Statistics of the DFA Factors

# Output from previous execution

/var/folders/zx/3v_qt0957xzg3nqtnkv007d00000gn/T/ipykernel_92294/4220933265.py:2: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  dts['early'] = pd.date_range(start=facs.index[0], end='31/12/1980',freq='M')
/var/folders/zx/3v_qt0957xzg3nqtnkv007d00000gn/T/ipykernel_92294/4220933265.py:3: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  dts['founding'] = pd.date_range(start='1/1/1981', end='31/12/2001',freq='M')
/var/folders/zx/3v_qt0957xzg3nqtnkv007d00000gn/T/ipykernel_92294/4220933265.py:4: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  dts['recent'] = pd.date_range(start='1/1/2002', end=facs.index[-1],freq='M')
/var/folders/zx/3v_qt0957xzg3nqtnkv007d00000gn/T/ipykernel_92294/4220933265.py:6: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  dts['1990s'] = pd.date_range(start='1/1/1991', end='31/12/1999',freq='M')

# Output from previous execution

========================================================

Period: 1926-07-31 00:00:00 to 1980-12-31 00:00:00

========================================================

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
Mkt-RF	0.0810	0.2050	0.3949	-0.2874	0.3881	-0.0841
SMB	0.0339	0.1143	0.2968	-0.0989	0.3596	-0.0419
HML	0.0503	0.1342	0.3749	-0.1319	0.3552	-0.0442

========================================================

Period: 1981-01-31 00:00:00 to 2001-12-31 00:00:00

========================================================

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
Mkt-RF	0.0779	0.1572	0.4953	-0.2319	0.1245	-0.0641
SMB	-0.0020	0.1173	-0.0172	-0.1741	0.2125	-0.0459
HML	0.0646	0.1099	0.5876	-0.0977	0.1224	-0.0416

========================================================

Period: 2002-01-31 00:00:00 to 2025-08-31 00:00:00

========================================================

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
Mkt-RF	0.0913	0.1535	0.5947	-0.1720	0.1360	-0.0773
SMB	0.0079	0.0884	0.0897	-0.0593	0.0714	-0.0392
HML	0.0012	0.1064	0.0113	-0.1383	0.1286	-0.0415

========================================================

Period: 1991-01-31 00:00:00 to 1999-12-31 00:00:00

========================================================

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
Mkt-RF	0.1556	0.1298	1.1988	-0.1605	0.1085	-0.0416
SMB	-0.0007	0.1042	-0.0070	-0.0694	0.0848	-0.0501
HML	0.0142	0.0922	0.1539	-0.0766	0.0651	-0.0406

========================================================

Period: 1981-01-31 00:00:00 to 2025-08-31 00:00:00

========================================================

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
Mkt-RF	0.0850	0.1551	0.5478	-0.2319	0.1360	-0.0723
SMB	0.0033	0.1029	0.0316	-0.1741	0.2125	-0.0418
HML	0.0310	0.1083	0.2860	-0.1383	0.1286	-0.0415

========================================================

Period: 1926-07-31 00:00:00 to 2025-08-31 00:00:00

========================================================

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
Mkt-RF	0.0828	0.1841	0.4495	-0.2874	0.3881	-0.0792
SMB	0.0201	0.1093	0.1839	-0.1741	0.3596	-0.0418
HML	0.0416	0.1232	0.3377	-0.1383	0.3552	-0.0424

# Output from previous execution

(<Figure size 400x400 with 2 Axes>,
 <Axes: title={'center': 'Correlation matrix (lower triangle)'}>)

Text(0.5, 1.0, 'founding')

(<Figure size 400x400 with 2 Axes>,
 <Axes: title={'center': 'Correlation matrix (lower triangle)'}>)

Text(0.5, 1.0, 'recent')

(<Figure size 400x400 with 2 Axes>,
 <Axes: title={'center': 'Correlation matrix (lower triangle)'}>)

Text(0.5, 1.0, 'modern')

(<Figure size 400x400 with 2 Axes>,
 <Axes: title={'center': 'Correlation matrix (lower triangle)'}>)

Text(0.5, 1.0, 'all')

# Output from previous execution

<Axes: >

<Axes: >

# Output from previous execution

	Mean	Vol	Sharpe	Min	Max	VaR (0.05)
SMALL LoBM	0.0117	0.2717	0.0431	-0.3477	0.3596	-0.1249
ME1 BM2	0.0884	0.2354	0.3756	-0.3128	0.4309	-0.0949
ME1 BM3	0.0902	0.2008	0.4493	-0.2919	0.1999	-0.0848
ME1 BM4	0.1125	0.1940	0.5800	-0.2896	0.2563	-0.0776
SMALL HiBM	0.1273	0.2084	0.6110	-0.2908	0.4121	-0.0882
ME2 BM1	0.0609	0.2447	0.2490	-0.3308	0.3024	-0.1032
ME2 BM2	0.0984	0.2054	0.4790	-0.3254	0.1892	-0.0834
ME2 BM3	0.1052	0.1864	0.5640	-0.2926	0.1832	-0.0803
ME2 BM4	0.1081	0.1819	0.5942	-0.2526	0.1869	-0.0753
ME2 BM5	0.1132	0.2137	0.5298	-0.3209	0.2596	-0.0933
ME3 BM1	0.0694	0.2237	0.3103	-0.3030	0.2217	-0.0995
ME3 BM2	0.1040	0.1871	0.5555	-0.2908	0.1874	-0.0786
ME3 BM3	0.0910	0.1729	0.5264	-0.2551	0.1669	-0.0732
ME3 BM4	0.1053	0.1797	0.5863	-0.2667	0.1666	-0.0722
ME3 BM5	0.1240	0.2024	0.6125	-0.3131	0.2291	-0.0845
ME4 BM1	0.0919	0.2008	0.4575	-0.2615	0.2538	-0.0835
ME4 BM2	0.0937	0.1761	0.5323	-0.2929	0.1553	-0.0723
ME4 BM3	0.0920	0.1742	0.5282	-0.2514	0.1681	-0.0762
ME4 BM4	0.1059	0.1741	0.6081	-0.3220	0.1627	-0.0688
ME4 BM5	0.1056	0.1990	0.5307	-0.3264	0.2037	-0.0857
BIG LoBM	0.0949	0.1634	0.5807	-0.2225	0.1490	-0.0758
ME5 BM2	0.0857	0.1544	0.5552	-0.2305	0.1607	-0.0641
ME5 BM3	0.0796	0.1529	0.5211	-0.2263	0.1425	-0.0711
ME5 BM4	0.0726	0.1704	0.4258	-0.2759	0.1636	-0.0738
BIG HiBM	0.1035	0.2040	0.5076	-0.2858	0.2199	-0.0890

# Output from previous execution

# Output from previous execution

	alpha	Mkt-RF	r-squared	Treynor Ratio	Info Ratio
SMALL LoBM	-0.1037	1.3585	0.6014	0.0086	-0.6047
ME1 BM2	-0.0106	1.1658	0.5900	0.0759	-0.0705
ME1 BM3	0.0010	1.0495	0.6571	0.0860	0.0088
ME1 BM4	0.0295	0.9773	0.6105	0.1151	0.2435
SMALL HiBM	0.0429	0.9939	0.5476	0.1281	0.3058
ME2 BM1	-0.0524	1.3341	0.7154	0.0457	-0.4018
ME2 BM2	0.0016	1.1390	0.7401	0.0864	0.0151
ME2 BM3	0.0171	1.0357	0.7426	0.1015	0.1812
ME2 BM4	0.0251	0.9765	0.6937	0.1107	0.2493
ME2 BM5	0.0188	1.1108	0.6505	0.1019	0.1488
ME3 BM1	-0.0383	1.2677	0.7725	0.0548	-0.3589
ME3 BM2	0.0112	1.0911	0.8179	0.0953	0.1408
ME3 BM3	0.0069	0.9895	0.7879	0.0920	0.0872
ME3 BM4	0.0211	0.9911	0.7320	0.1063	0.2271
ME3 BM5	0.0344	1.0543	0.6528	0.1176	0.2883
ME4 BM1	-0.0084	1.1800	0.8308	0.0779	-0.1016
ME4 BM2	0.0038	1.0577	0.8685	0.0886	0.0600
ME4 BM3	0.0065	1.0068	0.8036	0.0914	0.0838
ME4 BM4	0.0226	0.9803	0.7630	0.1080	0.2662
ME4 BM5	0.0165	1.0484	0.6679	0.1007	0.1439
BIG LoBM	0.0103	0.9955	0.8935	0.0953	0.1926
ME5 BM2	0.0071	0.9247	0.8631	0.0927	0.1249
ME5 BM3	0.0052	0.8760	0.7904	0.0909	0.0743
ME5 BM4	-0.0048	0.9102	0.6863	0.0797	-0.0501
BIG HiBM	0.0164	1.0260	0.6087	0.1009	0.1282

# Output from previous execution

Time-Series Test Plots

Cross-Sectional Test Plots

ESTIMATES

	premium-TS	premium-CS
Mkt-RF	0.0850	-0.1059
intercept	NaN	0.2058

MODEL FIT

	MAE-TS	MAE-CS	rsquared
error	0.0207	0.0141	0.3132

STATISTICAL SIGNIFICANCE

time-series	priced	premium
p-values
Mkt-RF	0.0003	0.0001
error	0.0000	NaN

"premium" p-value is the usual t-stat on the time-series factor mean.
"priced" p-value of factor is the t-stat of forming the tangency portfolio.
"priced" p-value of "error" is the joint-chi-squared test of the time-series alphas

# Output from previous execution

Time-Series Test Plots

Cross-Sectional Test Plots

ESTIMATES

	premium-TS	premium-CS
HML	0.0310	0.0346
Mkt-RF	0.0850	-0.0937
SMB	0.0033	-0.0025
intercept	NaN	0.1800

MODEL FIT

	MAE-TS	MAE-CS	rsquared
error	0.0141	0.0114	0.4798

STATISTICAL SIGNIFICANCE

time-series	priced	premium
p-values
Mkt-RF	0.0001	0.0001
SMB	0.8189	0.4163
HML	0.0098	0.0282
error	0.0000	NaN

"premium" p-value is the usual t-stat on the time-series factor mean.
"priced" p-value of factor is the t-stat of forming the tangency portfolio.
"priced" p-value of "error" is the joint-chi-squared test of the time-series alphas

# Output from previous execution

Time-Series Test Plots

Cross-Sectional Test Plots

ESTIMATES

	premium-TS	premium-CS
Tangency	0.3584	0.3584
intercept	NaN	0.0000

MODEL FIT

	MAE-TS	MAE-CS	rsquared
error	0.0000	0.0000	1.0000

STATISTICAL SIGNIFICANCE

time-series	priced	premium
p-values
Tangency	0.0000	0.0000
error	1.0000	NaN

"premium" p-value is the usual t-stat on the time-series factor mean.
"priced" p-value of factor is the t-stat of forming the tangency portfolio.
"priced" p-value of "error" is the joint-chi-squared test of the time-series alphas