The reflectance spectra of chirped fiber Bragg gratings can depend substantially on the direction from which the measurement is taken. The measured difference between forward and backward reflectance spectra measured in a linearly chirped grating was shown to be due to the measured excess loss. Simulation using the popular transfer-matrix model demonstrated that the observed asymmetric behavior could be obtained only when excess loss has an asymmetric spectral shape about the local Bragg wavelengths. Application of cladding mode excess losses to the result of a transfer-matrix model accounted for the experimental observation.