Time-Weighted vs Money-Weighted Returns Explained

Time-Weighted vs. Money-Weighted Returns: Choosing the Right Performance Metric

You’ve been diligently investing for years, carefully tracking your portfolio’s growth, but are you using the right metrics to measure your success? Selecting the appropriate performance measurement methodology isn’t just an academic exercise – it can dramatically change how you perceive your investment performance and influence your future decisions.

In our previous discussions on return metrics, we touched on different ways to measure investment performance. Now, we’re diving deeper into two critical methodologies that often cause confusion: time-weighted returns (TWR) and money-weighted returns (MWR).

The Fundamental Difference

Time-weighted and money-weighted returns answer two fundamentally different questions:

• Time-weighted return answers: “How well did my investment strategy perform?”
• Money-weighted return answers: “How well did my actual money perform?”

This distinction might seem subtle, but it creates a world of difference in how you evaluate performance.

Time-Weighted Return (TWR): Measuring Strategy Performance

What Exactly Is TWR?

Time-weighted return measures investment performance independent of investor cash flows. It isolates the performance of the assets themselves by removing the impact of the timing and size of deposits and withdrawals. This metric essentially answers: “How well would $1 invested at the start of the period have performed?”

When to Use TWR

TWR is the appropriate choice when:

1. Evaluating Investment Managers: Since investment managers typically don’t control when clients add or withdraw money, TWR provides a fair assessment of their investment decisions.

2. Comparing Against Benchmarks: Major indices like the S&P 500 are measured on a time-weighted basis, so comparing your performance using the same methodology ensures an apples-to-apples comparison.

3. Assessing Investment Strategy: When you want to isolate how well your investment selections performed, regardless of your deposit and withdrawal timing.

Real-World Example

Let’s say you have an investment portfolio that started the year at $100,000. The market drops 20% in the first quarter, and you decide to invest another $50,000 at this lower level. The market then recovers 30% by year-end.

Your naïve calculation might show:

• Starting value: $100,000
• Additional investment: $50,000
• Ending value: $180,000 ($80,000 + $50,000, both up 30% from their low points)
• Simple return: ($180,000 - $150,000) / $150,000 = 20%

But this doesn’t accurately measure how well your investment strategy performed. The time-weighted return would be:

• Q1 return: -20%
• Q2-Q4 return: +30%
• TWR = [(1 - 0.20) × (1 + 0.30)] - 1 = 0.04 or 4%

This 4% time-weighted return more accurately reflects the performance of your investment strategy, independent of the additional $50,000 you contributed.

Money-Weighted Return (MWR): Measuring Your Personal Experience

What Exactly Is MWR?

Money-weighted return, also known as the internal rate of return (IRR), accounts for both the timing and amount of cash flows in and out of your investments. It represents the discount rate that makes the net present value of all cash flows equal to zero. In simpler terms, it’s the rate that describes how your actual dollars performed, including the impact of when you added or withdrew money.

When to Use MWR

MWR is most appropriate when:

1. Evaluating Personal Investment Results: When you want to know how your specific investment experience performed, accounting for your timing of contributions and withdrawals.

2. Measuring Private Investments: For illiquid investments like private equity or real estate where investors have limited control over the timing of cash flows.

3. Pension Fund Management: When managing liabilities that occur at specific times, MWR helps match asset performance with future obligations.

Real-World Example

Using the same scenario as above:

• Starting value (time 0): $100,000
• Cash flow after 3 months (0.25 years): +$50,000
• Ending value after 12 months (1 year): $180,000

The money-weighted return (IRR) solves this equation: 0 = -$100,000 - $50,000/(1+MWR)^0.25 + $180,000/(1+MWR)^1

Using an IRR calculator, we find the MWR is approximately 16.5%.

This 16.5% return reflects your actual investment experience, including the benefit of investing additional funds when the market was down.

When TWR and MWR Tell Different Stories

The gap between time-weighted and money-weighted returns reveals valuable insights about investor timing:

• MWR > TWR: This indicates positive timing – you added money before gains or withdrew before losses.
• MWR < TWR: This suggests negative timing – you added money before losses or withdrew before gains.
• MWR ≈ TWR: Either your timing had minimal impact, or you made few/no contributions or withdrawals.

Example of Divergent Returns

Consider a volatile fund that returns +50% in Year 1, -30% in Year 2, and +40% in Year 3:

Scenario A: An investor places $10,000 at the beginning and makes no further transactions.

• TWR = [(1 + 0.5) × (1 + (-0.3)) × (1 + 0.4)] - 1 = 47%
• MWR = 47% (same as TWR since there are no cash flows)

Scenario B: An investor starts with $10,000, gets excited by Year 1’s performance and adds $20,000 at the start of Year 2, just before the 30% drop.

• TWR = still 47% (cash flows don’t affect it)
• MWR = approximately 15% (much lower due to the poorly timed large contribution)

Scenario C: An investor starts with $10,000, gets nervous after Year 1, and withdraws $5,000 before the Year 2 drop.

• TWR = still 47%
• MWR = approximately 67% (higher because they reduced exposure before the drop)

Common Calculation Methods

Calculating TWR

The industry standard for TWR is the Modified Dietz Method or the more precise Daily-Weighted Method:

1. Modified Dietz Method:

   • Divide the investment period into sub-periods where cash flows occur
   • Calculate return for each sub-period, adjusting for the timing of cash flows
   • Link the sub-period returns geometrically

2. Daily-Weighted Method:

   • Calculate returns for each day (or the smallest possible interval)
   • Link these daily returns geometrically

Many investment firms use portfolio management software that calculates TWR using daily-weighted methods for maximum accuracy.

Calculating MWR

Money-weighted return calculations typically use:

1. Internal Rate of Return (IRR):

   • The discount rate that makes the net present value of all cash flows equal to zero
   • Requires iterative calculation, usually performed with financial software

2. XIRR Function in Excel:

   • A convenient way to calculate IRR with irregular time periods
   • Requires dates and corresponding cash flow values

CAGR vs. TWR vs. MWR

Another metric that often enters the conversation is the Compound Annual Growth Rate (CAGR):

• CAGR: Measures the constant rate of return that would produce the same final value over the same time period.

For a portfolio with no cash flows, CAGR equals both TWR and MWR. However, when cash flows are involved, they diverge:

• CAGR simply connects starting and ending points without accounting for the path
• TWR accounts for the path but ignores cash flow timing
• MWR accounts for both the path and cash flow timing

Performance Attribution Analysis

Understanding whether performance differences are due to asset allocation, security selection, or timing is a process called performance attribution analysis. This analysis becomes more meaningful when using the appropriate return measurement method:

• Use TWR for analyzing manager skill in asset allocation and security selection
• Use MWR for analyzing the impact of timing decisions

Real-World Applications by Investment Type

Different investment contexts call for different performance metrics:

Individual Investors

• Use TWR to assess your investment strategy and compare against benchmarks
• Use MWR to understand your personal investment experience and the impact of your contribution/withdrawal decisions

Financial Advisors

• Use TWR to demonstrate investment selection skill
• Use MWR to show clients their actual experienced returns

Fund Managers

• Use TWR almost exclusively, as this is the industry standard for evaluating fund performance

Institutional Investors

• Use TWR for performance evaluation against benchmarks and peers
• Use MWR for liability-focused portfolios where cash flow timing matters

Common Pitfalls to Avoid

1. Using TWR to Evaluate Personal Financial Goals: If you’re saving for retirement, your actual money performance (MWR) matters more than your investment strategy performance in isolation.

2. Using MWR to Evaluate Investment Managers: Managers shouldn’t be penalized or rewarded for your timing decisions regarding contributions and withdrawals.

3. Ignoring the Gap Between TWR and MWR: A large difference between these metrics provides valuable feedback about your timing decisions.

4. Focusing on Short-Term Returns: Both TWR and MWR become more meaningful over longer periods that capture various market conditions.

Putting It All Together: A Decision Framework

To decide which metric to use, ask yourself:

1. What am I trying to evaluate?

   • The investment strategy itself → TWR
   • My overall investment experience → MWR

2. Who controlled the timing of cash flows?

   • I did → Consider MWR
   • The investment manager did → Consider TWR

3. What am I comparing against?

   • Market indices or other investments → TWR
   • My personal financial goals → MWR

Conclusion

Both time-weighted and money-weighted returns provide valuable but different perspectives on investment performance. TWR isolates your investment strategy’s performance, while MWR captures your actual investment experience.

The key to using these metrics effectively is understanding what question each answers. Most investors benefit from tracking both: TWR for evaluating their investment approach and comparing against benchmarks, and MWR for understanding their actual experienced returns including the impact of their timing decisions.

Rather than viewing one as superior to the other, consider them complementary tools in your performance measurement toolkit. By understanding both metrics, you’ll gain deeper insights into your investment performance and make more informed decisions going forward.

In our previous articles on risk metrics and risk-adjusted returns, we explored other dimensions of performance evaluation. Combined with a proper understanding of TWR and MWR, you now have a comprehensive framework for assessing your investments.

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