Definitions

Time-Weighted Return (TWR)

In the TWR calculation, positive net cash flows are assumed to be available for investment at the start of the day, affecting the daily return percentage. Negative net cash flows are assumed to occur at the end of the day, having no effect on the daily return percentage.

Daily TWR

Let: $\\$

• $\textmd{R}_d = \textmd{Nominal return of day} \space{d}$. $\\$
• $\textmd{IMV}_d = \textmd{Market value at the start of day} \space{d}$. $\\$
• $\textmd{PCF}_d = \textmd{Positive net cash flow (deposits minus withdrawals) of day} \space{d} \textmd{. If the net cash flow is negative it is treated as zero.}$

The daily time-weighted return for day $d$ can be calculated using:

$$\textmd{TWR}_d = \frac {\textmd{R}_d} {(\textmd{IMV}_d + \textmd{PCF}_d)}$$

TWR

The time-weighted return for $n$ day(s) can be calculated using:

$$\textmd{TWR} = \left( \prod_{d=1}^{n} (1 + \text{TWR}_d) \right) - 1$$