do I calculate MWR without specialized software? Several iterative methods can be used, but manual calculation is time-consuming and prone to errors. Using financial calculators or spreadsheet software with IRR functions is highly recommended.
What if I have irregular cash flows? Both MWR and TWR can accommodate irregular cash flows, but the calculations become more complex. Accurate calculations require the use of financial software or calculators.
Is there a situation where MWR is better than TWR for fund managers? While uncommon, in situations where a fund's strategy inherently involves significant and predictable cash flows (like a real estate fund), MWR might offer some relevant insight, but it would still be secondary to TWR.

Conclusion: A Holistic Approach to Investment Performance Measurement

Understanding the differences between money-weighted return and time-weighted return is crucial for accurately assessing investment performance. While both metrics offer valuable insights, they cater to different needs. Fund managers should prioritize TWR to demonstrate their investment expertise, while individual investors should focus on MWR to understand their actual investment returns. Using both metrics provides a comprehensive picture, allowing investors and managers to make informed decisions based on a clear and complete understanding of their investment success. By understanding the strengths and limitations of each metric, you can navigate the complexities of investment performance analysis effectively. Remember to choose the metric most relevant to your specific goal and always consider the context of your investment strategy.