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%	1.42%	1.58%	203.47	209.31	200.61	212.30
Weekly	3.89%	4.58%	3.86%	5.28%	3.12%	3.48%	200.04	212.90	193.90	219.65
Monthly	7.35%	10.03%	8.14%	11.36%	6.49%	7.24%	193.40	220.21	181.25	234.97
Quarterly	11.23%	15.88%	11.92%	17.70%	11.24%	12.54%	184.43	230.92	164.82	258.39
Annual	—	—	—	—	22.48%	25.09%	164.82	258.39	131.64	323.52
Option Time Horizon	—	—	—	—	8.65%	9.65%	189.28	225.01	173.60	245.33

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $206.37 | Strike (K): $210.00 (first OTM call ≥ spot) | Observed Mid-Price: $5.8000 (Bid $5.2000 / Ask $6.4000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.97% | Binomial IV (Annual): 22.48% (CRR binomial tree, American, n=20 steps) | BS IV: 22.75% (European Black-Scholes) | Yahoo IV (Annual): 25.09% → 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
2025-12-01	$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 16.82 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	0.89%	0.89%
-5.61% to -4.20%	60	0.73%	1.62%
-4.20% to -2.78%	198	2.40%	4.02%
-2.78% to -1.36%	857	10.41%	14.43%
-1.36% to 0.06%	2984	36.24%	50.66%
0.06% to 1.48%	2907	35.30%	85.96%
1.48% to 2.90%	778	9.45%	95.41%
2.90% to 4.31%	233	2.83%	98.24%
4.31% to 5.73%	78	0.95%	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%	81.58%	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	1.891%
Sample Variance	3.577%
Kurtosis	16.82
Skewness	-0.16
Range	42.866%
Minimum	-21.179%
Maximum	21.687%
Count	8235

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.255%	4185	50.82%	0.638%
Negative	-1.234%	3861	46.88%	-0.579%
Zero	0.000%	189	2.29%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.85%
20	1 Month	2.75%
60	1 Quarter	2.20%
250	1 Year	2.18%
750	3 Years	2.16%
1,250	5 Years	2.21%
2,500	10 Years	2.01%
5,000	20 Years	2.18%
12,500	50 Years	2.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.71. Further, an Excess Kurtosis of 43.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.15%	0	0.00%	0.00%
-3.15% to -1.81%	0	0.00%	0.00%
-1.81% to -0.48%	0	0.00%	0.00%
-0.48% to 0.86%	689	8.37%	8.37%
0.86% to 2.20%	4781	58.05%	66.42%
2.20% to 3.53%	1751	21.26%	87.68%
3.53% to 4.87%	568	6.90%	94.57%
4.87% to 6.21%	209	2.54%	97.11%
6.21% to 7.54%	80	0.97%	98.08%
Greater than 7.54%	158	1.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.41%	3.98%	90.65%	68.27%
±2σ	-1.37%	5.76%	96.38%	95.45%
±3σ	-3.15%	7.54%	98.08%	99.73%

Descriptive Statistics

Mean	2.196%
Standard Error	0.020%
Median	1.713%
Mode	1.575%
Standard Deviation	1.782%
Sample Variance	3.176%
Kurtosis	43.87
Skewness	4.71
Range	34.469%
Minimum	0.327%
Maximum	34.796%
Count	8236

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.196%	8236	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 22.34 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	0.83%	1.61%
-3.74% to -2.50%	227	2.76%	4.37%
-2.50% to -1.26%	835	10.14%	14.51%
-1.26% to -0.02%	2864	34.77%	49.28%
-0.02% to 1.22%	2984	36.23%	85.51%
1.22% to 2.46%	832	10.10%	95.62%
2.46% to 3.70%	241	2.93%	98.54%
3.70% to 4.94%	59	0.72%	99.26%
Greater than 4.94%	61	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.68%	1.63%	80.82%	68.27%
±2σ	-3.33%	3.29%	95.84%	95.45%
±3σ	-4.98%	4.94%	98.47%	99.73%

Descriptive Statistics

Mean	-0.022%
Standard Error	0.018%
Median	0.000%
Mode	0.000%
Standard Deviation	1.654%
Sample Variance	2.735%
Kurtosis	22.34
Skewness	0.70
Range	42.606%
Minimum	-17.105%
Maximum	25.501%
Count	8236

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.102%	3925	47.66%	0.525%
Negative	-1.101%	4093	49.70%	-0.547%
Zero	0.000%	218	2.65%	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 8.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.40%	17	1.00%	1.00%
-11.40% to -8.48%	18	1.05%	2.05%
-8.48% to -5.56%	42	2.46%	4.51%
-5.56% to -2.64%	180	10.54%	15.06%
-2.64% to 0.28%	575	33.68%	48.74%
0.28% to 3.20%	617	36.15%	84.89%
3.20% to 6.12%	183	10.72%	95.61%
6.12% to 9.04%	51	2.99%	98.59%
9.04% to 11.95%	10	0.59%	99.18%
Greater than 11.95%	14	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.61%	4.17%	79.85%	68.27%
±2σ	-7.51%	8.06%	95.72%	95.45%
±3σ	-11.40%	11.95%	98.18%	99.73%

Descriptive Statistics

Mean	0.278%
Standard Error	0.094%
Median	0.350%
Mode	0.000%
Standard Deviation	3.892%
Sample Variance	15.145%
Kurtosis	8.97
Skewness	0.07
Range	52.681%
Minimum	-23.444%
Maximum	29.237%
Count	1707

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.645%	933	54.66%	1.446%
Negative	-2.620%	761	44.58%	-1.168%
Zero	0.000%	13	0.76%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.16%
12	1 Quarter	5.27%
52	1 Year	5.22%
156	3 Years	5.19%
260	5 Years	5.28%
520	10 Years	4.67%
1,040	20 Years	4.94%
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 5.58. Further, an Excess Kurtosis of 59.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.30%	0	0.00%	0.00%
-8.30% to -4.86%	0	0.00%	0.00%
-4.86% to -1.42%	0	0.00%	0.00%
-1.42% to 2.02%	117	6.85%	6.85%
2.02% to 5.46%	1016	59.48%	66.33%
5.46% to 8.89%	373	21.84%	88.17%
8.89% to 12.33%	124	7.26%	95.43%
12.33% to 15.77%	30	1.76%	97.19%
15.77% to 19.21%	19	1.11%	98.30%
Greater than 19.21%	29	1.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.87%	10.04%	91.80%	68.27%
±2σ	-3.71%	14.63%	96.72%	95.45%
±3σ	-8.30%	19.21%	98.30%	99.73%

Descriptive Statistics

Mean	5.456%
Standard Error	0.111%
Median	4.324%
Mode	2.139%
Standard Deviation	4.585%
Sample Variance	21.026%
Kurtosis	59.96
Skewness	5.58
Range	80.961%
Minimum	0.741%
Maximum	81.702%
Count	1708

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.456%	1708	100.00%	5.456%
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 10.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.65%	11	0.64%	0.64%
-11.65% to -8.76%	13	0.76%	1.41%
-8.76% to -5.86%	48	2.81%	4.22%
-5.86% to -2.96%	194	11.36%	15.57%
-2.96% to -0.07%	635	37.18%	52.75%
-0.07% to 2.83%	559	32.73%	85.48%
2.83% to 5.72%	170	9.95%	95.43%
5.72% to 8.62%	46	2.69%	98.13%
8.62% 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%	81.09%	68.27%
±2σ	-7.79%	7.65%	95.61%	95.45%
±3σ	-11.65%	11.51%	98.13%	99.73%

Descriptive Statistics

Mean	-0.069%
Standard Error	0.093%
Median	-0.266%
Mode	0.000%
Standard Deviation	3.861%
Sample Variance	14.909%
Kurtosis	10.22
Skewness	1.17
Range	52.181%
Minimum	-21.557%
Maximum	30.624%
Count	1708

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.735%	780	45.67%	1.249%
Negative	-2.458%	916	53.63%	-1.318%
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 4.96 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	0.77%	1.79%
-15.38% to -9.87%	11	2.81%	4.59%
-9.87% to -4.36%	48	12.24%	16.84%
-4.36% to 1.16%	131	33.42%	50.26%
1.16% to 6.67%	127	32.40%	82.65%
6.67% to 12.18%	49	12.50%	95.15%
12.18% to 17.69%	14	3.57%	98.72%
17.69% to 23.20%	3	0.77%	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%	76.02%	68.27%
±2σ	-13.54%	15.85%	95.41%	95.45%
±3σ	-20.89%	23.20%	98.47%	99.73%

Descriptive Statistics

Mean	1.156%
Standard Error	0.371%
Median	1.126%
Mode	5.263%
Standard Deviation	7.348%
Sample Variance	53.997%
Kurtosis	4.96
Skewness	-0.73
Range	71.554%
Minimum	-42.780%
Maximum	28.774%
Count	392

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.802%	222	56.63%	3.286%
Negative	-4.911%	170	43.37%	-2.130%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	9.19%
12	1 Year	10.72%
36	3 Years	10.80%
60	5 Years	11.36%
120	10 Years	10.03%
240	20 Years	10.46%
600	50 Years	11.09%

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 34.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.98%	0	0.00%	0.00%
-17.98% to -10.45%	0	0.00%	0.00%
-10.45% to -2.93%	0	0.00%	0.00%
-2.93% to 4.59%	22	5.60%	5.60%
4.59% to 12.11%	241	61.32%	66.92%
12.11% to 19.64%	94	23.92%	90.84%
19.64% to 27.16%	15	3.82%	94.66%
27.16% to 34.68%	11	2.80%	97.46%
34.68% to 42.20%	4	1.02%	98.47%
Greater than 42.20%	6	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.08%	22.14%	91.60%	68.27%
±2σ	-7.95%	32.17%	96.95%	95.45%
±3σ	-17.98%	42.20%	98.47%	99.73%

Descriptive Statistics

Mean	12.113%
Standard Error	0.506%
Median	9.720%
Mode	7.182%
Standard Deviation	10.030%
Sample Variance	100.608%
Kurtosis	34.03
Skewness	4.82
Range	108.468%
Minimum	2.294%
Maximum	110.762%
Count	393

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.113%	393	100.00%	12.113%
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 20.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.70%	1	0.25%	0.25%
-24.70% to -18.60%	1	0.25%	0.51%
-18.60% to -12.49%	10	2.54%	3.05%
-12.49% to -6.39%	51	12.98%	16.03%
-6.39% to -0.28%	149	37.91%	53.94%
-0.28% to 5.82%	127	32.32%	86.26%
5.82% to 11.92%	39	9.92%	96.18%
11.92% to 18.03%	8	2.04%	98.22%
18.03% to 24.13%	2	0.51%	98.73%
Greater than 24.13%	5	1.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.42%	7.85%	80.41%	68.27%
±2σ	-16.56%	15.99%	96.44%	95.45%
±3σ	-24.70%	24.13%	98.47%	99.73%

Descriptive Statistics

Mean	-0.285%
Standard Error	0.411%
Median	-0.801%
Mode	-7.417%
Standard Deviation	8.138%
Sample Variance	66.228%
Kurtosis	20.78
Skewness	2.76
Range	97.821%
Minimum	-24.725%
Maximum	73.096%
Count	393

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.666%	177	45.04%	2.552%
Negative	-5.185%	215	54.71%	-2.837%
Zero	0.000%	1	0.25%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.11. 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 -22.06%	0	0.00%	0.76%
-22.06% to -13.63%	8	6.11%	6.87%
-13.63% to -5.21%	17	12.98%	19.85%
-5.21% to 3.21%	37	28.24%	48.09%
3.21% to 11.64%	44	33.59%	81.68%
11.64% to 20.06%	17	12.98%	94.66%
20.06% to 28.48%	6	4.58%	99.24%
28.48% 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	3.214%
Standard Error	0.981%
Median	3.387%
Mode	-42.379%
Standard Deviation	11.231%
Sample Variance	126.133%
Kurtosis	2.66
Skewness	-0.11
Range	89.274%
Minimum	-42.379%
Maximum	46.895%
Count	131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.253%	85	64.89%	6.004%
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	-1.291%
Standard Error	1.038%
Median	-2.774%
Mode	-2.682%
Standard Deviation	11.923%
Sample Variance	142.151%
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	-7.521%	85	64.39%	-4.843%
Zero	0.000%	0	0.00%	0.000%

ALL Deep Analytical Report