Diversification and asset allocation play important roles in determining the overall performance of hotel portfolios. What most hotel investors don’t realize, however, is that the foundation for a sound asset allocation strategy is built upon a widely accepted mathematical technique called mean-variance optimization (MVO). The MVO process combines hotel investments with different return and risk characteristics into portfolios that have the highest return for a given level of risk or the lowest possible risk for a given level of return based on a set of assumptions about risk, return, and return correlations. These hotel portfolios are known as efficient or optimal portfolios.

Many hotel investors claim to have highly diversified portfolios. Just because a hotel portfolio is geographically disperse doesn’t mean that it is geographically diverse in an economic sense. Many investors believe that their hotel portfolios are diversified because they have invested in a number of markets throughout the country. Holding hotels that tend to move in concert with each other does not lower portfolio risk! Refer to the first case study on our website which explains how we assisted a client diversify their portfolio.

In recent times, we have used cluster analysis, a statistical data tool and the subject of our post, to develop homogenous groupings of hotel markets in the U.S. and Canada for our clients seeking to construct efficient hotel portfolios. We have explored the diversification opportunities across U.S. and Canadian hotel markets and reported on the crucial economic factors for determining the relationship of hotel asset performance among different metros. If you would like to discuss these matters, please feel free to call us.

“Cluster analysis serves to empirically answer the question of which hotel markets are complements and which hotel markets are substitutes in the context of a diversified portfolio”.

Clustering Hotel Markets

The only economically rational and intelligent way to diversify a hotel portfolio in the U.S. is by metro area or location. While many investors claim they have ‘geographically diverse’ portfolios, there portfolios have been constructed using an intuitive approach which has invested in a number of different geographic locations in the hope that the variance of the expected return on the portfolio is lowered without calculating the correlations of hotel returns. Many investors have the misguided view that risk is proportionately reduced with each additional hotel or market in a portfolio, when in fact risk could be increasing if the added returns are highly correlated with the returns of existing assets.

Grouping hotel markets with similar characteristics is the first step in developing a rigorous and empirically based diversification and asset allocation strategy. By employing cluster analysis, a powerful statistical analysis technique, we are able to group hotel markets by maximizing within-group homogeneity while also maximizing differences between hotel market groups. While several different clustering techniques are available we have used K-means clustering as described in the footnote.

To illustrate the K-means clustering technique we have used data from STR’s annual Monthly Hotel Review. Based on year-end RevPAR for the Top 25 hotel markets we have calculated the RevPAR CAGR for an 8-year holding period ending 1995 to 2018 for each of the markets. A sample is illustrated in the accompanying table.

RevPAR CAGR for 8 – Year Holding Periods Ending 1995 – 2018 for a Sample of Top 25 Hotel Markets

Source: Hotel Investment Strategies, LLC based on an analysis of SRT data.

Two, three and four cluster profiles were established through the procedure before we settled on the three cluster profile for further analysis. Our cluster analysis allocated the 25 hotel markets to the different cluster profiles is illustrated below.

The Allocation of Top 25 Hotels Markets to Two, Three and Four Clusters Using RevPAR CAGR for 8 – Year Holding Periods Ending 1995 – 2018

Source: Hotel Investment Strategies, LLC based on SRT data.

The following graph provides the average RevPAR CAGR for 8-year holding periods for each of the three clusters in the three cluster profile. Each cluster shows a distinct pattern. Cluster 3, which includes San Francisco and Seattle has performed better than the other two clusters since about 2009. Cluster 1, which includes Los Angeles and New York, recorded superior growth for the period 1999-2008. At no time, apart from 1998, has Cluster 2, which includes Boston and Chicago, outperformed the other two clusters. For the period 2003 to 2012, Cluster 2 lagged both Cluster 1 and 2.

Average RevPAR CAGR for 8-Year Holding Periods Ending 1995-2018 for the Three Clusters of Top 25 US Hotel Markets

Source: Hotel Investment Strategies, LLC based on STR data.

Cluster 3, which includes the hotel markets of Oahu, Orlando, Phoenix, San Francisco, Settle, St Louis and Tampa, recorded the highest average RevPAR CAGR for 8-year holding periods (1995-2018) at 3.8% as illustrated in the graph below. At the same time it recorded the highest risk as noted by a standard deviation of 1.55%. On a risk-adjusted basis, cluster 1 had the best risk-adjusted RevPAR growth at 2.50% compared to clusters 2 and 3 that had risk-adjusted growth rates of 2.20% and 2.48% respectively.

The Location of the Three Hotel Market Clusters for the Top 25 US Hotel Markets

Source: Hotel Investment Strategies, LLC based on STR data. The relative size of a bubble depicts the number of markets in the cluster.

Quantifying how each cluster has performed in risk and return space helps different types of investors identify the types of clusters that meet their particular needs.

Cluster analysis can also be used on time series data such as room supply, room demand, occupancy and ADR. We have found cluster analysis useful to identify market areas that show long term potential for hotel investment, when we have combined underling economic drivers, such as employment and real personal income growth, with hotel metrics.

Our illustration of K-means clustering demonstrates how investors seeking to construct a diversified portfolio can acquire new hotels in markets that do not belong in the same cluster, effectively diversifying the volatility and capital returns in the overall portfolio.

K-means clustering
Clustering is the classification of objects or in our case hotel markets into different groups, or more precisely, the partitioning of a data set into subsets (clusters), so that the data in each subset (ideally) share some common trait – often proximity according to some defined distance measure. Data clustering is a common technique for statistical data analysis which is used in many fields, including real estate as illustrated by the references provided below.

The objective of cluster analysis is to assign observations to groups (“clusters”) so that observations within each group are similar to one another with respect to variables or attributes of interest, and the groups themselves stand apart from one another. In other words, the objective is to divide the observations into homogeneous and distinct groups.

The K-means algorithm assigns each point to the cluster whose center (also called centroid) is nearest. The center is the average of all the points in the cluster — that is, its coordinates are the arithmetic mean for each dimension separately over all the points in the cluster.

Example: The data set has three dimensions and the cluster has two points: X = (x1, x2, x3) and Y = (y1, y2, y3). Then the centroid Z becomes Z = (z1, z2, z3), where z1 = (x1 + y1)/2 and z2 = (x2 + y2)/2 and z3 = (x3 + y3)/2.

The algorithm steps are:(1)
• Choose the number of clusters, k.
• Randomly generate k clusters and determine the cluster centers, or directly generate k random points as cluster centers.
• Assign each point to the nearest cluster center.
• Re-compute the new cluster centers.

Repeat the two previous steps until some convergence criterion is me(usually that the assignment hasn’t changed). The main advantages of this algorithm are its simplicity and speed which allows it to run on large datasets. Cluster analysis is often accompanied by discriminant analysis, a statistical analysis tool that identifies the variables that distinguish one cluster from another. This statistical tool involves a linear combination, or variate, of two or more independent (or explanatory) variables that best discriminate between the cluster groups already identified.

(1) MacQueen, J. B. (1967). Some Methods for Classification and Analysis of Multivariate Observations, Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, University of California Press, 1:281-297

Further articles on the application of cluster analysis in real estate include:
(1) Jackson, Cath and White, Michael. Challenging Traditional Real Estate Market Classifications for Investment Diversification. Journal of Real Estate Portfolio Management, Sep-Dec 2005, Vol. 11 Issue 3.

(2) Smith, Allen; Hess, Robert and Youguo Liang. Clustering the U.S. Real Estate Markets. Journal of Real Estate Portfolio Management, May-Aug 2005, Vol. 11 Issue 2.

(3) Cheng, Ping and Black, Roy T. Geographic Diversification and Economic Fundamentals in Apartment Markets: A Demand Perspective. Journal of Real Estate Portfolio Management, 1998, Vol. 4 Issue 2.

(4) Gallagher, Mark and Mansour, Asieh. An Analysis of Hotel Real Estate Market Dynamics. Journal of Real Estate Research, 2000, Vol. 19. No.1/2.

(5) Goetzman, William N. and Wachter, Susan M. Clustering Methods for Real Estate Portfolios. Real Estate Economics, 1995, Vol. 23, Issue 3.

(6) Hunter, Maura Quinn. How to Identify and Evaluate Industry Risk in a Loan Portfolio: A Five Step Approach. The Journal of Lending & Credit Risk Management, 1998, 28-35.