# True Time-Weighted Return

Money-weighted and time-weighted rates of return are two methods of measuring performance, or the rate of return on an investment portfolio.

True time-weighted return is a measure of portfolio return that is not sensitive to cash in- and out-flows to and from the portfolio. Given that cash flows are not a function of portfolio performance, true time-weighted return does not employ money-weighted calculations the way Dietz or internal rate of return do. Instead, true time-weighted return calculates the return of the portfolio as time-weighted average of its constituents’ returns, irrespective of cash additions and withdrawals to the portfolio. StatPro Revolution uses true time-weighted returns.

Wikipedia suggests “True time-weighted rate of return (TWROR) 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 equal and opposite movement of value in the opposite direction, 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. 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).”

Investment managers are judged on investment activity which is under their control. If they have no control over the timing of flows, then compensating for the timing of flows using the true time-weighted return method is a superior measure of the performance of the investment manager.

A quick example would help illustrate the point. Assume your portfolio’s value was \$1,000 at the beginning of the month, and \$1900 at the end of the month. On the 10th day of the month, you deposit \$250, and on the 20th day of the month you deposit another \$250. The overall value of your portfolio (after the deposits are made) on the 10th day is \$1,300, and \$1,700 on the 20th day. Therefore, there are three “sub-periods”- the first includes days 1-10, the second days 11-20, and finally the third is for days 21-30.

In order to calculate the time weighted return, we first need to calculate the return of each sub period.

• The return of sub period one is: [(\$1,300-\$250)-\$1,000] / \$1,000 = 5%.
• The return of sub period two is: [ (\$1,700-\$250)-\$1,300 ] / \$1,300 = 11.5%
• The return of sub period three is: [ (\$1,900-\$1,700) ] / \$1,700 = 11.8%

Finally, we compound the returns together to calculate the overall time-weighted rate of return:

Time-weighted rate of return: [(1+0.05)*(1+0.115)*(1+0.118)]^0.33 -1 = 9.39%