Table A1 Fama-French asset pricing model...

Table A1

Fama-French asset pricing model and GPT

Geopolitical threats GPT: January 1994–December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	3.00	2.20	3.04	1.09	1.32	1.97	2.75	3.43	2.71	2.67
	(0.56)	(0.70)	(0.55)	(0.90)	(0.86)	(0.74)	(0.60)	(0.49)	(0.61)	(0.61)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.200	−0.326	0.254	0.409	−0.712	−0.133	−0.215	0.275	−0.170	−0.298
	(0.79)	(1.43)	(0.97)	(1.20)	(2.97)	(0.55)	(0.62)	(1.13)	(0.62)	(1.05)
	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	0.788	1.000	0.767	0.947	1.353	1.030	1.383	0.730	1.163	1.218
MKT	(7.67)	(10.55)	(11.25)	(3.47)	(12.65)	(7.34)	(7.34)	(7.15)	(8.53)	(8.01)
SMB	0.217	0.349	0.027	0.005	0.406	0.196	0.390	0.188	0.242	0.214
SMB	(4.33)	(4.44)	(0.27)	(0.04)	(6.45)	(3.03)	(3.17)	(3.61)	(2.44)	(2.21)
HML	0.631	0.878	0.524	0.300	1.023	0.667	0.989	0.581	0.801	0.887
HML	(5.96)	(6.18)	(3.12)	(1.05)	(10.27)	(5.42)	(3.76)	(5.35)	(4.09)	(4.95)
GPT	0.016	0.012	0.015	0.016	0.020	0.021	0.037	0.017	0.028	0.023
GPT	(0.76)	(0.70)	(0.78)	(0.72)	(2.09)	(1.06)	(2.70)	(0.83)	(1.61)	(1.27)

Geopolitical threats GPT: January 1994–December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	3.00	2.20	3.04	1.09	1.32	1.97	2.75	3.43	2.71	2.67
	(0.56)	(0.70)	(0.55)	(0.90)	(0.86)	(0.74)	(0.60)	(0.49)	(0.61)	(0.61)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.200	−0.326	0.254	0.409	−0.712	−0.133	−0.215	0.275	−0.170	−0.298
	(0.79)	(1.43)	(0.97)	(1.20)	(2.97)	(0.55)	(0.62)	(1.13)	(0.62)	(1.05)
	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	0.788	1.000	0.767	0.947	1.353	1.030	1.383	0.730	1.163	1.218
MKT	(7.67)	(10.55)	(11.25)	(3.47)	(12.65)	(7.34)	(7.34)	(7.15)	(8.53)	(8.01)
SMB	0.217	0.349	0.027	0.005	0.406	0.196	0.390	0.188	0.242	0.214
SMB	(4.33)	(4.44)	(0.27)	(0.04)	(6.45)	(3.03)	(3.17)	(3.61)	(2.44)	(2.21)
HML	0.631	0.878	0.524	0.300	1.023	0.667	0.989	0.581	0.801	0.887
HML	(5.96)	(6.18)	(3.12)	(1.05)	(10.27)	(5.42)	(3.76)	(5.35)	(4.09)	(4.95)
GPT	0.016	0.012	0.015	0.016	0.020	0.021	0.037	0.017	0.028	0.023
GPT	(0.76)	(0.70)	(0.78)	(0.72)	(2.09)	(1.06)	(2.70)	(0.83)	(1.61)	(1.27)

Geopolitical Acts GPA: January 1994–December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	3.03	3.71	2.40	3.25	0.87	1.50	2.45	3.87	3.08	3.53
	(0.55)	(0.45)	(0.66)	(0.52)	(0.93)	(0.83)	(0.65)	(0.42)	(0.54)	(0.47)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.173	−0.258	−0.336	0.245	0.324	−0.702	−0.119	−0.259	0.244	−0.201
	(0.67)	(0.95)	(1.48)	(0.94)	(0.98)	(3.01)	(0.50)	(0.74)	(0.99)	(0.73)
	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	0.821	1.204	0.996	0.775	1.029	1.333	1.032	1.425	0.758	1.202
MKT	(7.27)	(7.91)	(10.02)	(10.22)	(4.16)	(12.16)	(7.10)	(7.51)	(6.99)	(8.29)
SMB	0.244	0.234	0.369	0.049	0.034	0.429	0.231	0.427	0.216	0.282
SMB	(5.49)	(2.71)	(5.17)	(0.53)	(0.27)	(6.99)	(3.77)	(3.57)	(4.73)	(3.04)
HML	0.631	0.843	0.882	0.525	0.297	1.035	0.658	0.969	0.589	0.800
HML	(6.47)	(5.18)	(6.59)	(3.30)	(1.04)	(10.11)	(5.13)	(3.83)	(5.89)	(4.37)
GPA	0.021	0.032	0.012	0.017	0.025	0.018	0.025	0.036	0.020	0.030
GPA	(2.62)	(3.37)	(1.27)	(3.30)	(2.93)	(1.65)	(2.46)	(3.65)	(2.96)	(3.64)

Geopolitical Acts GPA: January 1994–December 2023
	$J_{T_{1}}$	$J_{T_{2}}$	$J_{T_{3}}$	$J_{T_{4}}$	$J_{T_{5}}$	$J_{T_{6}}$	$J_{T_{7}}$	$J_{T_{8}}$	$J_{T_{9}}$	$J_{T_{10}}$
	3.03	3.71	2.40	3.25	0.87	1.50	2.45	3.87	3.08	3.53
	(0.55)	(0.45)	(0.66)	(0.52)	(0.93)	(0.83)	(0.65)	(0.42)	(0.54)	(0.47)
	α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
	0.173	−0.258	−0.336	0.245	0.324	−0.702	−0.119	−0.259	0.244	−0.201
	(0.67)	(0.95)	(1.48)	(0.94)	(0.98)	(3.01)	(0.50)	(0.74)	(0.99)	(0.73)
	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	0.821	1.204	0.996	0.775	1.029	1.333	1.032	1.425	0.758	1.202
MKT	(7.27)	(7.91)	(10.02)	(10.22)	(4.16)	(12.16)	(7.10)	(7.51)	(6.99)	(8.29)
SMB	0.244	0.234	0.369	0.049	0.034	0.429	0.231	0.427	0.216	0.282
SMB	(5.49)	(2.71)	(5.17)	(0.53)	(0.27)	(6.99)	(3.77)	(3.57)	(4.73)	(3.04)
HML	0.631	0.843	0.882	0.525	0.297	1.035	0.658	0.969	0.589	0.800
HML	(6.47)	(5.18)	(6.59)	(3.30)	(1.04)	(10.11)	(5.13)	(3.83)	(5.89)	(4.37)
GPA	0.021	0.032	0.012	0.017	0.025	0.018	0.025	0.036	0.020	0.030
GPA	(2.62)	(3.37)	(1.27)	(3.30)	(2.93)	(1.65)	(2.46)	(3.65)	(2.96)	(3.64)

Note(s): This table reports the average pricing errors (α_i), coefficients of β_k,i and 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

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 indices (GPT, geopolitical threats, and GPA, geopolitical acts), 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 GPT and GPA indices. 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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