XLI

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.06 -0.05 -0.03 -0.02 -0.01 0.00 0.01 0.03 0.05 0.05 1.48

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.06	-0.05	-0.03	-0.02	-0.01	0.00	0.01	0.03	0.05	0.05	1.48

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace 0.001 0.198

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	0.001	0.198

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.840 0.058 -14.472 0.0000

|log-return| -71.757 3.072 -23.358 0.0000

I(right-tail) 0.177 0.079 2.228 0.0261

|log-return|*I(right-tail) -10.662 4.494 -2.372 0.0178

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.840	0.058	-14.472	0.0000
\|log-return\|	-71.757	3.072	-23.358	0.0000
I(right-tail)	0.177	0.079	2.228	0.0261
\|log-return\|*I(right-tail)	-10.662	4.494	-2.372	0.0178

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.537 0.345 0.561 0.773

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.537	0.345	0.561	0.773

XLF

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.11 -0.10 -0.04 -0.03 -0.01 0.00 0.01 0.04 0.10 0.14 1.18

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.11	-0.10	-0.04	-0.03	-0.01	0.00	0.01	0.04	0.10	0.14	1.18

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace 0.158 0.164

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	0.158	0.164

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.958 0.053 -18.231 0.0000

|log-return| -40.634 1.729 -23.507 0.0000

I(right-tail) 0.027 0.073 0.365 0.7154

|log-return|*I(right-tail) -1.309 2.467 -0.530 0.5959

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.958	0.053	-18.231	0.0000
\|log-return\|	-40.634	1.729	-23.507	0.0000
I(right-tail)	0.027	0.073	0.365	0.7154
\|log-return\|*I(right-tail)	-1.309	2.467	-0.530	0.5959

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.439 0.358 0.734 0.745

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.439	0.358	0.734	0.745

XLY

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.06 -0.05 -0.03 -0.02 -0.01 0.00 0.01 0.03 0.05 0.06 0.44

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.06	-0.05	-0.03	-0.02	-0.01	0.00	0.01	0.03	0.05	0.06	0.44

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace 0.262 0.182

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	0.262	0.182

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.919 0.057 -16.239 0.0000

|log-return| -68.910 2.991 -23.036 0.0000

I(right-tail) 0.255 0.078 3.261 0.0011

|log-return|*I(right-tail) -12.994 4.408 -2.948 0.0033

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.919	0.057	-16.239	0.0000
\|log-return\|	-68.910	2.991	-23.036	0.0000
I(right-tail)	0.255	0.078	3.261	0.0011
\|log-return\|*I(right-tail)	-12.994	4.408	-2.948	0.0033

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.458 0.696 0.803 0.720

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.458	0.696	0.803	0.720

XLP

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.04 -0.03 -0.02 -0.01 0.00 0.00 0.01 0.02 0.02 0.04 0.54

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.04	-0.03	-0.02	-0.01	0.00	0.00	0.01	0.02	0.02	0.04	0.54

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace -0.015 0.189

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	-0.015	0.189

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.924 0.060 -15.334 0.0000

|log-return| -119.454 5.353 -22.313 0.0000

I(right-tail) 0.330 0.081 4.069 0.0001

|log-return|*I(right-tail) -24.925 7.802 -3.195 0.0014

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.924	0.060	-15.334	0.0000
\|log-return\|	-119.454	5.353	-22.313	0.0000
I(right-tail)	0.330	0.081	4.069	0.0001
\|log-return\|*I(right-tail)	-24.925	7.802	-3.195	0.0014

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.683 0.946 0.972 0.681

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.683	0.946	0.972	0.681

XLK

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.06 -0.05 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.04 0.05 1.46

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.06	-0.05	-0.03	-0.02	-0.01	0.00	0.01	0.02	0.04	0.05	1.46

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace -0.284 0.155

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	-0.284	0.155

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.895 0.058 -15.552 0.0000

|log-return| -77.163 3.344 -23.078 0.0000

I(right-tail) 0.131 0.078 1.690 0.0912

|log-return|*I(right-tail) -5.568 4.756 -1.171 0.2419

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.895	0.058	-15.552	0.0000
\|log-return\|	-77.163	3.344	-23.078	0.0000
I(right-tail)	0.131	0.078	1.690	0.0912
\|log-return\|*I(right-tail)	-5.568	4.756	-1.171	0.2419

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.523 0.474 0.522 0.667

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.523	0.474	0.522	0.667

XLV

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.04 -0.04 -0.02 -0.01 0.00 0.00 0.01 0.02 0.03 0.04 0.21

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.04	-0.04	-0.02	-0.01	0.00	0.00	0.01	0.02	0.03	0.04	0.21

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Logistic -0.068 0.083

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Logistic	-0.068	0.083

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.977 0.057 -17.174 0.0000

|log-return| -93.834 4.201 -22.335 0.0000

I(right-tail) 0.250 0.078 3.223 0.0013

|log-return|*I(right-tail) -14.737 6.130 -2.404 0.0164

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.977	0.057	-17.174	0.0000
\|log-return\|	-93.834	4.201	-22.335	0.0000
I(right-tail)	0.250	0.078	3.223	0.0013
\|log-return\|*I(right-tail)	-14.737	6.130	-2.404	0.0164

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.441 0.855 0.943 0.647

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.441	0.855	0.943	0.647

XLU

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.05 -0.04 -0.02 -0.01 -0.01 0.00 0.01 0.02 0.03 0.04 1.37

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.05	-0.04	-0.02	-0.01	-0.01	0.00	0.01	0.02	0.03	0.04	1.37

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Logistic -0.321 0.097

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Logistic	-0.321	0.097

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.899 0.056 -16.004 0.0000

|log-return| -94.911 4.101 -23.145 0.0000

I(right-tail) 0.005 0.076 0.067 0.9462

|log-return|*I(right-tail) 6.995 5.593 1.251 0.2113

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.899	0.056	-16.004	0.0000
\|log-return\|	-94.911	4.101	-23.145	0.0000
I(right-tail)	0.005	0.076	0.067	0.9462
\|log-return\|*I(right-tail)	6.995	5.593	1.251	0.2113

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.748 0.946 0.974 0.593

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.748	0.946	0.974	0.593

XLE

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.10 -0.07 -0.03 -0.02 -0.01 0.00 0.01 0.03 0.06 0.07 1.40

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.10	-0.07	-0.03	-0.02	-0.01	0.00	0.01	0.03	0.06	0.07	1.40

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace 0.025 0.164

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	0.025	0.164

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.954 0.053 -17.859 0.0000

|log-return| -50.293 2.170 -23.176 0.0000

I(right-tail) 0.171 0.075 2.284 0.0225

|log-return|*I(right-tail) -9.644 3.285 -2.936 0.0034

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.954	0.053	-17.859	0.0000
\|log-return\|	-50.293	2.170	-23.176	0.0000
I(right-tail)	0.171	0.075	2.284	0.0225
\|log-return\|*I(right-tail)	-9.644	3.285	-2.936	0.0034

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.573 0.382 0.522 0.550

**Hurst exponent (of daily return price)**
12-day	24-day	48-day	96-day
0.573	0.382	0.522	0.550

XLB

Percentile values of daily loss(gain) in per cent
0.5 1 5 10 25 50 75 90 95 99 99.5

-0.07 -0.06 -0.03 -0.02 -0.01 0.00 0.01 0.03 0.05 0.06 0.00

**Percentile values of daily loss(gain) in per cent**
0.5	1	5	10	25	50	75	90	95	99	99.5
-0.07	-0.06	-0.03	-0.02	-0.01	0.00	0.01	0.03	0.05	0.06	0.00

Daily log-return distribution fitting results
Distribution Location, a Scale, b

Laplace 0.026 0.184

**Daily log-return distribution fitting results**
Distribution	Location, a	Scale, b
Laplace	0.026	0.184

Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable Coef(b) s.e.(b) t-value P-value

Constant -0.838 0.059 -14.245 0.0000

|log-return| -62.572 2.703 -23.145 0.0000

I(right-tail) 0.171 0.080 2.135 0.0330

|log-return|*I(right-tail) -10.417 3.988 -2.612 0.0091

**Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]**
Variable	Coef(b)	s.e.(b)	t-value	P-value
Constant	-0.838	0.059	-14.245	0.0000
\|log-return\|	-62.572	2.703	-23.145	0.0000
I(right-tail)	0.171	0.080	2.135	0.0330
\|log-return\|*I(right-tail)	-10.417	3.988	-2.612	0.0091

Hurst exponent (of daily return price)
12-day 24-day 48-day 96-day

0.513 0.439 0.229 0.499