Co‐skewness and Co‐kurtosis in Global Real Estate Securities

Abstract

We explore the question of whether co‐skewness and co‐kurtosis risk measures can be added to supplement to the covariance risk in pricing global real estate securities and risk premium estimation. Based on a generalized four‐moment CAPM with two alternative world market proxies, we examine Linear, Quadratic and Cubic Market Models using GMM and time‐varying Kalman‐Filter methodologies. Our results show that the second moment is important in explaining real estate securities returns. Furthermore, some real estate securities also display significant time‐varying co‐skewness and/or co‐kurtosis. Co‐kurtosis is more important than co‐skewness in pricing global real estate securities. We further find that the co‐skewness and co‐kurtosis coefficients and the resulting risk premia are sensitive to the market proxy used. The findings of this study provide additional insights into the risk‐return characteristics, pricing and portfolio design in global real estate securities.

Keywords:

• Higher‐moment CAPM
• co‐skewness
• co‐kurtosis
• time‐varying
• risk premia

Notes

1. The M‐GARCH approach to modeling time‐varying beta has been utilized in various studies including Giannopoulos (1995) and Brooks et al. (2002). Other studies utilizing the augmented market model of Schwert and Seguin (1990) include Koutmos et al. (1994), Koutmos and Kniff (2002) and Episcopos (1996). The KF method has been used by various authors including Brooks et al. (2002).

2. Unlike maximum likelihood estimation, the GMM procedure is a robust estimator because it doe not require information regarding the exact distribution of the disturbances. It is distribution free and is used when the assumption of normality is inappropriate (as in the present study). It only requires some specification of certain moment conditions. A main requirement of the GMM estimation is to write the moment condition as an orthogonality condition between an expression including the parameters and a set of instrumental variables. The GMM estimator selects parameter estimates so that the sample correlations between the instruments and disturbances are as close to zero as possible. The estimated parameters are consistent and asymptotical normal. We use the GMM procedure to estimate each equation for each market individually. The system GMM approach is not adopted because when all 19 markets are considered jointly, the GMM system becomes too large with excessive orthogonality conditions. Consequently the estimation results may become unreliable. We also agree with a referee's comment that the use of GMM seems to be overkill given only 132 monthly observations for each time series. Our humble responses are that the time series data length is the longest that we can have from the Datastream. As a robustness check, we also check the GMM results using Newey‐West (NW) estimation procedure and find no significant differences on the results between using the GMM and NW procedures. We wish to thank the referee for raising this concern and hope that our responses are acceptable.

3. Datastream is a popular financial database that contains a rich source of real estate securities data and is available at the University library. We note that Global Property Research (GPR) database provides another alternative but individual users first need to be subscribers of the database.As the exchange‐based real estate indexes for the European markets are not available from the Datastream, we have to use the DS real estate indexes for the 19 regions. The detailed composition and construction of the various real estate securities indexes by the Datastream are not available except that each index contains all real estate related firms classified by the Datastream. Hence, as pointed out by a referee, some markets will have mainly REITS or property trusts while other markets' securitized real estate indexes will consist of homebuilders and real estate construction companies. Hence, this data limitation must be borne in mind when examining the results and conclusions of the paper. We wish to thank the referee for raising this concern.

4. The mainland China is now the engine of world economy that would stimulate China's property market to become a popular target for real estate investors in Asia and internationally. Many foreign funds have entered into China property market especially in Shanghai. China real estate stock market started to emerge in beginning 1990. By 1993, listed real estate investment companies have accounted for about 10% of the China stock market. To‐date, there are more than 20 real estate companies listed on the Shanghai Stock Exchange. The proxy for real estate company performance in Mainland China is Shanghai SE Real Estate Index. Real estate related firms accounts for over 30% of Hong Kong stock market capitalization. In addition, total value of real estate exceeds the total value of all shares and money. To‐date, there are more than 100 property companies listed on the Hong Kong Stock Exchange, with some property companies from the mainland China. Finally, many of the Hong Kong property companies have holdings on the mainland. The Hang Seng Property Index is the proxy benchmark for listed property performance in Hong Kong.

5. In this study, we use two world market proxy: Morgan Stanley Capital International World Market Index (MSWD) which has been commonly used in many stock market studies; and Datastream World Real Estate Index (DSWR). From the standpoint of a US investor, these two world market proxies include the US stock and real estate market performances. Alternatively, as suggested by a referee, we can also use the MSWD (with the US component excluded) and the DSWR (with the NAREIT component excluded). In these circumstances, the US investor will purely be interested in the performances of major foreign markets excluding the own market (i.e. US) performance. We wish to thank the referee for raising this comment.

6. This issue is beyond the scope of the present study.

7. Additionally, a bi‐moments condition is one where both the co‐skewness and co‐kurtosis coefficients are statistically significant, but not the covariance, in the Cubic Market Model. None of the 19 real estate securities displays this condition.

8.

The TIC always lies between zero and one, where zero indicates a perfect fit.

9. As mentioned above, the economic intuition for coskewness and cokurtosis present in some markets can only be speculated. One possible economic explanation (see Hwang and Satchell, 1999) could be due to the evolving degree of real estate market integration associated with high market volatility in Asian (emerging) markets. In addition, the significance of higher co‐moments in some markets might be related to the non‐inclusion of some other variables like a national stock market proxy or factors such as firm size and value etc (see also endnote 7). Further deliberation of these issues are beyond the scope of this research. We wish to thank the referee for raising this comment.

10. A referee has commented that when additional factors such as the Fama‐French (1992)'s size and value factors, Chen et al. (1986) or APT type macroeconomic factors are included in the higher‐moment CAPM models, the significance of co‐skewness and co‐kurtosis found in some markets might be eliminated. Our humble responses are: to the best of our knowledge, there are only two relevant stock market studies that combine the two approaches; the first is by Hung et al. (2004) who suggest that using higher co‐moments (i.e. co‐skewness and co‐kurtosis) of the return distribution as factors, in addition to the Fama and French (1992)'s size and value factors, does not contribute greatly to the ability to explain the cross section of UK stock returns. On the contrary, Lin and Wang (2003) find that even after controlling for the firm size and value factors, co‐skewness still plays an important role in pricing Taiwan stock market returns (co‐kurtosis was not investigated in the study). As there are no similar studies conducted on global real estate securities, our speculation is that the significance of co‐skewness and co‐kurtosis, if carefully examined in an extended model with size, value and other macroeconomic factors (the main problem is multicollinearity among the selected independent variables), can still play a role in pricing real estate stock returns in some markets such as Asia‐Pacific emerging markets whose returns are non‐normally distributed. An extended investigation of this kind is thus left for future research. Finally, we wish to thank the referee for raising this comment.