The Impact of Seasonality on Investment Statistics Derived from Quarterly Returns

Executive Summary. The sample variance, covariance and correlation functions are not consistent estimators for the corresponding true distributional parameters when applied to returns that display seasonal behavior. Seasonality in quarterly appraisal-based returns generates sample bias that can be either upward or downward, depending on whether assets are appraised in the same or different quarters. The bias is material in magnitude and does not decrease as sample size increases. Seasonality acts in such a way as to exaggerate the apparent contribution of MPT to real estate portfolio diversification. Seasonally induced correlation bias appears to have affected some real estate diversification studies that base derivations upon quarterly return indices. The bias source can be avoided by substituting annual returns for quarterly returns in portfolio optimization input.