For earthquake‐resistant design purposes, ground‐motion intensity is usually characterized using response spectra. The amplitude of response spectral ordinates of horizontal components varies significantly with changes in orientation. This change in intensity with orientation is commonly known as ground‐motion directionality. Although this directionality has been attributed to several factors, such as topographic irregularities, near‐fault effects, and local geologic heterogeneities, the mechanism behind this phenomenon is still not well understood. This work studies the directionality characteristics of earthquake ground‐motion intensity using synthetic ground motions and compares their directionality to that of recorded ground motions. The two principal components of horizontal acceleration are sampled independently using a stochastic model based on finite‐duration time‐modulated filtered Gaussian white‐noise processes. By using the same stochastic process to sample both horizontal components of motion, the variance of horizontal ground acceleration has negligible orientation dependence. However, these simulations’ response spectral ordinates present directionality levels comparable to those found in real ground motions. It is shown that the directionality of the simulated ground motions changes for each realization of the stochastic process and is a consequence of the duration being finite. Simulated ground motions also present similar directionality trends to recorded earthquake ground motions, such as the increase of average directionality with increasing period of vibration and decrease with increasing significant duration. These results suggest that most of the orientation dependence of horizontal response spectra is primarily explained by the finite significant duration of earthquake ground motion causing inherent randomness in response spectra, rather than by some physical mechanism causing polarization of shaking.