Calculating the Money Weighted Return
The money-weighted return accounts for the money invested and provides the investor with information on the actual return the investor earns on the investment.
The internal rate of return is the discount rate at which the sum of present values of cash flows will equal zero.
In general, the equation may be expressed as follows:
where T is the number of periods, is the cash flow at time t, and IRR is the internal rate of return or the money-weighted rate of return.
A cash flow can be positive or negative; a positive cash flow is an inflow where money flows to the investor, whereas a negative cash flow is an outflow where money flows away from the investor.
Time-Weighted Returns
The time-weighted rate of return measures the compound rate of growth of USD1 initially invested in the portfolio over a stated measurement period. For the evaluation of portfolios of publicly traded securities, the time-weighted rate of return is the preferred performance measure as it neutralises the effect of cash withdrawals or additions to the portfolio, which are generally outside of the control of the portfolio manager.
Computing Time-Weighted Returns
To compute an exact time-weighted rate of return on a portfolio, take the following three steps:
- Price the portfolio immediately prior to any significant addition or withdrawal of funds. Break the overall evaluation period into subperiods based on the dates of cash inflows and outflows.
- Calculate the holding period return on the portfolio for each subperiod.
- Link or compound holding period returns to obtain an annual rate of return for the year (the time-weighted rate of return for the year). If the investment is for more than one year, take the geometric mean of the annual returns to obtain the time-weighted rate of return over that measurement period.
If is the time-weighted return for year i, we calculate an annualised time-weighted return as the geometric mean of N annual returns, as follows:
