second year, we would expect the overall return over the two-year period to be the result of compounding a 100% gain ($500) with a 25% loss (also $500). The time-weighted return is found by multiplying together the growth factors for each year, i.e. the growth factors before and after the second transfer into the portfolio, then subtracting one, and expressing the result as a percentage: . We can see from the time-weighted return that the absence of any net gain over the two-year period was due to bad timing of the cash inflow at the beginning of the second year. The time-weighted return appears in this example to overstate the return to the investor, because he sees no net gain. However, by reflecting the performance each year compounded together on an equalized basis, the time-weighted return recognizes the performance of the investment activity independently of the poor timing of the cash flow at the beginning of Year 2. If all the money had been invested at the beginning of Year 1, the return by any measure would most likely have been 50%. $1,500 would have grown by 100% to $3,000 at the end of Year 1, and then declined by 25% to $2,250 at the end of Year 2, resulting in an overall gain of $750, i.e. 50% of $1,500. The difference is a matter of perspective. Adjustment for flows The return of a portfolio in the absence of flows is: where is the portfolio's final value, is the portfolio's initial value, and is the portfolio's return over the period. The growth factor is: External flows during the period being analyzed complicate the performance calculation. If external flows are not taken into account, the performance measurement is distorted: A flow into the portfolio would cause this method to overstate the true performance, while flows out of the portfolio would cause it to understate the true performance. To compensate for an external flow into the portfolio at the beginning of the period, adjust the portfolio's initial value by adding . The return is: and the corresponding growth factor is: To compensate for an external flow into the portfolio just before the valuation at the end of the period, adjust the portfolio's final value by subtracting . The return is: and the corresponding growth factor is: Time-weighted return compensating for external flows Suppose that the portfolio is valued immediately after each external