# Time-weighted return

The time-weighted return (TWR) is a method of calculating investment return. To apply the time-weighted return method, combine the returns over sub-periods, by compounding them together, resulting in the overall period return. The rate of return over each different sub-period is weighted according to the duration of the sub-period.

The time-weighted method differs from other methods of calculating investment return only in the particular way it compensates for external flows - see below.

The time-weighted return is a measure of the historical performance of an investment portfolio which compensates for external flows. External flows are net movements of value which result from transfers of cash, securities or other instruments, into or out of the portfolio, with no simultaneous equal and opposite movement of value in the opposite direction, as in the case of a purchase or sale, and which are not income from the investments in the portfolio, such as interest, coupons or dividends.

To compensate for external flows, the overall time interval under analysis is divided into contiguous sub-periods at each point in time within the overall time period whenever there is an external flow. In general, these sub-periods will be of unequal lengths. The returns over the sub-periods between external flows are linked geometrically (compounded) together, i.e. by multiplying together the growth factors in all the sub-periods. (The growth factor in each sub-period is equal to 1 plus the return over the sub-period.)

To illustrate the problem of external flows, consider the following example.

Suppose an investor transfers \$500 into a portfolio at the beginning of Year 1, and another \$1,000 at the beginning of Year 2, and the portfolio has a total value of \$1,500 at the end of the Year 2. The net gain over the two-year period is zero, so intuitively, we might expect that the return over the whole 2-year period to be 0%. If the cash flow of \$1,000 at the beginning of Year 2 is ignored, then the simple method of calculating the return without compensating for the flow will be 200% (\$1,000 divided by \$500). Intuitively, 200% is incorrect.