Table 3 Summary of regression results...

Table 3

Summary of regression results for FF3 alternative models

Variable	Model	Mean	Std. dev	Skew	Kurt	P10	P50	P90
Panel A. Distribution of estimated alpha and betas
α	FF3_E1	0.002	0.159	−0.313	5.251	−0.164	0.005	0.162
	FF3_E3	0.005	0.158	−0.307	5.451	−0.159	0.005	0.168
	FF3_E5	0.007	0.158	−0.165	4.850	−0.159	0.005	0.170
RM_RF	FF3_E1	1.017	0.279	−0.282	−0.134	0.650	1.032	1.367
	FF3_E3	1.019	0.278	−0.305	−0.108	0.654	1.035	1.366
	FF3_E5	1.021	0.279	−0.317	−0.129	0.654	1.040	1.365
SMB	FF3_E1	0.773	0.383	−0.440	0.105	0.241	0.822	1.223
	FF3_E3	0.765	0.398	−0.441	0.041	0.209	0.815	1.238
	FF3_E5	0.760	0.416	−0.408	−0.009	0.169	0.811	1.250
HML	FF3_E1	0.086	0.362	−1.195	2.938	−0.332	0.141	0.480
	FF3_E3	0.072	0.376	−1.067	2.430	−0.374	0.127	0.489
	FF3_E5	0.076	0.402	−1.038	2.323	−0.413	0.127	0.517
Adjusted R²	FF3_E1	0.163	0.081	0.737	0.882	0.065	0.154	0.271
	FF3_E3	0.164	0.082	0.752	0.963	0.065	0.154	0.271
	FF3_E5	0.164	0.082	0.767	1.034	0.065	0.154	0.272
Panel B. Distribution of t-values for alpha and betas
α	FF3_E1	−0.132	7.226	−43.145	1887.310	−1.033	0.033	1.091
	FF3_E3	−0.118	7.232	−43.150	1887.600	−1.024	0.030	1.114
	FF3_E5	−0.113	7.180	−43.127	1886.230	−1.040	0.036	1.135
RM_RF	FF3_E1	21.227	9.945	0.817	1.131	9.637	19.999	33.914
	FF3_E3	21.312	9.946	0.797	1.104	9.602	20.121	33.998
	FF3_E5	21.580	9.963	0.790	1.088	9.795	20.385	34.262
SMB	FF3_E1	9.779	5.289	−0.349	0.304	3.154	9.926	16.440
	FF3_E3	9.342	5.309	−0.401	0.334	2.759	9.589	15.958
	FF3_E5	8.951	5.315	−0.420	0.308	2.221	9.218	15.536
HML	FF3_E1	1.495	4.413	−0.148	2.115	−3.480	1.452	6.644
	FF3_E3	1.342	4.497	−0.118	1.526	−3.756	1.250	6.764
	FF3_E5	1.333	4.584	−0.227	1.205	−3.983	1.305	6.989

Variable	Model	Mean	Std. dev	Skew	Kurt	P10	P50	P90
Panel A. Distribution of estimated alpha and betas
α	FF3_E1	0.002	0.159	−0.313	5.251	−0.164	0.005	0.162
	FF3_E3	0.005	0.158	−0.307	5.451	−0.159	0.005	0.168
	FF3_E5	0.007	0.158	−0.165	4.850	−0.159	0.005	0.170
RM_RF	FF3_E1	1.017	0.279	−0.282	−0.134	0.650	1.032	1.367
	FF3_E3	1.019	0.278	−0.305	−0.108	0.654	1.035	1.366
	FF3_E5	1.021	0.279	−0.317	−0.129	0.654	1.040	1.365
SMB	FF3_E1	0.773	0.383	−0.440	0.105	0.241	0.822	1.223
	FF3_E3	0.765	0.398	−0.441	0.041	0.209	0.815	1.238
	FF3_E5	0.760	0.416	−0.408	−0.009	0.169	0.811	1.250
HML	FF3_E1	0.086	0.362	−1.195	2.938	−0.332	0.141	0.480
	FF3_E3	0.072	0.376	−1.067	2.430	−0.374	0.127	0.489
	FF3_E5	0.076	0.402	−1.038	2.323	−0.413	0.127	0.517
Adjusted R²	FF3_E1	0.163	0.081	0.737	0.882	0.065	0.154	0.271
	FF3_E3	0.164	0.082	0.752	0.963	0.065	0.154	0.271
	FF3_E5	0.164	0.082	0.767	1.034	0.065	0.154	0.272
Panel B. Distribution of t-values for alpha and betas
α	FF3_E1	−0.132	7.226	−43.145	1887.310	−1.033	0.033	1.091
	FF3_E3	−0.118	7.232	−43.150	1887.600	−1.024	0.030	1.114
	FF3_E5	−0.113	7.180	−43.127	1886.230	−1.040	0.036	1.135
RM_RF	FF3_E1	21.227	9.945	0.817	1.131	9.637	19.999	33.914
	FF3_E3	21.312	9.946	0.797	1.104	9.602	20.121	33.998
	FF3_E5	21.580	9.963	0.790	1.088	9.795	20.385	34.262
SMB	FF3_E1	9.779	5.289	−0.349	0.304	3.154	9.926	16.440
	FF3_E3	9.342	5.309	−0.401	0.334	2.759	9.589	15.958
	FF3_E5	8.951	5.315	−0.420	0.308	2.221	9.218	15.536
HML	FF3_E1	1.495	4.413	−0.148	2.115	−3.480	1.452	6.644
	FF3_E3	1.342	4.497	−0.118	1.526	−3.756	1.250	6.764
	FF3_E5	1.333	4.584	−0.227	1.205	−3.983	1.305	6.989

Note(s): This table summarizes the regression results for the alternative FF3 models (FF3_E1, FF3_E3, FF3_E5), each constructed by sequentially excluding top market-cap stocks. Panel A presents the distribution of estimated alphas and factor loadings (betas), while Panel B reports the distribution of their corresponding t-values. The analysis covers 1,940 stocks listed on the KOSPI and KOSDAQ markets in Korea between 2001 and 2022, each with a minimum of three years of trading history. Alpha values are annualized by multiplying daily estimates by 252

Source(s): Author’s own work

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