ALL - 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	1.89%	1.78%	1.65%	2.21%	1.79%	1.95%	203.44	210.83	199.84	214.63
Weekly	3.89%	4.58%	3.86%	5.26%	3.93%	4.28%	199.12	215.40	191.44	224.04
Monthly	7.35%	10.02%	8.13%	11.28%	8.18%	8.92%	190.83	224.76	175.84	243.92
Quarterly	11.23%	15.88%	11.92%	17.70%	14.17%	15.45%	179.74	238.63	155.99	274.96
Annual	—	—	—	—	28.34%	30.90%	155.99	274.96	117.49	365.06
Option Time Horizon	—	—	—	—	10.70%	11.66%	186.09	230.48	167.21	256.51

Calculation Notes: Computed at 2026-03-23T16:34 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $207.10 | Strike (K): $210.00 (first OTM call ≥ spot) | Observed Mid-Price: $7.8000 (Bid $7.1000 / Ask $8.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.95% | Binomial IV (Annual): 28.34% (CRR binomial tree, American, n=20 steps) | BS IV: 28.57% (European Black-Scholes) | Yahoo IV (Annual): 30.90% → 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
2026-03-02	$1.0800
2025-12-01	$1.0000
2025-08-29	$1.0000
2025-06-09	$1.0000
2025-03-10	$1.0000
2024-11-29	$0.9200
2024-08-30	$0.9200
2024-05-31	$0.9200
2024-03-01	$0.9200
2023-11-29	$0.8900
2023-08-30	$0.8900
2023-06-01	$0.8900
2023-02-27	$0.8900
2022-11-29	$0.8500
2022-08-30	$0.8500
2022-06-02	$0.8500
2022-02-25	$0.8500
2021-11-29	$0.8100
2021-08-30	$0.8100
2021-06-03	$0.8100
2021-03-03	$0.8100
2020-11-27	$0.5400
2020-08-27	$0.5400
2020-05-28	$0.5400
2020-02-28	$0.5400
2019-11-27	$0.5000
2019-08-29	$0.5000
2019-05-30	$0.5000
2019-02-27	$0.5000
2018-11-29	$0.4600
2018-08-30	$0.4600
2018-05-30	$0.4600
2018-03-02	$0.4600
2017-11-29	$0.3700
2017-08-29	$0.3700
2017-06-01	$0.3700
2017-02-24	$0.3700
2016-11-28	$0.3300
2016-08-29	$0.3300
2016-06-01	$0.3300
2016-02-25	$0.3300
2015-11-25	$0.3000
2015-08-27	$0.3000
2015-05-27	$0.3000
2015-02-26	$0.3000
2014-11-25	$0.2800
2014-08-27	$0.2800
2014-05-28	$0.2800
2014-02-27	$0.2800
2013-11-26	$0.2500
2013-08-28	$0.2500
2013-05-29	$0.2500
2013-02-26	$0.2500
2012-11-28	$0.2200
2012-08-29	$0.2200
2012-05-30	$0.2200
2012-03-01	$0.2200
2011-11-28	$0.2100
2011-08-29	$0.2100
2011-05-26	$0.2100
2011-03-09	$0.2100
2010-11-26	$0.2000
2010-08-27	$0.2000
2010-05-26	$0.2000
2010-03-10	$0.2000
2009-11-25	$0.2000
2009-08-27	$0.2000
2009-05-27	$0.2000
2009-03-11	$0.2000
2008-11-25	$0.4100
2008-08-27	$0.4100
2008-05-28	$0.4100
2008-03-12	$0.4100
2007-11-28	$0.3800
2007-08-29	$0.3800
2007-05-30	$0.3800
2007-03-07	$0.3800
2006-11-28	$0.3500
2006-08-29	$0.3500
2006-05-26	$0.3500
2006-03-08	$0.3500
2005-11-28	$0.3200
2005-08-29	$0.3200
2005-05-26	$0.3200
2005-03-09	$0.3200
2004-11-26	$0.2800
2004-08-27	$0.2800
2004-05-26	$0.2800
2004-02-25	$0.2800
2003-11-25	$0.2400
2003-08-27	$0.2300
2003-05-28	$0.2300
2003-02-26	$0.2300
2002-11-26	$0.2100
2002-08-28	$0.2100
2002-05-29	$0.2100
2002-02-26	$0.2100
2001-11-28	$0.1900
2001-08-29	$0.1900
2001-05-29	$0.1900
2001-02-26	$0.1900
2000-11-28	$0.1700
2000-08-29	$0.1700
2000-05-26	$0.1700
2000-02-25	$0.1700
1999-11-26	$0.1500
1999-08-27	$0.1500
1999-05-26	$0.1500
1999-02-24	$0.1500
1998-11-25	$0.1350
1998-08-27	$0.1350
1998-05-27	$0.1350
1998-02-25	$0.1350
1997-11-24	$0.1200
1997-08-27	$0.1200
1997-05-28	$0.1200
1997-02-26	$0.1200
1996-11-25	$0.1060
1996-08-28	$0.1060
1996-05-29	$0.1060
1996-02-27	$0.1060
1995-11-28	$0.0975
1995-08-17	$0.0975
1995-06-02	$0.0975
1995-03-03	$0.0975
1994-12-02	$0.0900
1994-09-01	$0.0900
1994-06-02	$0.0900
1994-03-14	$0.0900
1993-12-02	$0.0900
1993-09-09	$0.0900

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.16. Further, an Excess Kurtosis of 16.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.61%	73	0.88%	0.88%
-5.61% to -4.19%	60	0.73%	1.61%
-4.19% to -2.77%	199	2.41%	4.02%
-2.77% to -1.36%	859	10.40%	14.43%
-1.36% to 0.06%	2992	36.24%	50.67%
0.06% to 1.48%	2914	35.30%	85.96%
1.48% to 2.89%	781	9.46%	95.42%
2.89% to 4.31%	233	2.82%	98.24%
4.31% to 5.73%	78	0.94%	99.19%
Greater than 5.73%	67	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.83%	1.95%	81.54%	68.27%
±2σ	-3.72%	3.84%	95.49%	95.45%
±3σ	-5.61%	5.73%	98.30%	99.73%

Descriptive Statistics

Mean	0.059%
Standard Error	0.021%
Median	0.038%
Mode	0.000%
Standard Deviation	1.889%
Sample Variance	3.570%
Kurtosis	16.85
Skewness	-0.16
Range	42.866%
Minimum	-21.179%
Maximum	21.687%
Count	8256

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.254%	4195	50.81%	0.637%
Negative	-1.233%	3872	46.90%	-0.578%
Zero	0.000%	189	2.29%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.96%
20	1 Month	2.13%
60	1 Quarter	2.34%
250	1 Year	2.14%
750	3 Years	2.13%
1,250	5 Years	2.21%
2,500	10 Years	2.02%
5,000	20 Years	2.18%
12,500	50 Years	2.30%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.72. Further, an Excess Kurtosis of 43.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.14%	0	0.00%	0.00%
-3.14% to -1.81%	0	0.00%	0.00%
-1.81% to -0.47%	0	0.00%	0.00%
-0.47% to 0.86%	692	8.38%	8.38%
0.86% to 2.20%	4791	58.02%	66.40%
2.20% to 3.53%	1758	21.29%	87.70%
3.53% to 4.87%	569	6.89%	94.59%
4.87% to 6.20%	208	2.52%	97.11%
6.20% to 7.54%	81	0.98%	98.09%
Greater than 7.54%	158	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.42%	3.98%	90.67%	68.27%
±2σ	-1.36%	5.76%	96.39%	95.45%
±3σ	-3.14%	7.54%	98.09%	99.73%

Descriptive Statistics

Mean	2.196%
Standard Error	0.020%
Median	1.715%
Mode	1.575%
Standard Deviation	1.780%
Sample Variance	3.169%
Kurtosis	43.97
Skewness	4.72
Range	34.469%
Minimum	0.327%
Maximum	34.796%
Count	8257

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.196%	8257	100.00%	2.196%
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 0.70. Further, an Excess Kurtosis of 22.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.98%	65	0.79%	0.79%
-4.98% to -3.74%	68	0.82%	1.61%
-3.74% to -2.50%	227	2.75%	4.36%
-2.50% to -1.26%	841	10.19%	14.55%
-1.26% to -0.02%	2868	34.73%	49.28%
-0.02% to 1.22%	2988	36.19%	85.47%
1.22% to 2.46%	838	10.15%	95.62%
2.46% to 3.69%	242	2.93%	98.55%
3.69% to 4.93%	59	0.71%	99.26%
Greater than 4.93%	61	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.67%	1.63%	80.78%	68.27%
±2σ	-3.33%	3.28%	95.82%	95.45%
±3σ	-4.98%	4.93%	98.47%	99.73%

Descriptive Statistics

Mean	-0.022%
Standard Error	0.018%
Median	0.000%
Mode	0.000%
Standard Deviation	1.652%
Sample Variance	2.731%
Kurtosis	22.35
Skewness	0.70
Range	42.606%
Minimum	-17.105%
Maximum	25.501%
Count	8257

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.101%	3936	47.67%	0.525%
Negative	-1.101%	4103	49.69%	-0.547%
Zero	0.000%	218	2.64%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.07. Further, an Excess Kurtosis of 8.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.39%	17	0.99%	0.99%
-11.39% to -8.47%	19	1.11%	2.10%
-8.47% to -5.55%	41	2.40%	4.50%
-5.55% to -2.64%	180	10.52%	15.02%
-2.64% to 0.28%	578	33.78%	48.80%
0.28% to 3.19%	615	35.94%	84.75%
3.19% to 6.11%	186	10.87%	95.62%
6.11% to 9.03%	50	2.92%	98.54%
9.03% to 11.94%	11	0.64%	99.18%
Greater than 11.94%	14	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.61%	4.17%	79.84%	68.27%
±2σ	-7.50%	8.05%	95.68%	95.45%
±3σ	-11.39%	11.94%	98.19%	99.73%

Descriptive Statistics

Mean	0.277%
Standard Error	0.094%
Median	0.345%
Mode	0.000%
Standard Deviation	3.888%
Sample Variance	15.119%
Kurtosis	8.99
Skewness	0.07
Range	52.681%
Minimum	-23.444%
Maximum	29.237%
Count	1711

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.643%	935	54.65%	1.444%
Negative	-2.617%	763	44.59%	-1.167%
Zero	0.000%	13	0.76%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	4.33%
12	1 Quarter	5.25%
52	1 Year	5.05%
156	3 Years	5.07%
260	5 Years	5.26%
520	10 Years	4.68%
1,040	20 Years	4.95%
2,600	50 Years	5.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.59. Further, an Excess Kurtosis of 60.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.29%	0	0.00%	0.00%
-8.29% to -4.85%	0	0.00%	0.00%
-4.85% to -1.42%	0	0.00%	0.00%
-1.42% to 2.02%	117	6.83%	6.83%
2.02% to 5.45%	1020	59.58%	66.41%
5.45% to 8.89%	372	21.73%	88.14%
8.89% to 12.32%	125	7.30%	95.44%
12.32% to 15.76%	30	1.75%	97.20%
15.76% to 19.19%	18	1.05%	98.25%
Greater than 19.19%	30	1.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.87%	10.03%	91.82%	68.27%
±2σ	-3.71%	14.61%	96.73%	95.45%
±3σ	-8.29%	19.19%	98.25%	99.73%

Descriptive Statistics

Mean	5.453%
Standard Error	0.111%
Median	4.327%
Mode	2.139%
Standard Deviation	4.580%
Sample Variance	20.980%
Kurtosis	60.10
Skewness	5.59
Range	80.961%
Minimum	0.741%
Maximum	81.702%
Count	1712

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.453%	1712	100.00%	5.453%
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 1.17. Further, an Excess Kurtosis of 10.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.64%	11	0.64%	0.64%
-11.64% to -8.75%	13	0.76%	1.40%
-8.75% to -5.86%	48	2.80%	4.21%
-5.86% to -2.96%	195	11.39%	15.60%
-2.96% to -0.07%	636	37.15%	52.75%
-0.07% to 2.82%	561	32.77%	85.51%
2.82% to 5.72%	170	9.93%	95.44%
5.72% to 8.61%	46	2.69%	98.13%
8.61% to 11.51%	11	0.64%	98.77%
Greater than 11.51%	21	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.93%	3.79%	81.13%	68.27%
±2σ	-7.79%	7.65%	95.62%	95.45%
±3σ	-11.64%	11.50%	98.13%	99.73%

Descriptive Statistics

Mean	-0.069%
Standard Error	0.093%
Median	-0.267%
Mode	0.000%
Standard Deviation	3.858%
Sample Variance	14.884%
Kurtosis	10.23
Skewness	1.17
Range	52.181%
Minimum	-21.557%
Maximum	30.624%
Count	1712

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.732%	782	45.68%	1.248%
Negative	-2.456%	918	53.62%	-1.317%
Zero	0.000%	12	0.70%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.73. Further, an Excess Kurtosis of 4.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.89%	4	1.02%	1.02%
-20.89% to -15.38%	3	0.76%	1.78%
-15.38% to -9.87%	11	2.80%	4.58%
-9.87% to -4.36%	48	12.21%	16.79%
-4.36% to 1.15%	132	33.59%	50.38%
1.15% to 6.66%	126	32.06%	82.44%
6.66% to 12.17%	50	12.72%	95.17%
12.17% to 17.68%	14	3.56%	98.73%
17.68% to 23.20%	3	0.76%	99.49%
Greater than 23.20%	2	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.19%	8.50%	76.08%	68.27%
±2σ	-13.54%	15.85%	95.42%	95.45%
±3σ	-20.89%	23.20%	98.47%	99.73%

Descriptive Statistics

Mean	1.154%
Standard Error	0.371%
Median	1.114%
Mode	5.263%
Standard Deviation	7.347%
Sample Variance	53.986%
Kurtosis	4.94
Skewness	-0.73
Range	71.554%
Minimum	-42.780%
Maximum	28.774%
Count	393

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.818%	222	56.49%	3.287%
Negative	-4.900%	171	43.51%	-2.132%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	8.83%
12	1 Year	10.35%
36	3 Years	10.38%
60	5 Years	11.28%
120	10 Years	10.01%
240	20 Years	10.46%
600	50 Years	11.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.82. Further, an Excess Kurtosis of 34.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.97%	0	0.00%	0.00%
-17.97% to -10.45%	0	0.00%	0.00%
-10.45% to -2.94%	0	0.00%	0.00%
-2.94% to 4.58%	21	5.33%	5.33%
4.58% to 12.10%	243	61.68%	67.01%
12.10% to 19.61%	94	23.86%	90.86%
19.61% to 27.13%	15	3.81%	94.67%
27.13% to 34.65%	11	2.79%	97.46%
34.65% to 42.16%	4	1.02%	98.48%
Greater than 42.16%	6	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.08%	22.12%	91.62%	68.27%
±2σ	-7.95%	32.14%	96.95%	95.45%
±3σ	-17.97%	42.16%	98.48%	99.73%

Descriptive Statistics

Mean	12.098%
Standard Error	0.505%
Median	9.711%
Mode	7.182%
Standard Deviation	10.022%
Sample Variance	100.448%
Kurtosis	34.09
Skewness	4.82
Range	108.468%
Minimum	2.294%
Maximum	110.762%
Count	394

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.098%	394	100.00%	12.098%
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 2.76. Further, an Excess Kurtosis of 20.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.69%	1	0.25%	0.25%
-24.69% to -18.59%	1	0.25%	0.51%
-18.59% to -12.49%	10	2.54%	3.05%
-12.49% to -6.39%	52	13.20%	16.24%
-6.39% to -0.28%	148	37.56%	53.81%
-0.28% to 5.82%	128	32.49%	86.29%
5.82% to 11.92%	39	9.90%	96.19%
11.92% to 18.02%	8	2.03%	98.22%
18.02% to 24.12%	2	0.51%	98.73%
Greater than 24.12%	5	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.42%	7.85%	80.46%	68.27%
±2σ	-16.55%	15.98%	96.45%	95.45%
±3σ	-24.69%	24.12%	98.48%	99.73%

Descriptive Statistics

Mean	-0.285%
Standard Error	0.410%
Median	-0.792%
Mode	-7.417%
Standard Deviation	8.135%
Sample Variance	66.180%
Kurtosis	20.76
Skewness	2.76
Range	97.821%
Minimum	-24.725%
Maximum	73.096%
Count	394

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.653%	178	45.18%	2.554%
Negative	-5.202%	215	54.57%	-2.839%
Zero	0.000%	1	0.25%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.12. Further, an Excess Kurtosis of 2.66 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.48%	1	0.76%	0.76%
-30.48% to -22.05%	0	0.00%	0.76%
-22.05% to -13.63%	8	6.11%	6.87%
-13.63% to -5.21%	17	12.98%	19.85%
-5.21% to 3.22%	37	28.24%	48.09%
3.22% to 11.64%	44	33.59%	81.68%
11.64% to 20.06%	17	12.98%	94.66%
20.06% to 28.49%	6	4.58%	99.24%
28.49% to 36.91%	0	0.00%	99.24%
Greater than 36.91%	1	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.02%	14.45%	71.76%	68.27%
±2σ	-19.25%	25.68%	96.18%	95.45%
±3σ	-30.48%	36.91%	98.47%	99.73%

Descriptive Statistics

Mean	3.216%
Standard Error	0.981%
Median	3.387%
Mode	-42.379%
Standard Deviation	11.231%
Sample Variance	126.134%
Kurtosis	2.66
Skewness	-0.12
Range	89.274%
Minimum	-42.379%
Maximum	46.895%
Count	131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.255%	85	64.89%	6.005%
Negative	-7.945%	46	35.12%	-2.790%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	12.45%
12	3 Years	16.44%
20	5 Years	17.70%
40	10 Years	16.74%
80	20 Years	17.68%
200	50 Years	18.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.49. Further, an Excess Kurtosis of 15.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.98%	0	0.00%	0.00%
-25.98% to -14.07%	0	0.00%	0.00%
-14.07% to -2.17%	0	0.00%	0.00%
-2.17% to 9.74%	13	9.85%	9.85%
9.74% to 21.65%	72	54.55%	64.39%
21.65% to 33.56%	34	25.76%	90.15%
33.56% to 45.47%	6	4.55%	94.70%
45.47% to 57.37%	2	1.52%	96.21%
57.37% to 69.28%	1	0.76%	96.97%
Greater than 69.28%	4	3.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.77%	37.53%	93.18%	68.27%
±2σ	-10.10%	53.41%	96.21%	95.45%
±3σ	-25.98%	69.28%	96.97%	99.73%

Descriptive Statistics

Mean	21.651%
Standard Error	1.382%
Median	17.296%
Mode	24.955%
Standard Deviation	15.877%
Sample Variance	252.073%
Kurtosis	15.07
Skewness	3.49
Range	110.983%
Minimum	4.264%
Maximum	115.247%
Count	132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.651%	132	100.00%	21.651%
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 2.16. Further, an Excess Kurtosis of 11.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.06%	0	0.00%	0.00%
-37.06% to -28.12%	1	0.76%	0.76%
-28.12% to -19.18%	2	1.52%	2.27%
-19.18% to -10.23%	17	12.88%	15.15%
-10.23% to -1.29%	56	42.42%	57.58%
-1.29% to 7.65%	34	25.76%	83.33%
7.65% to 16.59%	12	9.09%	92.42%
16.59% to 25.54%	9	6.82%	99.24%
25.54% to 34.48%	0	0.00%	99.24%
Greater than 34.48%	1	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.21%	10.63%	77.27%	68.27%
±2σ	-25.14%	22.55%	96.97%	95.45%
±3σ	-37.06%	34.48%	99.24%	99.73%

Descriptive Statistics

Mean	-1.292%
Standard Error	1.038%
Median	-2.774%
Mode	-2.682%
Standard Deviation	11.923%
Sample Variance	142.155%
Kurtosis	11.77
Skewness	2.16
Range	106.015%
Minimum	-31.366%
Maximum	74.649%
Count	132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.974%	47	35.61%	3.551%
Negative	-7.522%	85	64.39%	-4.844%
Zero	0.000%	0	0.00%	0.000%

ALL Deep Analytical Report