Risk is the possibility of suffering loss.
Risk is generally defined as the exposure to loss or harm. This can also include opportunity loss. The measure of risk includes both likelihood or probability of loss and the magnitude of the loss. The greater the likelihood or the greater the magnitude of the loss the greater the risk.
Risk generally has a negative connotation, but "taking a risk" can be seen positively. Presumably one "takes a risk" (i.e., risks potential loss) because doing so means the commensurate possiblity of gain.
In economic theory, financial risk includes the possiblitiy of gain as a negative risk, thereby equating risk with both positive as well as negative outcomes. In the case of the Efficient Market Hypothesis, this definition reduces to a measure of the variance or volatility in returns. Many economists, as well as Fools, do not believe in this hypothesis!