Money-Weighted Return Solved For R Where Σ CF

Money-Weighted Return Solved For R Where Σ CF_t / (1 + R)^t = 0

Money-Weighted Return Formula:

\[ \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t} = 0 \]

Money-Weighted Return (r):

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1. What is Money-Weighted Return?

Money-Weighted Return (MWR), also known as Internal Rate of Return (IRR), is a measure of investment performance that accounts for the timing and size of cash flows. It solves for the rate r that makes the net present value of all cash flows equal to zero.

2. How Does the Calculator Work?

The calculator uses the money-weighted return formula:

\[ \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t} = 0 \]

Where:

\( CF_t \) — Cash flow at time period t (negative for investments, positive for returns)
\( t \) — Time period (typically in years)
\( r \) — Money-weighted rate of return

Explanation: The calculator uses an iterative numerical method to solve for r that makes the sum of discounted cash flows equal to zero.

3. Importance of Money-Weighted Return

Details: MWR provides a personalized rate of return that reflects the actual investment experience, accounting for the timing of contributions and withdrawals. It's particularly useful for evaluating investment performance when cash flows are irregular.

4. Using the Calculator

Tips: Enter cash flows as comma-separated values (negative for investments, positive for returns/withdrawals). Enter corresponding time periods. Ensure both lists have the same number of values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between money-weighted and time-weighted returns?
A: MWR is affected by cash flow timing, while TWR eliminates the impact of cash flows and measures pure investment performance.

Q2: When should I use money-weighted return?
A: Use MWR when you want to measure your personal investment performance, especially when making regular contributions or withdrawals.

Q3: What are typical money-weighted return values?
A: Returns vary widely by investment type and market conditions. Positive returns indicate growth, negative returns indicate loss.

Q4: Are there limitations to money-weighted return?
A: MWR can be misleading when comparing different investment strategies, as it's heavily influenced by cash flow timing rather than investment skill.

Q5: How accurate is the calculation?
A: The calculator provides a close approximation using numerical methods. For exact calculations, more sophisticated financial software may be needed.