XLK - Detail Report

Quick Overview

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)	Binomial IV (Period)	Yahoo IV (Period)	1σ Lower (68.27%)	1σ Upper	2σ Lower (95.45%)	2σ Upper
Daily	1.63%	1.37%	1.35%	1.96%	—	2.02%	138.47	143.33	136.10	145.83
Weekly	3.43%	3.43%	3.38%	4.79%	—	4.46%	135.63	146.33	130.57	152.00
Monthly	6.55%	7.19%	6.81%	10.24%	—	9.28%	130.17	152.47	120.27	165.02
Quarterly	9.93%	12.98%	10.44%	17.74%	—	16.06%	122.85	161.56	107.12	185.27
Annual	—	—	—	—	—	32.13%	107.12	185.27	81.46	243.66
Option Time Horizon	—	—	—	—	—	12.36%	126.79	156.53	114.11	173.93

Calculation Notes: Computed at 2026-02-22T14:25 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $140.88 | Strike (K): $141.00 (first OTM call ≥ spot) | Observed Mid-Price: $6.1500 (Bid $5.3500 / Ask $6.9500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.79% | Binomial IV (Annual): 0.00% (CRR binomial tree, American, n=20 steps) | BS IV: 27.39% (European Black-Scholes) | Yahoo IV (Annual): 32.13% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2025-12-22	$0.2190
2025-09-22	$0.1790
2025-06-23	$0.1990
2025-03-24	$0.1875
2024-12-23	$0.1930
2024-09-23	$0.1995
2024-06-24	$0.2000
2024-03-18	$0.1695
2023-12-18	$0.2110
2023-09-18	$0.1800
2023-06-20	$0.1810
2023-03-20	$0.1580
2022-12-19	$0.1825
2022-09-19	$0.1585
2022-06-21	$0.1615
2022-03-21	$0.1430
2021-12-20	$0.1585
2021-09-20	$0.1365
2021-06-21	$0.1300
2021-03-22	$0.1365
2020-12-21	$0.1490
2020-09-21	$0.1235
2020-06-22	$0.1405
2020-03-23	$0.1855
2019-12-20	$0.1475
2019-09-20	$0.1265
2019-06-21	$0.1390
2019-03-15	$0.1165
2018-12-21	$0.1325
2018-09-21	$0.1270
2018-06-15	$0.1275
2018-03-16	$0.1090
2017-12-15	$0.1190
2017-09-15	$0.1045
2017-06-16	$0.1115
2017-03-17	$0.1025
2016-12-16	$0.1080
2016-09-16	$0.0980
2016-06-17	$0.1055
2016-03-18	$0.1100
2015-12-18	$0.1080
2015-09-18	$0.0915
2015-06-19	$0.0965
2015-03-20	$0.0865
2014-12-19	$0.1080
2014-09-19	$0.0870
2014-06-20	$0.0880
2014-03-21	$0.0785
2013-12-20	$0.0855
2013-09-20	$0.0790
2013-06-21	$0.0775
2013-03-15	$0.0620
2012-12-21	$0.0840
2012-09-21	$0.0650
2012-06-15	$0.0545
2012-03-16	$0.0480
2011-12-16	$0.0545
2011-09-16	$0.0470
2011-06-17	$0.0490
2011-03-18	$0.0420
2010-12-17	$0.0450
2010-09-17	$0.0405
2010-06-18	$0.0395
2010-03-19	$0.0365
2009-12-18	$0.0395
2009-09-18	$0.0385
2009-06-19	$0.0405
2009-03-20	$0.0385
2008-12-19	$0.0405
2008-09-19	$0.0355
2008-06-20	$0.0345
2008-03-20	$0.0030
2007-12-21	$0.0615
2007-09-21	$0.0265
2007-06-15	$0.0090
2006-12-15	$0.0675
2006-09-15	$0.0220
2005-12-16	$0.0740
2004-12-17	$0.2090
2003-12-19	$0.0705
2002-12-20	$0.0205
1999-12-17	$0.0005

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.30. Further, an Excess Kurtosis of 7.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.85%	48	0.70%	0.70%
-4.85% to -3.62%	102	1.49%	2.20%
-3.62% to -2.40%	271	3.97%	6.16%
-2.40% to -1.18%	706	10.34%	16.50%
-1.18% to 0.05%	2129	31.17%	47.67%
0.05% to 1.27%	2501	36.61%	84.28%
1.27% to 2.50%	741	10.85%	95.13%
2.50% to 3.72%	207	3.03%	98.16%
3.72% to 4.95%	74	1.08%	99.24%
Greater than 4.95%	52	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.58%	1.68%	78.38%	68.27%
±2σ	-3.22%	3.31%	94.54%	95.45%
±3σ	-4.85%	4.95%	98.54%	99.73%

Descriptive Statistics

Mean	0.049%
Standard Error	0.020%
Median	0.110%
Mode	0.000%
Standard Deviation	1.633%
Sample Variance	2.668%
Kurtosis	7.49
Skewness	0.30
Range	29.916%
Minimum	-13.814%
Maximum	16.102%
Count	6831

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.079%	3685	53.95%	0.582%
Negative	-1.186%	3070	44.94%	-0.533%
Zero	0.000%	76	1.11%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.96%
20	1 Month	2.45%
60	1 Quarter	1.89%
250	1 Year	2.06%
750	3 Years	1.81%
1,250	5 Years	1.96%
2,500	10 Years	1.78%
5,000	20 Years	1.73%
12,500	50 Years	1.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.51. Further, an Excess Kurtosis of 29.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.29%	0	0.00%	0.00%
-2.29% to -1.26%	0	0.00%	0.00%
-1.26% to -0.23%	0	0.00%	0.00%
-0.23% to 0.79%	1078	15.78%	15.78%
0.79% to 1.82%	3312	48.48%	64.26%
1.82% to 2.85%	1388	20.32%	84.57%
2.85% to 3.87%	575	8.42%	92.99%
3.87% to 4.90%	259	3.79%	96.78%
4.90% to 5.92%	107	1.57%	98.35%
Greater than 5.92%	113	1.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.45%	3.19%	86.50%	68.27%
±2σ	-0.92%	4.55%	95.76%	95.45%
±3σ	-2.29%	5.92%	98.35%	99.73%

Descriptive Statistics

Mean	1.819%
Standard Error	0.017%
Median	1.441%
Mode	0.952%
Standard Deviation	1.368%
Sample Variance	1.872%
Kurtosis	29.82
Skewness	3.51
Range	26.220%
Minimum	0.249%
Maximum	26.469%
Count	6832

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.819%	6832	100.00%	1.819%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.05. Further, an Excess Kurtosis of 6.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.02%	52	0.76%	0.76%
-4.02% to -3.01%	62	0.91%	1.67%
-3.01% to -2.00%	187	2.74%	4.41%
-2.00% to -0.99%	771	11.29%	15.69%
-0.99% to 0.03%	2570	37.62%	53.31%
0.03% to 1.04%	2030	29.71%	83.02%
1.04% to 2.05%	736	10.77%	93.79%
2.05% to 3.06%	255	3.73%	97.53%
3.06% to 4.08%	110	1.61%	99.14%
Greater than 4.08%	59	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.32%	1.38%	77.62%	68.27%
±2σ	-2.67%	2.73%	94.54%	95.45%
±3σ	-4.02%	4.08%	98.38%	99.73%

Descriptive Statistics

Mean	0.027%
Standard Error	0.016%
Median	-0.045%
Mode	0.000%
Standard Deviation	1.350%
Sample Variance	1.822%
Kurtosis	6.22
Skewness	-0.05
Range	21.770%
Minimum	-13.686%
Maximum	8.084%
Count	6832

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.018%	3218	47.10%	0.479%
Negative	-0.878%	3520	51.52%	-0.452%
Zero	0.000%	94	1.38%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.09. Further, an Excess Kurtosis of 2.20 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.06%	14	0.99%	0.99%
-10.06% to -7.49%	20	1.41%	2.40%
-7.49% to -4.92%	56	3.95%	6.35%
-4.92% to -2.34%	168	11.86%	18.21%
-2.34% to 0.23%	411	29.00%	47.21%
0.23% to 2.81%	507	35.78%	82.99%
2.81% to 5.38%	166	11.71%	94.71%
5.38% to 7.95%	43	3.03%	97.74%
7.95% to 10.53%	21	1.48%	99.22%
Greater than 10.53%	11	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.20%	3.66%	75.58%	68.27%
±2σ	-6.63%	7.10%	93.65%	95.45%
±3σ	-10.06%	10.53%	98.24%	99.73%

Descriptive Statistics

Mean	0.232%
Standard Error	0.091%
Median	0.403%
Mode	0.000%
Standard Deviation	3.432%
Sample Variance	11.777%
Kurtosis	2.20
Skewness	-0.09
Range	30.579%
Minimum	-14.244%
Maximum	16.335%
Count	1417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.392%	806	56.88%	1.361%
Negative	-2.640%	606	42.77%	-1.129%
Zero	0.000%	5	0.35%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	5.14%
12	1 Quarter	3.91%
52	1 Year	4.95%
156	3 Years	4.45%
260	5 Years	4.79%
520	10 Years	4.28%
1,040	20 Years	4.10%
2,600	50 Years	4.71%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.44. Further, an Excess Kurtosis of 9.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.48%	0	0.00%	0.00%
-5.48% to -2.91%	0	0.00%	0.00%
-2.91% to -0.34%	0	0.00%	0.00%
-0.34% to 2.23%	257	18.12%	18.12%
2.23% to 4.81%	657	46.33%	64.46%
4.81% to 7.38%	266	18.76%	83.22%
7.38% to 9.95%	137	9.66%	92.88%
9.95% to 12.52%	47	3.31%	96.19%
12.52% to 15.09%	24	1.69%	97.88%
Greater than 15.09%	30	2.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.38%	8.23%	84.41%	68.27%
±2σ	-2.05%	11.66%	95.20%	95.45%
±3σ	-5.48%	15.09%	97.88%	99.73%

Descriptive Statistics

Mean	4.806%
Standard Error	0.091%
Median	3.862%
Mode	1.654%
Standard Deviation	3.429%
Sample Variance	11.759%
Kurtosis	9.93
Skewness	2.44
Range	35.295%
Minimum	0.784%
Maximum	36.079%
Count	1418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.806%	1418	100.00%	4.806%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 2.51 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.11%	5	0.35%	0.35%
-10.11% to -7.58%	19	1.34%	1.69%
-7.58% to -5.05%	44	3.10%	4.80%
-5.05% to -2.52%	179	12.62%	17.42%
-2.52% to 0.01%	530	37.38%	54.80%
0.01% to 2.54%	386	27.22%	82.02%
2.54% to 5.07%	156	11.00%	93.02%
5.07% to 7.61%	58	4.09%	97.11%
7.61% to 10.14%	23	1.62%	98.73%
Greater than 10.14%	18	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.36%	3.39%	76.09%	68.27%
±2σ	-6.74%	6.76%	93.79%	95.45%
±3σ	-10.11%	10.14%	98.38%	99.73%

Descriptive Statistics

Mean	0.011%
Standard Error	0.090%
Median	-0.241%
Mode	0.000%
Standard Deviation	3.375%
Sample Variance	11.390%
Kurtosis	2.51
Skewness	0.67
Range	28.748%
Minimum	-10.666%
Maximum	18.082%
Count	1418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.686%	641	45.20%	1.214%
Negative	-2.218%	769	54.23%	-1.203%
Zero	0.000%	8	0.56%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.35. Further, an Excess Kurtosis of 1.34 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.69%	2	0.61%	0.61%
-18.69% to -13.78%	4	1.23%	1.84%
-13.78% to -8.86%	17	5.21%	7.06%
-8.86% to -3.94%	40	12.27%	19.33%
-3.94% to 0.97%	91	27.91%	47.24%
0.97% to 5.89%	107	32.82%	80.06%
5.89% to 10.80%	49	15.03%	95.09%
10.80% to 15.72%	11	3.37%	98.47%
15.72% to 20.63%	4	1.23%	99.69%
Greater than 20.63%	1	0.31%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.58%	7.53%	73.31%	68.27%
±2σ	-12.14%	14.08%	94.17%	95.45%
±3σ	-18.69%	20.63%	99.08%	99.73%

Descriptive Statistics

Mean	0.972%
Standard Error	0.363%
Median	1.582%
Mode	-0.838%
Standard Deviation	6.554%
Sample Variance	42.949%
Kurtosis	1.34
Skewness	-0.35
Range	49.674%
Minimum	-24.906%
Maximum	24.768%
Count	326

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.059%	194	59.51%	3.011%
Negative	-5.037%	132	40.49%	-2.040%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	6.80%
12	1 Year	9.88%
36	3 Years	9.58%
60	5 Years	10.24%
120	10 Years	9.39%
240	20 Years	8.81%
600	50 Years	10.06%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.94. Further, an Excess Kurtosis of 4.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.75%	0	0.00%	0.00%
-10.75% to -5.36%	0	0.00%	0.00%
-5.36% to 0.03%	0	0.00%	0.00%
0.03% to 5.42%	57	17.43%	17.43%
5.42% to 10.81%	157	48.01%	65.44%
10.81% to 16.21%	59	18.04%	83.49%
16.21% to 21.60%	28	8.56%	92.05%
21.60% to 26.99%	12	3.67%	95.72%
26.99% to 32.38%	4	1.22%	96.94%
Greater than 32.38%	10	3.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.63%	18.00%	84.40%	68.27%
±2σ	-3.56%	25.19%	94.80%	95.45%
±3σ	-10.75%	32.38%	96.94%	99.73%

Descriptive Statistics

Mean	10.815%
Standard Error	0.398%
Median	8.481%
Mode	5.440%
Standard Deviation	7.189%
Sample Variance	51.677%
Kurtosis	4.45
Skewness	1.94
Range	43.949%
Minimum	2.504%
Maximum	46.453%
Count	327

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.815%	327	100.00%	10.815%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.95. Further, an Excess Kurtosis of 2.49 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.68%	0	0.00%	0.00%
-20.68% to -15.58%	2	0.61%	0.61%
-15.58% to -10.47%	10	3.06%	3.67%
-10.47% to -5.36%	48	14.68%	18.35%
-5.36% to -0.25%	126	38.53%	56.88%
-0.25% to 4.86%	82	25.08%	81.96%
4.86% to 9.96%	32	9.79%	91.74%
9.96% to 15.07%	17	5.20%	96.94%
15.07% to 20.18%	7	2.14%	99.08%
Greater than 20.18%	3	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.06%	6.56%	73.70%	68.27%
±2σ	-13.87%	13.37%	94.80%	95.45%
±3σ	-20.68%	20.18%	99.08%	99.73%

Descriptive Statistics

Mean	-0.252%
Standard Error	0.377%
Median	-1.149%
Mode	-1.902%
Standard Deviation	6.811%
Sample Variance	46.395%
Kurtosis	2.49
Skewness	0.95
Range	52.701%
Minimum	-19.106%
Maximum	33.595%
Count	327

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.859%	133	40.67%	2.383%
Negative	-4.465%	193	59.02%	-2.635%
Zero	0.000%	1	0.31%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.56. Further, an Excess Kurtosis of 0.56 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.16%	0	0.00%	0.00%
-27.16% to -19.71%	4	3.67%	3.67%
-19.71% to -12.26%	5	4.59%	8.26%
-12.26% to -4.81%	12	11.01%	19.27%
-4.81% to 2.64%	27	24.77%	44.04%
2.64% to 10.09%	37	33.94%	77.98%
10.09% to 17.53%	17	15.60%	93.58%
17.53% to 24.98%	6	5.50%	99.08%
24.98% to 32.43%	1	0.92%	100.00%
Greater than 32.43%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.30%	12.57%	73.39%	68.27%
±2σ	-17.23%	22.50%	93.58%	95.45%
±3σ	-27.16%	32.43%	100.00%	99.73%

Descriptive Statistics

Mean	2.636%
Standard Error	0.951%
Median	3.233%
Mode	2.675%
Standard Deviation	9.932%
Sample Variance	98.638%
Kurtosis	0.56
Skewness	-0.56
Range	50.588%
Minimum	-25.248%
Maximum	25.340%
Count	109

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.943%	74	67.89%	5.393%
Negative	-8.585%	35	32.11%	-2.757%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	16.55%
12	3 Years	18.25%
20	5 Years	17.74%
40	10 Years	16.61%
80	20 Years	15.63%
200	50 Years	17.19%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.90. Further, an Excess Kurtosis of 3.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.16%	0	0.00%	0.00%
-19.16% to -9.42%	0	0.00%	0.00%
-9.42% to 0.31%	0	0.00%	0.00%
0.31% to 10.05%	17	15.45%	15.45%
10.05% to 19.78%	58	52.73%	68.18%
19.78% to 29.52%	19	17.27%	85.45%
29.52% to 39.25%	6	5.45%	90.91%
39.25% to 48.99%	4	3.64%	94.55%
48.99% to 58.72%	4	3.64%	98.18%
Greater than 58.72%	2	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.80%	32.76%	84.55%	68.27%
±2σ	-6.18%	45.74%	94.55%	95.45%
±3σ	-19.16%	58.72%	98.18%	99.73%

Descriptive Statistics

Mean	19.783%
Standard Error	1.238%
Median	16.906%
Mode	4.797%
Standard Deviation	12.980%
Sample Variance	168.493%
Kurtosis	3.84
Skewness	1.90
Range	67.514%
Minimum	4.797%
Maximum	72.311%
Count	110

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.783%	110	100.00%	19.783%
Negative	0.000%	0	0.00%	0.000%
Zero	0.000%	0	0.00%	0.000%

Open-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.21. Further, an Excess Kurtosis of 1.99 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.56%	0	0.00%	0.00%
-32.56% to -24.73%	0	0.00%	0.00%
-24.73% to -16.90%	2	1.82%	1.82%
-16.90% to -9.07%	20	18.18%	20.00%
-9.07% to -1.24%	46	41.82%	61.82%
-1.24% to 6.59%	23	20.91%	82.73%
6.59% to 14.42%	10	9.09%	91.82%
14.42% to 22.25%	3	2.73%	94.55%
22.25% to 30.08%	4	3.64%	98.18%
Greater than 30.08%	2	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.68%	9.20%	75.45%	68.27%
±2σ	-22.12%	19.64%	94.55%	95.45%
±3σ	-32.56%	30.08%	98.18%	99.73%

Descriptive Statistics

Mean	-1.240%
Standard Error	0.995%
Median	-3.066%
Mode	-19.044%
Standard Deviation	10.440%
Sample Variance	109.001%
Kurtosis	1.99
Skewness	1.21
Range	54.059%
Minimum	-19.044%
Maximum	35.015%
Count	110

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.270%	40	36.36%	3.371%
Negative	-7.245%	70	63.64%	-4.610%
Zero	0.000%	0	0.00%	0.000%

XLK Deep Analytical Report