Cumulative Return

Definition

The cumulative return on an investment is the aggregate amount that the investment has gained or lost over time, independent of the amount of time involved.

The cumulative return can be expressed as a simple return using arithmetic average or as a compounded return using geometric average. We measure the cumulative return with the compounding effect, assuming the profits are reinvested. Different from CAGR, this value is not annualized.

Formula

$\text{Compounded Return} = \left(\prod_{i=1}^{n} 1 + R_i\right) - 1$

where $R_i$ is the return for period $i$.

$\text{Cumulative Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}}$

where the End Value is expressed using compounded return.