Time-Weighted Return (TWR)

The time-weighted rate of return (TWR) is a measure of return. The TWR is used to calculate the performance of investment strategies. The basis for calculating the TWR are the returns of the individual periods, for example days.

Time-Weighted Rate of Return (TWR)

Tag	Deposit and Withdrawal*	Start value	End value	Profit / Loss	in %	Decimal
1		100 CHF	110 CHF	+ 10 CHF	+ 10.00 %	+ 0.1000
2	(+ 100 CHF)*	110 CHF	90 CHF	− 20 CHF	− 18.18 %	− 0.1818
3	(− 100 CHF)*	90 CHF	105 CHF	+ 15 CHF	+ 16.66 %	+ 0.1666
TWR						+ 0.0500

The daily returns are added by 1 and then multiplied together:

TWR = (1 + 0.1000) * (1 +(− 0.1818)) * (1 + 0.1666) − 1 = 0.05 = + 5 %

Advantage TWR

The TWR has the advantage that it can be used to compare the performance of different portfolios. A comparison is possible because deposits and withdrawals are ignored when calculating the TWR.

Disadvantage TWR

The disadvantage of the TWR is that it can deviate from the effective performance of the portfolio. This can even go so far that the portfolio has lost value in francs, but the TWR is still positive (or vice versa).

Effective performance

Tag	Deposit and Withdrawal*	Start value	End value	Profit / Loss	in %	Decimal
1		100 CHF	110 CHF	+ 10 CHF	+ 10.00 %	+ 0.1000
2	+ 100 CHF	210 CHF	172 CHF	− 38 CHF	− 18.18 %	− 0.1818
3	− 100 CHF	72 CHF	84 CHF	+ 12 CHF	+ 16.66 %	+ 0.1666
Total				− 16 CHF

Since the deposit was made on the second day immediately before a bad day, the loss increased from 20 to 38 francs. Moreover, this loss could not be compensated equally well on the next day, as the 100 francs had already been withdrawn again beforehand. This resulted in a total loss of 16 francs.

The calculation of the TWR, on the other hand, remains unchanged and still results in a positive performance of 5%:

TWR = (1 + 0.1000) * (1 +(− 0.1818)) * (1 + 0.1666) − 1 = 0.05 = + 5 %