Return on investment

The return on investment (ROI) is a calculation used in business used to determine whether a proposed investment is wise, and how well it will repay the investor. It is calculated as the ratio of the amount gained (taken as positive), or lost (taken as negative), relative to the basis. The basis is the amount risked ("invested") to obtain that gain or loss, and is always positive.

In mathematical terms, the ROI is (V_f - V_b) / V_b, where V_f is the final value and V_b is the basis.

Interestingly, to compensate for a negative ROI one needs a positive ROI that is higher in magnitude. For example, to recoup a 50% loss one needs to realize a 100% gain.