Fear of risk provides a rationale for protracted economic downturns. We develop a real business cycle model where investors with decreasing relative risk aversion choose between a risky and a safe technology that exhibit decreasing returns. Because of a feedback effect from the interest rate to risk aversion, two equilibria can emerge: a standard equilibrium and a "safe" one in which investors invest in safer assets. We refer to the dynamics of this second equilibrium as a safety trap because it is self-reinforcing as investors accumulate more wealth and show it to be consistent with Japan's lost decade.