In this paper we raise a question on the reliability of option implied risk aversion. We prove that given any number of options, there exist numerous risk aversion functions which are piecewise constant, have only two values, either a lower bound or an upper bound on the true risk aversion function, and are consistent with the prices of all these options. Similar results are proved with respect to the true risk aversion function's derivatives. These results show that the errors in the estimation of risk aversion and its derivatives caused purely by market incompleteness can be infinitely large and it is extremely difficult to ensure that the risk aversion function we extract from option prices is the true one.