Money Weighted Return Calculation Formula

The money weighted return calculation formula is a financial metric that accounts for the time value of money by weighting returns based on the amount of money invested at each period. This method provides a more accurate measure of investment performance than simple arithmetic averages, especially for investments that change in size over time.

What is Money Weighted Return?

Money weighted return is a performance measure that considers both the amount of money invested and the time period over which the investment was held. Unlike simple arithmetic averages, which treat all periods equally, money weighted return accounts for the fact that money invested earlier has more time to grow.

This method is particularly useful for evaluating the performance of investments that change in size over time, such as mutual funds or accounts that receive contributions or withdrawals. It provides a more accurate picture of an investor's actual return on investment.

Money Weighted Return Formula

The money weighted return formula is calculated by summing the present value of all cash flows and then dividing by the initial investment. The formula is:

Money Weighted Return Formula

Money Weighted Return = (Present Value of All Cash Flows) / Initial Investment

The present value of cash flows is calculated using the discount rate to account for the time value of money.

Where:

Present Value of All Cash Flows - The sum of all cash flows discounted back to the present value
Initial Investment - The amount of money invested at the beginning of the period

The present value of cash flows is calculated using the formula:

Present Value of Cash Flows

PV = Σ (Cash Flow / (1 + r)^t)

Where:

PV - Present Value
Cash Flow - The amount of money received or paid at each period
r - Discount rate (the minimum rate of return required by investors)
t - Time period

How to Calculate Money Weighted Return

Calculating money weighted return involves several steps:

Identify all cash flows - List all contributions, withdrawals, and returns over the investment period.
Determine the discount rate - Choose an appropriate discount rate based on the investor's required rate of return.
Calculate the present value of each cash flow - Use the discount rate to calculate the present value of each cash flow.
Sum the present values - Add up all the present values to get the total present value of all cash flows.
Divide by the initial investment - Divide the total present value by the initial investment to get the money weighted return.

Important Considerations

When calculating money weighted return, it's important to:

Use a consistent discount rate throughout the calculation
Account for all contributions and withdrawals
Ensure that the time periods are correctly aligned
Consider the impact of taxes and fees on the calculation

Example Calculation

Let's look at an example to illustrate how to calculate money weighted return.

Scenario

An investor makes an initial investment of $10,000. Over the next three years, the investor contributes an additional $2,000 at the end of each year. The investment earns annual returns of 5%, 6%, and 7% respectively. The investor's required rate of return (discount rate) is 4%.

Step 1: Identify Cash Flows

Year	Cash Flow	Return	Total Cash Flow
0	-10,000	0	-10,000
1	2,000	5%	2,000 + (2,000 * 0.05) = 2,100
2	2,000	6%	2,000 + (2,000 * 0.06) = 2,120
3	2,000	7%	2,000 + (2,000 * 0.07) = 2,140

Step 2: Calculate Present Value of Cash Flows

Year	Cash Flow	Present Value
0	-10,000	-10,000 / (1 + 0.04)^0 = -10,000
1	2,100	2,100 / (1 + 0.04)^1 = 2,018.07
2	2,120	2,120 / (1 + 0.04)^2 = 2,004.16
3	2,140	2,140 / (1 + 0.04)^3 = 1,978.74

Step 3: Sum Present Values and Calculate Money Weighted Return

Total Present Value = -10,000 + 2,018.07 + 2,004.16 + 1,978.74 = 1,000.97

Money Weighted Return = Total Present Value / Initial Investment = 1,000.97 / 10,000 = 0.100097 or 10.01%

Interpretation

The money weighted return of 10.01% indicates that the investment provided a 10.01% return on the initial investment, accounting for the time value of money and all contributions.

Comparison with Other Methods

Money weighted return differs from other performance measures in several ways:

Method	Description	Key Advantages	Key Limitations
Money Weighted Return	Accounts for the time value of money and all contributions	Provides a more accurate measure of investment performance	Requires more complex calculations
Internal Rate of Return (IRR)	Determines the discount rate that makes the net present value of all cash flows zero	Considers the time value of money	Can be misleading with multiple cash flows
Annualized Return	Calculates the average annual return over a period	Simple to calculate and understand	Does not account for the time value of money

While money weighted return provides a more accurate measure of investment performance, it requires more complex calculations than other methods. Investors should choose the method that best fits their needs and the characteristics of the investment.

FAQ

What is the difference between money weighted return and internal rate of return (IRR)?: Money weighted return accounts for the time value of money by weighting returns based on the amount of money invested at each period, while IRR determines the discount rate that makes the net present value of all cash flows zero.
When should I use money weighted return instead of annualized return?: Money weighted return is more appropriate when evaluating investments that change in size over time, such as mutual funds or accounts that receive contributions or withdrawals. Annualized return is simpler but does not account for the time value of money.
How does the discount rate affect the money weighted return calculation?: The discount rate represents the minimum rate of return required by investors. A higher discount rate will result in a lower money weighted return, as it accounts for the opportunity cost of investing the money elsewhere.
Can money weighted return be negative?: Yes, money weighted return can be negative if the total present value of all cash flows is less than the initial investment. This indicates that the investment did not meet the investor's required rate of return.
Is money weighted return suitable for all types of investments?: Money weighted return is particularly useful for evaluating investments that change in size over time. For investments that maintain a constant size, other performance measures such as annualized return may be more appropriate.