# Measuring Market Integration: US Stock and REIT Markets

## Abstract

Tests of financial market integration traditionally test for equality of risk premia for a common set of assumed risk factors. Failure to reject the equality of market risk premia can arise because the markets do not share a common factor, i.e. the underlying factor model assumptions are incorrect. In this paper we propose a new methodology that solves this joint hypothesis problem. The first step in our approach tests for the presence of common factors using canonical correlation analysis. The second step of our approach subsequently tests for the equality of risk premia using Generalized Method of Moments (GMM). We illustrate our methodology by examining market integration of US Real Estate Investment Trust (REIT) and Stock markets over the period from 1985 to 2013. We find strong evidence that REIT and stock market integration varies through time. In the earlier part of our data period, the markets do not share a common factor, consistent with markets not being integrated. We also show that during this period, the GMM tests fail to reject the equality of risk premia, highlighting the joint hypothesis problem. The markets in the latter half of our sample show evidence of both a common factor and the equality of risk premia suggesting that REIT and Stock markets are integrated in more recent times.

## Keywords

Market integration Canonical correlation Financial markets REIT Stock GMM Risk premia Common factor Factor model Principal components## Notes

### Acknowledgements

We thank Mark Flannery, Ren-Raw Chen, Shu-Heng Chen, An Yan, Yuewu Xu, Andre de Souza, seminar participants at Fordham University, the Indian School of Business and participants at the 1st Conference on Recent Developments in Financial Econometrics and Applications for their comments and suggestions.

## References

- 1.Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models.
*Econometrics, 70*, 191–221.CrossRefGoogle Scholar - 2.Bai, J., & Ng, S. (2006). Evaluating latent and observed factors in macroeconomics and finance.
*Journal of Econometrics, 131*, 507–537.CrossRefGoogle Scholar - 3.Bekaert, G., Hodrick, R., & Zhang, X. (2009). International stock return comovement.
*Journal of Finance, 64*, 2591–2626.CrossRefGoogle Scholar - 4.Bekeart, G., & Harvey, C. (1995). Time-varying world market integration.
*Journal of Finance, 50*, 403–444.CrossRefGoogle Scholar - 5.Blackburn, D., & Chidambaran, N. (2014).
*Is the world stock return comovement changing?*In Working Paper, Fordham University.Google Scholar - 6.Carrieri, F., Errunza, V., & Hogan, K. (2007). Characterizing world market integration through time.
*Journal of Financial and Quantitative Analysis, 42*, 915–940.CrossRefGoogle Scholar - 7.Errunza, V., & Losq, E. (1985). International asset pricing under mild segmentation: Theory and test.
*Journal of Finance, 40*, 105–124.CrossRefGoogle Scholar - 8.Fama, E., & MacBeth, J. (1973). Risk, return, and equilibrium: Empirical tests.
*Journal of Political Economy, 81*, 607–636.CrossRefGoogle Scholar - 9.Goyal, A., Perignon, C. & Villa, C. (2008). How common are common return factors across NYSE and Nasdaq?
*Journal of Financial Economics, 90*, 252–271.CrossRefGoogle Scholar - 10.Gultekin, M., Gultekin, N. B. & Penati, A. (1989). Capital controls and international capital market segmentation: The evidence from the Japanese and American stock markets.
*Journal of Finance, 44*, 849–869.CrossRefGoogle Scholar - 11.Gyourko, J., & Keim, D. (1992). What does the stock market tell us about real estate returns.
*Journal of the American Real Estate and Urban Economics Association, 20*, 457–485.CrossRefGoogle Scholar - 12.Jagannathan, R., & Wang, Z. (1998). An asymptotic theory for estimating beta-pricing models using cross-sectional regression.
*Journal of Finance, 53*, 1285–1309.CrossRefGoogle Scholar - 13.Ling, D., & Naranjo, A. (1999). The integration of commercial real estate markets and stock markets.
*Real Estate Economics, 27*, 483–515.CrossRefGoogle Scholar - 14.Liow, K. H., & Webb, J. (2009). Common factors in international securitized real estate markets.
*Review of Financial Economics, 18*, 80–89.CrossRefGoogle Scholar - 15.Liu, C., Hartzell, D., Greig, W., & Grissom, T. (1990). The integration of the real estate market and the stock market: Some preliminary evidence.
*Journal of Real Estate Finance and Economics, 3*, 261–282.CrossRefGoogle Scholar - 16.Liu, C., & Mei, J. (1992). The predictability of returns on equity REITs and their co-movement with other assets.
*Journal of Real Estate Finance and Economics, 5*, 401–418.Google Scholar - 17.Mei, J., & Saunders, A. (1997). Have U.S. financial institutions’ real estate investments exhibited trend-chasing behavior?
*Review of Economics and Statistics, 79*, 248–258.CrossRefGoogle Scholar - 18.Miles, M., Cole, R., & Guilkey, D. (1990). A different look at commercial real estate returns.
*Real Estate Economics, 18*, 403–430.CrossRefGoogle Scholar - 19.Newey, W., & West, K. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix.
*Econometrica, 55*, 703–708.CrossRefGoogle Scholar - 20.Pukthuanthong, K., & Roll, R. (2009). Global market integration: An alternative measure and its application.
*Journal of Financial Economics, 94*, 214–232.CrossRefGoogle Scholar - 21.Schnare, A., & Struyk, R. (1976). Segmentation in urban housing markets.
*Journal of Urban Economics, 3*, 146–166.CrossRefGoogle Scholar - 22.Shanken, J. (1992). On the estimation of beta pricing models.
*Review of Financial Studies, 5*, 1–34.CrossRefGoogle Scholar - 23.Stock, J., & Watson, M. (2002). Forecasting using principal components from a large number of predictors.
*Journal of the American Statistical Association, 97*, 1167–1179, 32.Google Scholar - 24.Stulz, R. (1981). A model of international asset pricing.
*Journal of Financial Economics, 9*, 383–406.CrossRefGoogle Scholar - 25.Titman, S., & Warga, A. (1986). Risk and the performance of real estate investment trusts: A multiple index approach.
*Real Estate Economics, 14*, 414–431.CrossRefGoogle Scholar