Money Weighted Return Calculation

Money weighted return is a financial metric that calculates the average return of an investment portfolio, where each investment's return is weighted by its contribution to the total investment amount. This method provides a more accurate representation of portfolio performance than simple arithmetic averaging, especially when investments have different sizes.

What is Money Weighted Return?

Money weighted return is a performance measurement that accounts for the size of each investment in a portfolio. Unlike simple arithmetic averaging, which treats all investments equally, money weighted return gives more weight to larger investments, reflecting their greater impact on overall portfolio performance.

This metric is particularly useful for:

Evaluating the performance of diversified portfolios
Comparing different investment strategies
Assessing the effectiveness of asset allocation
Benchmarking against market indices or peer groups

The money weighted return calculation takes into account both the returns of individual investments and their relative sizes in the portfolio.

How to Calculate Money Weighted Return

Calculating money weighted return involves these steps:

Identify all investments in your portfolio
Determine the initial investment amount for each position
Calculate the return for each investment
Multiply each return by its corresponding investment amount
Sum all the weighted returns
Divide by the total investment amount to get the money weighted return

For accurate results, ensure you're using consistent time periods and currency units across all investments in your portfolio.

The Formula

The money weighted return (MWR) is calculated using this formula:

MWR = (Σ (Return_i × Investment_i)) / Σ Investment_i

Where:

Return_i = Return of investment i
Investment_i = Initial investment amount for position i
Σ = Summation operator

The formula calculates the total weighted returns and divides by the total investment amount to get the average return.

Worked Example

Let's calculate the money weighted return for a portfolio with two investments:

Investment	Initial Amount ($)	Return (%)
Stock A	10,000	8%
Bond B	5,000	5%

Using the formula:

MWR = [(0.08 × 10,000) + (0.05 × 5,000)] / (10,000 + 5,000)

MWR = [800 + 250] / 15,000

MWR = 1,050 / 15,000

MWR = 0.07 or 7%

The money weighted return for this portfolio is 7%.

Interpreting the Results

Interpreting money weighted return requires understanding several key points:

Portfolio Performance: A higher money weighted return indicates better overall portfolio performance, considering the size of each investment.
Risk Adjustment: The metric doesn't account for risk, so it's important to consider volatility when evaluating results.
Time Period: Money weighted return should be calculated over consistent time periods for accurate comparison.
Benchmarking: Compare your money weighted return against industry benchmarks or peer portfolios to assess performance.

Money weighted return is most meaningful when comparing portfolios with similar asset allocations and risk profiles.

FAQ

What is the difference between money weighted return and arithmetic average return?: Money weighted return accounts for the size of each investment, while arithmetic average return treats all investments equally. Money weighted return provides a more accurate representation of portfolio performance.
How often should I calculate money weighted return?: Money weighted return is typically calculated at regular intervals (monthly, quarterly, or annually) to track portfolio performance over time.
Can money weighted return be negative?: Yes, if the total weighted returns are negative, the money weighted return will also be negative, indicating overall portfolio losses.
Is money weighted return suitable for all types of investments?: Money weighted return works well for diversified portfolios but may not be appropriate for single-asset investments or portfolios with very different risk profiles.
How does money weighted return compare to time weighted return?: Money weighted return focuses on the size of investments, while time weighted return considers the duration each investment was held. Both metrics provide different perspectives on portfolio performance.