How to Calculate Time Weighted Returns

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:

time-weighted

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
beginning and ending market values

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 $          110,000.0010.00%
2 $    110,000.00 $          125,000.0013.64%
3 $    125,000.00 $          115,000.00-8.00%
4 $    115,000.00 $          132,000.0014.78%
5 $    132,000.00 $          130,000.00-1.52%
holding period returns

Once we know each of the individual HPRs, we can calculate the geometric average in order to determine the TWR:

time-weighted returns

Using an HP12C calculator, we can calculate the TWR using the following keystrokes:

hp12c

[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.