How can there be a positive Dollar Gain (DG) and a negative Time Weighted Return (TWR)? Or vice versa? These “strange but true” returns occur more frequently than you might expect.
First, remember that TWR measures the growth of the average dollar in a portfolio. Dollar gain is the actual number of dollars gained or lost over the time period. TWR is a percentage. Dollar Gain is straight addition.
Consider this example: The portfolio starts with $100 and grows by $10. The client then withdraws $70. After the withdrawal, the portfolio loses $6.00.
[table]| Dollar Gain | Time Weighted Return |
| $100 + $10 = $110 (+$10 gain) $110 – $70 = $40 (-$70 withdrawal) $40 – $6 = $34 (-$6 loss) which results in a +$4.00 DG (+10-6=4). |
$10 gain / $100 start value = +10% return $6 loss /$40 start value = -15% return which results in -6.5% TWR |
Now let’s reverse the gain & loss. The portfolio starts with $100 and loses $10. Then the client withdraws $70. After the withdrawal, the portfolio gains $6.00.
[table]| Dollar Gain | Time Weighted Return |
| $100 – $10 = $90 (-$10 loss) $90 – $70 = $20 (-$70 withdrawal) $20 + $6 = $26 (+$6 gain) which results in a -$4.00 DG (-10+6 = -4) |
$10 loss / $100 start value = -10% return $6 gain /$20 start value = +30% return which results in a positive 17% TWR. |
When you see a strange combination Dollar Gain and TWR, look for money moving in or out of the portfolio, and then consider how well the portfolio did before and after the money moved.
Of course, the other possible explanation is bad data. Accurate performance returns depend on accurate data entry.
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