From ACT Wiki
Rewarded and unrewarded risk can be a useful way to analyse risks.
It can indicate whether a particular risk is a legitimate risk for the organisation (and consistent with the organisation’s strategic plan) or not.
An example of a rewarded risk is a capital investment decision, such as acquiring a business or a new machine, launching a new product and so on.
Such an investment will be made because there is a reasonable expectation of an acceptable net positive return within the organisation's strategic plan, and hence an expectation of an increase in shareholders' wealth.