Experimental studies show that people's risk preferences depend non-linearly on probabilities, but relatively little is know about how probability weighting influences investment decisions. In this paper we analyse the portfolio choice problem of investors who maximize rank-dependent utility in a single-period complete market. We prove that investors with a less risk averse preference relation in general choose a more risky final wealth distribution, receiving a risk premium in return for accepting conditional-zero-mean noise (more risk). We also propose a new scenario-based notion of less risk taking that can be applied when state probabilities are unknown.