The Rank-Size Rule and Challenges in Diversifying Commercial Real Estate Portfolios

Abstract

The strategy of geographically diversifying a portfolio of commercial real estate assets is an intuitive approach for risk management. However, due to high concentrations of these assets in major metropolitan areas, investors may face additional constraints in the portfolio optimization process. The rank-size rule, a log-linear relationship between city rank and size, provides one of the greatest empirical regularities in regional science. As such, it serves as a possible theoretical guide to the weights given to properties by location in a commercial real estate portfolio. This paper sets forth some ideas relating to the concentration side of portfolio variance and the limiting effect that large concentrations may have on the ability to diversify risk. Two variants of the rank-size relationship – the Zipf distribution and the parabolic fractal distribution – are fitted to a variety of datasets to provide a sense of the degree of concentration in the commercial real estate industry. These empirical findings suggest the presence of limitations to geographical diversification that have varying degrees of severity across different property types or sectors of the commercial real estate market.