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We analyse whether the idiosyncratic risk puzzle reported by Ang et al. can be explained by the existence of market participants with different investment horizons. We adopt a wavelet multiresolution analysis to decompose the returns distribution for different time scales. Our approach divides the nonlinear link between expected returns and idiosyncratic risk into two linear relationships, a positive one for long-run investors and a negative one for short-run investors, indicating that the puzzle disappears as the wavelet scale increases (long-term horizons). Our results are robust to several types of wavelets, to different definitions of short-term investors and to various measures of idiosyncratic risk.