Most asset managers will publish their results in both time-weighted (TWRR) and dollar-weighted (DWRR) rates of return. TWRR is typically used by portfolio manages to compare their portfolio’s return to either other managed accounts or to an index. TWRR is more difficult to calculate for individuals because it requires more data. One must have not only their cash flows and dates that they moved in and out of the fund (as with DWRR), but the mark-to-market values of their total portfolio at the time of each cash flow. Investment firms with active investment funds will often calculate TWRR daily.
TWRR makes the portfolio comparable to other like accounts by eliminating the effects of external cash flows. It can also be used by individuals that want to measure their market timing. The calculator “Dollar_Time” inputs for both TWRR and DWRR look like this:
I used dynamic named ranges so that the user can enter a number of cash flows, without having to adjust the formulas.
The formulas for TWRR and DWRR are below:
The TWRR formula subtracts the cash flows from the total market values (including cash flows) and divides the results by the previous market value of the account. The results of each of these is then multiplied by each other using the PRODUCT function and then annualized. The calculation would look something like this:
The formula converts the change in market values at each date, starting with one dollar. The PRODUCT function then links these changes into what could be called the Dollar Trail. The chart below shows the Dollar Trail:
Note that the TWRR in this example is negative. The chart shows that the percentage change of one dollar, linked together at each cash flow date, never gets back to a dollar. It ends at $0.998 which is an annual return of -0.108%, while the DWRR is positive at 3.618%. This can be a problem for individuals with using TWRR. It can show a negative return when it is obvious that the return is positive and vice versa. The MWRR calculation, tells the investor how the money that was invested in the fund actually performed. When the TWRR is lower than the DWRR, it means the timing of the cash flows was beneficial to the return and when TWRR is higher than MWRR, the cash flows had a negative impact on return. The chart below shows that deposits were made at lower market levels, and withdrawals were made at higher market levels, for a positive impact.
All spreadsheets created in Excel 2013