# Money-weighted rate of return

Money-weighted rate of return

Money-weighted rate of return MWWR measures the performance of assets. Money-weighted rate of return shows the rate at which present value of cash flows and terminal values is equal to initial investment. This rate of return is calculated on the basis of the initial and final value and cash flows, if they occur in a given period. It is a rate at which investor earns and loses exactly zero. Therefore, it is equal to internal rate of return (IRR) over the assessed period (P. Moles, N. Terry 2002, s.359; S. Illmery, W. Marty 2003 s.42).

## How to calculate MWRR

It is calculated as follows$MV0=\frac{CF_1}{(1 - r_m)}+\frac{CF_2}{(1 - r_m)^2}+…+\frac{CF_n + MV_n}{(1 + r_m)^n}$

Where:

MV0 - the initial value of the fund,

CFt - the cash flow at period t,

rm - the internal rate of return that equates the value of the cash flows 1 to m to the current value.

MVn - the final value of the fund,

To calculate money-weighted rate of return investor should take into account outflows (e.g. costs of investment, reinvested dividend, withdrawals) and inflows (investments sold, dividends received, contributions). The net present value (NPV) should be calculated at the rate which results in NPV equal to zero. It can be calculated using IRR equation, however that equation has some limitations due to non-linear characteristics of NPV. The most often money-weighted rate of return is using for venture capital and private equity asset categories. The reason is that the initial investment appraisal for non-quoted investments often uses a MWRR approach and the assets are illiquid and difficult to value accurately (P. Moles, N. Terry 2002, s.359).

## Example

The example of using money-weighted rate of return is from CFA Program Curriculum 2018 Level I

„To illustrate the money-weighted rate of return, consider an investment that cover two-year horizon. At time t=0, an inwestor buys one share at $200. At time t=1, he purchases an additional share at$225. At the end of year 2, t=2, for $235 each. During both years, the stock pays a per share dividend of$5. The t=1 dividend is not reinvested(…)

$$200 + \frac{225}{(1 + r)} = \frac{5}{(1 + r)} + \frac{480}{(1 + r)^2}$$

The left-hand side of this equation details the outflows: $200 at time t=0 and$225 at time t=1. The $225 outflow is discounted back one period because it occurs at t=1. The right-hand side of the equation shows the present value of thr inflows:$5 at time t=1 (discounted back one period) and $480 (the$10 dividend plus the \$470 sale proceeds) at time t=2 (discounted back two periods).”(CFA Institute 2017, s.370-371) There are two alternatives methods for calculating portfolio returns in a most period setting when the portfolio is an object of additions and withdrawal – time-weighted rate of return and money-weighted rate of return. Time-weighted rate of return is calculated normally in the case in the investment management industry. Money-weighted rate of return can be appropriate if the investor exercises control over additions and withdrawals to the portfolio and have control over the timing because these have greatly influence the mentioned rate of return ( C. Bacon 2013 ).

Advantages of using money-weighted rate of return:

• Easy to interpret (mainly due to the percentage expression of profitability,
• The assessment takes into account the net benefit from the entire life cycle of the investment,
• It is possible to specify the limit cost of capital used to finance the project,
• The level of the meter does not depend directly on the discount rate, so it can be used in the efficiency assessment also when the discount rate is not known (S. Garrett 2013, s.109).