# Money-weighted Rate of Return

Money-weighted return is the internal rate of return of an investment. It is the rate of return that equates the initial value of an investment with future cash flows such as dividends and sale proceeds. Over multiple periods, it inherently overweights and underweights individual period returns with high and low starting investment value.

## Formula & Example

Let’s say you are evaluating performance of a stock-only mutual fund. The value of mutual fund’s assets under management (AUM) as at 1 January 2017 is $20 million, the fund earned dividends of$0.5 million and $0.7 million in the first and second six-month periods. Around the year end, net increase in assets under management amounted to$2 million. Total mutual investment value as at 30 June 2018 is $25 million. The following table summarizes the cash flow of the fund: Value ($ million) 1-Jan-17 30-Jun-17 31-Dec-17 30-Jun-18
Initial value -20
Dividends 0.5 0.5
Net increase in assets -2
Closing value 25
Cash flows -20 0.5 -1.5 25

Using Excel IRR function, the periodic money-weighted rate of return works out to 6.22%. It can be worked out using trial-and-error method based on the following algebraic function:

$$\text{0}=-\text{\20m}-\frac{\text{\1.5m}}{{(\text{1}+\text{r})}^\text{2}}+\frac{\text{\0.5m}}{{(\text{1}+\text{r})}^\text{1}}+\frac{\text{\0.7m}}{{(\text{1}+\text{r})}^\text{2}}+\frac{\text{\25m}}{{(\text{1}+\text{r})}^\text{3}}$$

In the composite return calculation over the whole period, highest value is assigned to investment performance of the last semi-annual period ending 30 June 2018 because it has the highest initial investment value i.e. $2.2 million and lowest weight is assigned to the initial half-year ending 30 June 2017 because it has the lowest initial investment value i.e.$20 million.

Because the money weighted rate of return doesn’t assign equal weight to each investment period, it is not a good measure of investment returns because a fund manager is not able to control investment inflows and outflows and hence they shouldn’t determine his/her ultimate return. Time-weighted rate of return is a better measure because it doesn't depend on relative value of assets under management.