The purpose of this paper is to characterize and prove robustness properties of risk-sensitive controllers precisely. The authors mainly presented the following two results: (1) explicit bounds of the average output power in terms of the input power, (2) a stochastic version of the small gain theorem, which is expressed in terms of the risk-sensitive criterion. In particular, (2) provides a motivation for the use of a risk-sensitive criterion in stochastic robustness.