We perform theoretical analysis and systematic measurement of the degree-of-polarization and eye-closure penalty for optical signals with orthogonal polarizations. Both the theory and experiment show that the symmetry of the DOP is maintained for the orthogonal polarizations under both first and higher-order PMD, whereas the symmetry of eye-closure penalty is broken under second-order PMD. As a result, an orthogonal polarization pair can have large disparity of eye-closure penalty despite an identical degree-of-polarization. We also demonstrate a novel approach to estimate the maximum eye-closure penalty asymmetry with three orthogonal polarizations on the Poincare sphere.