Time-weighted returns (TWRs) measure the geometric average of a series of holding period returns (HPRs), in order to calculate the annualized compounding rate of return of a portfolio over time.
The following formula is used to calculate TWRs:
Let’s assume that an investor had a portfolio with the following beginning and ending market values over five periods:
| Period | Beg MV | End MV |
| 1 | $ 100,000.00 | $ 110,000.00 |
| 2 | $ 110,000.00 | $ 125,000.00 |
| 3 | $ 125,000.00 | $ 115,000.00 |
| 4 | $ 115,000.00 | $ 132,000.00 |
| 5 | $ 132,000.00 | $ 130,000.00 |
In order to calculate the TWR, we must first calculate the HPRs for each of the individual periods:
| Period | Beg MV | End MV | HPR |
| 1 | $ 100,000.00 | $ 110,000.00 | 10.00% |
| 2 | $ 110,000.00 | $ 125,000.00 | 13.64% |
| 3 | $ 125,000.00 | $ 115,000.00 | -8.00% |
| 4 | $ 115,000.00 | $ 132,000.00 | 14.78% |
| 5 | $ 132,000.00 | $ 130,000.00 | -1.52% |
Once we know each of the individual HPRs, we can calculate the geometric average in order to determine the TWR:
Using an HP12C calculator, we can calculate the TWR using the following keystrokes:
[1.10][ENTER]
[1.1364][*]
[0.92][*]
[1.1478][*]
[0.9848][*]
[5][1/x][y^x]
The Excel model used to calculate TWRs can be found here.