How to Solve for Money Weighted Return Without Calculator

Money Weighted Return is a financial metric that calculates the average return of an investment portfolio, taking into account the amount of money invested in each component. This method provides a more accurate representation of overall portfolio performance than simple arithmetic averages, especially when investments have different sizes.

What is Money Weighted Return?

Money Weighted Return is calculated by multiplying each investment's return by its weight in the portfolio, then summing these products. The weight of each investment is determined by the proportion of the total portfolio value that it represents.

This method is particularly useful in finance for evaluating the performance of diversified portfolios. Unlike arithmetic mean returns, which treat all investments equally, money weighted returns reflect the actual contribution of each investment to the overall portfolio performance.

The Formula

Money Weighted Return (MWR) is calculated using the formula:

MWR = Σ (Return_i × Weight_i)

Where:

Return_i = Return of investment i
Weight_i = (Investment Value_i / Total Portfolio Value)

The Σ symbol indicates that you sum the products of each investment's return and its weight across the entire portfolio.

Step-by-Step Calculation

List all investments in your portfolio with their current values and returns.
Calculate the total portfolio value by summing all investment values.
Determine each investment's weight by dividing its value by the total portfolio value.
Multiply each investment's return by its weight.
Sum all the weighted returns to get the money weighted return.

Worked Example

Consider a portfolio with three investments:

Investment	Value ($)	Return (%)
Stock A	50,000	8%
Bond B	30,000	5%
Real Estate C	20,000	6%

Total portfolio value = $50,000 + $30,000 + $20,000 = $100,000

Calculations:

Stock A weight = 50,000 / 100,000 = 0.5 (50%)
Bond B weight = 30,000 / 100,000 = 0.3 (30%)
Real Estate C weight = 20,000 / 100,000 = 0.2 (20%)

Money Weighted Return = (0.08 × 0.5) + (0.05 × 0.3) + (0.06 × 0.2) = 0.04 + 0.015 + 0.012 = 0.067 or 6.7%

Interpreting Results

The money weighted return provides several insights:

Portfolio performance: It shows how well the entire portfolio performed, accounting for the size of each investment.
Risk assessment: Larger investments have a greater impact on the overall return, so they should be carefully managed.
Rebalancing opportunities: If certain investments are underperforming, the money weighted return can help identify areas needing attention.

Note: Money weighted return is different from arithmetic mean return. For example, if all investments had the same return, both methods would yield identical results. However, when returns vary significantly, money weighted return provides a more accurate picture of portfolio performance.

FAQ

What's the difference between money weighted return and arithmetic mean return?

Money weighted return accounts for the size of each investment in the portfolio, while arithmetic mean return treats all investments equally. Money weighted return is more accurate for evaluating portfolio performance.

When should I use money weighted return instead of simple average?

Use money weighted return when your portfolio contains investments of different sizes. It provides a more accurate representation of overall portfolio performance.

Can money weighted return be negative?

Yes, if the weighted sum of returns is negative, the money weighted return will also be negative, indicating overall portfolio loss.

How often should I calculate money weighted return?

Calculate it regularly, especially after major market movements or changes in your portfolio composition, to monitor performance accurately.