Table 3 Fama-French asset pricing model...

Table 3

Fama-French asset pricing model and GPR

Portfolio: NAREITs indices (January 1994–December 2023)
	GMM − BIC
	p₁	p₂	p₃	p₄	p₅	p₆	p₇	p₈	p₉	p₁₀
	−20.26	−20.58	−19.96	−22.63	−22.03	−20.88	−20.22	−20.07	−20.64	−21.06
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	3.29	2.97	3.58	0.92	1.51	2.67	3.32	3.47	2.89	2.48
	(0.52)	(0.57)	(0.47)	(0.92)	(0.82)	(0.62)	(0.51)	(0.49)	(0.58)	(0.65)
	DW₁	DW₂	DW₃	DW₄	DW₅	DW₆	DW₇	DW₈	DW₉	DW₁₀
	2.23	2.24	2.18	2.34	2.11	2.26	2.26	2.23	2.27	2.26
	DWH₁	DWH₂	DWH₃	DWH₄	DWH₅	DWH₆	DWH₇	DWH₈	DWH₉	DWH₁₀
	2.87	1.99	4.55	2.07	0.57	1.92	4.10	2.92	5.55	4.98
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.181	−0.330	0.229	0.369	−0.707	−0.129	−0.222	0.258	−0.217	−0.341
	(0.71)	(1.44)	(0.87)	(1.09)	(2.92)	(0.53)	(0.64)	(1.06)	(0.79)	(1.22)
	β_k,1	β_k,2	β_k,3	β_k,4	β_k,5	β_k,6	β_k,7	β_k,8	β_k,9	β_k,10
MKT	0.807	1.017	0.780	0.979	1.344	1.031	1.361	0.740	1.187	1.257
MKT	(7.55)	(10.39)	(11.03)	(3.58)	(11.99)	(7.19)	(7.34)	(7.05)	(8.55)	(8.08)
SMB	0.223	0.373	0.062	0.008	0.420	0.200	0.440	0.198	0.290	0.246
SMB	(4.97)	(5.24)	(0.65)	(0.06)	(6.74)	(3.04)	(3.73)	(4.24)	(3.16)	(2.71)
HML	0.618	0.898	0.556	0.263	1.024	0.628	1.052	0.579	0.853	0.899
HML	(6.16)	(6.70)	(3.44)	(0.91)	(10.05)	(4.95)	(4.17)	(5.61)	(4.59)	(5.16)
GPR	0.028	0.021	0.021	0.033	0.024	0.038	0.042	0.026	0.038	0.041
GPR	(4.61)	(3.86)	(4.77)	(3.52)	(3.98)	(5.53)	(6.42)	(4.60)	(6.83)	(6.93)

Portfolio: NAREITs indices (January 1994–December 2023)
	GMM − BIC
	p₁	p₂	p₃	p₄	p₅	p₆	p₇	p₈	p₉	p₁₀
	−20.26	−20.58	−19.96	−22.63	−22.03	−20.88	−20.22	−20.07	−20.64	−21.06
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	3.29	2.97	3.58	0.92	1.51	2.67	3.32	3.47	2.89	2.48
	(0.52)	(0.57)	(0.47)	(0.92)	(0.82)	(0.62)	(0.51)	(0.49)	(0.58)	(0.65)
	DW₁	DW₂	DW₃	DW₄	DW₅	DW₆	DW₇	DW₈	DW₉	DW₁₀
	2.23	2.24	2.18	2.34	2.11	2.26	2.26	2.23	2.27	2.26
	DWH₁	DWH₂	DWH₃	DWH₄	DWH₅	DWH₆	DWH₇	DWH₈	DWH₉	DWH₁₀
	2.87	1.99	4.55	2.07	0.57	1.92	4.10	2.92	5.55	4.98
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.181	−0.330	0.229	0.369	−0.707	−0.129	−0.222	0.258	−0.217	−0.341
	(0.71)	(1.44)	(0.87)	(1.09)	(2.92)	(0.53)	(0.64)	(1.06)	(0.79)	(1.22)
	β_k,1	β_k,2	β_k,3	β_k,4	β_k,5	β_k,6	β_k,7	β_k,8	β_k,9	β_k,10
MKT	0.807	1.017	0.780	0.979	1.344	1.031	1.361	0.740	1.187	1.257
MKT	(7.55)	(10.39)	(11.03)	(3.58)	(11.99)	(7.19)	(7.34)	(7.05)	(8.55)	(8.08)
SMB	0.223	0.373	0.062	0.008	0.420	0.200	0.440	0.198	0.290	0.246
SMB	(4.97)	(5.24)	(0.65)	(0.06)	(6.74)	(3.04)	(3.73)	(4.24)	(3.16)	(2.71)
HML	0.618	0.898	0.556	0.263	1.024	0.628	1.052	0.579	0.853	0.899
HML	(6.16)	(6.70)	(3.44)	(0.91)	(10.05)	(4.95)	(4.17)	(5.61)	(4.59)	(5.16)
GPR	0.028	0.021	0.021	0.033	0.024	0.038	0.042	0.026	0.038	0.041
GPR	(4.61)	(3.86)	(4.77)	(3.52)	(3.98)	(5.53)	(6.42)	(4.60)	(6.83)	(6.93)

Note(s): This table reports the average pricing errors (α_i), coefficients of β_k,i and four goodness-of-fit statistics obtained from the GMM estimation of system (1) using monthly data from January 1994 to December 2023. We use the FTSE Nareit U.S. REIT indices for 10 real estate sectors. p1: Apartment; p2: Diversified; p3: Healthcare; p4: Industrial; p5: Lodging Resorts; p6: Office; p7: Regional Malls; p8: Residential; p9: Retail; p10: Shopping Centers. J_T is Hansen’s statistic (to test the model’s over-identifying restrictions) and p-values are provided in parentheses. GMM − BIC is Andrews (1999) Bayesian information criterion. DW is Durbin and Watson’s statistic (to test for the autocorrelation in the residuals), and DWH is Durbin, Wu and Hausmann specification test. The model is the four-factor APM. The factors are the market excess return (MKT), SMB and HML the Fama and French size (small minus big) and book-to-market (high minus low) factors, and the geopolitical risk index (GPR), introduced by Caldara and Iacoviello (2022). For the estimates (α and β) the t-stats are provided in parentheses. The table reports the results of the augmented Fama and French asset pricing models, adding the GPR index. N.B. critical values for t-stats are 1.645 (at 10%), 1.960 (at 5%), 2.576 (at 1%)

Source(s): Table created by authors

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