# ROI Calculation

## Time-weighted ROI¶

According to the Global Investment Performance Standards (GIPS), cTrader Copy applies the time-weighted ROI (TWR) calculation method.

The TWR method suggests that cash inflows, cash outflows, and amounts invested over different periods have no impact on the resulting value.

The history of any account is divided into sub-periods; so each time a new deposit or withdrawal occurs, a new sub-period is formed. The ending of the day also forms a new sub-period. The ROI of each sub-period is calculated by the formula:

``````Rn = (Equity at the end of the sub-period - Equity at the beginning of the sub-period - Deposits + Withdrawals) / Equity at the beginning of the sub-period
``````

To apply the TWR method, combine the ROI for sub-periods, by compounding them together, resulting in the overall period ROI.

``````TWR (%) = ((1 + R1) * (1 + R2) * ... * (1 + Rn) - 1) * 100%, where R1, R2,... Rn is ROI for the sub-period.
``````

Example

An investor had USD 1,000 in equity at the beginning of the period. The investor opened a position, and their equity at the end of the day increased to USD 1,100.

``````ROI (sub-period) = (1,100 - 1,000) / 1,000 = 0.1
TWR (%) = (1 + 0.1 - 1) = 0.1 * 100% = 10%
``````

The investor can deposit an additional USD 900, which will increase the resulting equity to USD 2,000.

``````ROI (sub-period) = (2,000 - 1,100 - 900) / 1,100 = 0
TWR (%) = (1 + 0.1 ) * (1 + 0) - 1 = 0.1 * 100% = 10%
``````

Note

The last sub-period that was formed is due to the deposit amount not affecting the resulting TWR (%).

By the end of the next day, the investor's equity reaches USD 2,100 through trading.

``````ROI (sub-period) = (2,100 - 2,000) / 2,000 = 0.05 or 5%
``````

You can see that USD 100 was earned on this step giving a change in ROI on a less percentage amount than USD 100 that was earned during the first step (5% vs. 10%).

The reason for this is that ROI depends on the starting amount that is used for trading. In these two cases, different starting amount was used to make a profit.

The resulting TWR (%) is calculated as follows:

``````TWR (%) = (1 + 0.1) * (1 + 0) * (1 + 0.05) - 1 = 0.155 * 100% = 15.5%
``````

## ROI Update Frequency¶

The ROI is updated:

• Every 15 minutes for strategy providers' accounts.
• Daily for copy-trading accounts and accounts that do not provide strategies.