Abstract
The capital asset pricing model (CAPM), Fama-French (FF), and Pástor-Stambaugh (PS) factor models are examined using a new dynamic rolling regression version of the generalized method of moments (GMM) method. This rolling regression framework not only allows us to investigate phases of the business cycle, but also permits regression estimates to vary through time due to changes in the development and efficiency of the sectors. The principal reasons for using the dynamic GMM with robust instruments is that some of these factors are measured with errors and the disturbances may be non-spherical. The CAPM appears as the most parsimonious model to explain the FF sector returns. Furthermore, the rolling GMM approach is clearly more sensitive to dynamic financial episodes than the ordinary least squares approach. In particular, liquidity has some anticipatory power, as it is able to forecast the 2007–2009 crises with heightened volatility starting in late 2005.
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Notes
Our selection of 60 months follows the convention of Reilly and Brown (2009, p. 219). They note that there is no theoretically correct time interval for estimating returns. They conclude that the 60-month period is widely used by Morningstar and others, for example, and seems to be neither too long nor too short.
For more detail, see Pástor-Stambaugh (2003). For a discussion of liquidity measures, see Johann and Theissen (2013).
HAC is the heteroscedasticity and autocorrelation consistent estimator. We used the “Iterate to Convergence” Newey and West (1987) methodology of EViews 8.1.
The assumption of a normally distributed matrix of errors is used to simplify the mathematical proof of the consistency of the estimators in this paper. This assumption is in no way a limitation in the modeling process of the time series used in this paper. Our proposed GMMd estimator is based on the higher moments of the observed financial data and is thus able to capture the data’s non-linearity, which is one of the important goals of this estimator.
See Benninga (2014), p. 276.
See Roll (1977) for a discussion of the problems in testing the CAPM theory.
French’s website is http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
Pástor’s website is http://faculty.chicagobooth.edu/lubos.pastor/research/liq_data_1962_2013.txt
Markowitz (2012) noted that the mean-variance model still works well in the presence of moderate amounts of skewness and kurtosis.
The LIQ variable is really a measure of illiquidity, not liquidity, as correctly noted by Bodie et al. (2015, p. 406).
For an introduction to non-linear models including multivariate GARCH processes with financial applications, see Racicot (2012).
We conducted other experiments where the dynamic conditional correlation (DCC) between the average of the returns of the FF 12 sector and SMB and the average and LIQ is computed. We find that the DCC correlation between the average and SMB is much higher than the one obtain for LIQ. This is further evidence that SMB could be a good proxy for LIQ.
Although not shown, similar results were obtained for the FF model.
We have conducted further experiments using OLS to benchmark our results for the dynamic GMMd. The results are quite similar although GMMd is more sensitive to the financial crises observed in our sample, which is the virtues the dynamic estimator proposed in this article.
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Racicot, FÉ., Rentz, W.F. & Kahl, A.L. Rolling Regression Analysis of the Pástor-Stambaugh Model: Evidence from Robust Instrumental Variables. Int Adv Econ Res 23, 75–90 (2017). https://doi.org/10.1007/s11294-016-9620-x
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DOI: https://doi.org/10.1007/s11294-016-9620-x