CI - 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	2.02%	1.94%	1.74%	2.33%	2.63%	2.84%	252.68	266.35	246.11	273.46
Weekly	4.42%	5.36%	4.51%	5.43%	5.80%	6.26%	244.81	274.91	231.02	291.33
Monthly	8.76%	14.79%	10.28%	12.00%	12.07%	13.02%	229.93	292.71	203.78	330.27
Quarterly	15.22%	29.91%	19.67%	20.45%	20.91%	22.56%	210.48	319.75	170.77	394.11
Annual	—	—	—	—	41.82%	45.12%	170.77	394.11	112.41	598.72
Option Time Horizon	—	—	—	—	15.78%	17.03%	221.55	303.78	189.20	355.72

Calculation Notes: Computed at 2026-03-23T16:33 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $259.42 | Strike (K): $270.00 (first OTM call ≥ spot) | Observed Mid-Price: $12.2500 (Bid $11.0000 / Ask $13.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 2.30% | Binomial IV (Annual): 41.82% (CRR binomial tree, American, n=20 steps) | BS IV: 42.32% (European Black-Scholes) | Yahoo IV (Annual): 45.12% → 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
2026-03-05	$1.5600
2025-12-04	$1.5100
2025-09-04	$1.5100
2025-06-03	$1.5100
2025-03-05	$1.5100
2024-12-04	$1.4000
2024-09-04	$1.4000
2024-06-04	$1.4000
2024-03-05	$1.4000
2023-12-05	$1.2300
2023-09-05	$1.2300
2023-06-06	$1.2300
2023-03-07	$1.2300
2022-12-05	$1.1200
2022-09-06	$1.1200
2022-06-07	$1.1200
2022-03-08	$1.1200
2021-12-06	$1.0000
2021-09-07	$1.0000
2021-06-07	$1.0000
2021-03-09	$1.0000
2020-03-09	$0.0400
2019-03-08	$0.0400
2018-03-09	$0.0400
2017-03-08	$0.0400
2016-03-09	$0.0400
2015-03-10	$0.0400
2014-03-10	$0.0400
2013-03-08	$0.0400
2012-03-08	$0.0400
2011-03-09	$0.0400
2010-03-09	$0.0400
2009-03-09	$0.0400
2008-03-07	$0.0400
2007-12-11	$0.0100
2007-09-10	$0.0100
2007-06-08	$0.0100
2007-03-09	$0.0083
2006-12-07	$0.0083
2006-09-07	$0.0083
2006-06-08	$0.0083
2006-03-09	$0.0083
2005-12-08	$0.0083
2005-09-08	$0.0083
2005-06-09	$0.0083
2005-03-10	$0.0083
2004-12-09	$0.0083
2004-09-09	$0.0083
2004-06-10	$0.0083
2004-03-11	$0.1100
2003-12-09	$0.1100
2003-09-09	$0.1100
2003-06-06	$0.1100
2003-03-07	$0.1100
2002-12-11	$0.1100
2002-09-10	$0.1100
2002-06-10	$0.1100
2002-03-11	$0.1100
2001-12-13	$0.1067
2001-09-10	$0.1067
2001-06-08	$0.1067
2001-03-09	$0.1067
2000-12-20	$0.1033
2000-09-08	$0.1033
2000-06-08	$0.1033
2000-03-09	$0.1033
1999-12-21	$0.1000
1999-09-08	$0.1000
1999-06-09	$0.1000
1999-03-10	$0.1000
1998-12-22	$0.0960
1998-09-09	$0.0960
1998-06-10	$0.0960
1998-03-11	$0.0956
1997-12-10	$0.0922
1997-09-10	$0.0922
1997-06-10	$0.0922
1997-03-11	$0.0922
1996-12-11	$0.0889
1996-09-10	$0.0889
1996-06-10	$0.0889
1996-03-11	$0.0889
1995-12-11	$0.0844
1995-09-08	$0.0844
1995-06-08	$0.0844
1995-03-07	$0.0844
1994-12-07	$0.0844
1994-09-06	$0.0844
1994-06-06	$0.0844
1994-03-07	$0.0844
1993-12-07	$0.0844
1993-09-03	$0.0844
1993-06-07	$0.0844
1993-03-08	$0.0844
1992-12-07	$0.0844
1992-09-04	$0.0844
1992-06-08	$0.0844
1992-03-09	$0.0844
1991-12-09	$0.0844
1991-09-06	$0.0844
1991-06-06	$0.0844
1991-03-07	$0.0844
1990-12-07	$0.0844
1990-09-06	$0.0844
1990-06-06	$0.0844
1990-03-07	$0.0844
1989-12-07	$0.0822
1989-09-06	$0.0822
1989-06-06	$0.0822
1989-03-07	$0.0822
1988-12-07	$0.0822
1988-09-06	$0.0822
1988-06-06	$0.1252
1988-03-07	$0.0822
1987-12-07	$0.0778
1987-09-04	$0.0778
1987-06-08	$0.0778
1987-03-09	$0.0778
1986-12-08	$0.0722
1986-09-08	$0.0722
1986-06-06	$0.0722
1986-03-07	$0.0722
1985-12-09	$0.0722
1985-09-06	$0.0722
1985-06-06	$0.0722
1985-03-07	$0.0722
1984-12-07	$0.0722
1984-09-06	$0.0722
1984-06-06	$0.0722
1984-03-07	$0.0722
1983-12-05	$0.0689
1983-09-02	$0.0689
1983-06-06	$0.0689
1983-03-07	$0.0689
1982-12-07	$0.0639
1982-09-07	$0.0639
1982-06-07	$0.0639

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.82. Further, an Excess Kurtosis of 29.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.00%	79	0.71%	0.71%
-6.00% to -4.49%	81	0.73%	1.44%
-4.49% to -2.97%	314	2.83%	4.28%
-2.97% to -1.45%	1178	10.63%	14.91%
-1.45% to 0.06%	3958	35.72%	50.62%
0.06% to 1.58%	3741	33.76%	84.38%
1.58% to 3.10%	1248	11.26%	95.64%
3.10% to 4.62%	321	2.90%	98.54%
4.62% to 6.13%	92	0.83%	99.37%
Greater than 6.13%	70	0.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.96%	2.09%	80.69%	68.27%
±2σ	-3.98%	4.11%	95.93%	95.45%
±3σ	-6.01%	6.13%	98.66%	99.73%

Descriptive Statistics

Mean	0.064%
Standard Error	0.019%
Median	0.029%
Mode	0.000%
Standard Deviation	2.023%
Sample Variance	4.091%
Kurtosis	29.20
Skewness	-0.82
Range	65.364%
Minimum	-41.824%
Maximum	23.540%
Count	11082

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.373%	5593	50.47%	0.693%
Negative	-1.356%	5141	46.39%	-0.629%
Zero	0.000%	348	3.14%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.67%
20	1 Month	2.68%
60	1 Quarter	2.61%
250	1 Year	2.57%
750	3 Years	2.34%
1,250	5 Years	2.33%
2,500	10 Years	2.46%
5,000	20 Years	2.75%
12,500	50 Years	2.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 10.28. Further, an Excess Kurtosis of 311.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.51%	0	0.00%	0.00%
-3.51% to -2.05%	0	0.00%	0.00%
-2.05% to -0.60%	0	0.00%	0.00%
-0.60% to 0.86%	806	7.27%	7.27%
0.86% to 2.32%	6418	57.91%	65.18%
2.32% to 3.78%	2608	23.53%	88.71%
3.78% to 5.24%	733	6.61%	95.33%
5.24% to 6.69%	255	2.30%	97.63%
6.69% to 8.15%	101	0.91%	98.54%
Greater than 8.15%	162	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.38%	4.26%	91.83%	68.27%
±2σ	-1.57%	6.21%	97.13%	95.45%
±3σ	-3.51%	8.15%	98.54%	99.73%

Descriptive Statistics

Mean	2.320%
Standard Error	0.018%
Median	1.891%
Mode	1.389%
Standard Deviation	1.944%
Sample Variance	3.778%
Kurtosis	311.13
Skewness	10.28
Range	83.944%
Minimum	0.170%
Maximum	84.114%
Count	11083

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.320%	11083	100.00%	2.320%
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 1.14. Further, an Excess Kurtosis of 22.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.22%	70	0.63%	0.63%
-5.22% to -3.92%	83	0.75%	1.38%
-3.92% to -2.62%	349	3.15%	4.53%
-2.62% to -1.32%	1303	11.76%	16.29%
-1.32% to -0.02%	3652	32.95%	49.24%
-0.02% to 1.28%	3898	35.17%	84.41%
1.28% to 2.59%	1222	11.03%	95.43%
2.59% to 3.89%	336	3.03%	98.47%
3.89% to 5.19%	92	0.83%	99.30%
Greater than 5.19%	78	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.75%	1.72%	78.91%	68.27%
±2σ	-3.49%	3.45%	95.76%	95.45%
±3σ	-5.22%	5.19%	98.66%	99.73%

Descriptive Statistics

Mean	-0.017%
Standard Error	0.016%
Median	0.000%
Mode	0.000%
Standard Deviation	1.735%
Sample Variance	3.010%
Kurtosis	22.72
Skewness	1.14
Range	48.109%
Minimum	-16.145%
Maximum	31.964%
Count	11083

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.220%	5195	46.87%	0.572%
Negative	-1.192%	5482	49.46%	-0.590%
Zero	0.000%	406	3.66%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.10. Further, an Excess Kurtosis of 9.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.96%	21	0.92%	0.92%
-12.96% to -9.64%	25	1.09%	2.01%
-9.64% to -6.33%	62	2.70%	4.71%
-6.33% to -3.01%	263	11.46%	16.17%
-3.01% to 0.31%	768	33.48%	49.65%
0.31% to 3.62%	754	32.87%	82.52%
3.62% to 6.94%	294	12.82%	95.34%
6.94% to 10.26%	76	3.31%	98.65%
10.26% to 13.57%	15	0.65%	99.30%
Greater than 13.57%	16	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.11%	4.73%	78.73%	68.27%
±2σ	-8.54%	9.15%	95.42%	95.45%
±3σ	-12.96%	13.57%	98.39%	99.73%

Descriptive Statistics

Mean	0.307%
Standard Error	0.092%
Median	0.336%
Mode	0.000%
Standard Deviation	4.422%
Sample Variance	19.551%
Kurtosis	9.14
Skewness	-0.10
Range	76.571%
Minimum	-39.511%
Maximum	37.060%
Count	2294

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.158%	1229	53.58%	1.692%
Negative	-3.053%	1041	45.38%	-1.385%
Zero	0.000%	24	1.05%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.00%
12	1 Quarter	5.86%
52	1 Year	5.95%
156	3 Years	5.53%
260	5 Years	5.43%
520	10 Years	5.77%
1,040	20 Years	6.33%
2,600	50 Years	5.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 9.24. Further, an Excess Kurtosis of 162.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.01%	0	0.00%	0.00%
-10.01% to -5.99%	0	0.00%	0.00%
-5.99% to -1.97%	0	0.00%	0.00%
-1.97% to 2.05%	93	4.05%	4.05%
2.05% to 6.08%	1414	61.61%	65.66%
6.08% to 10.10%	553	24.10%	89.76%
10.10% to 14.12%	138	6.01%	95.77%
14.12% to 18.14%	48	2.09%	97.86%
18.14% to 22.16%	20	0.87%	98.74%
Greater than 22.16%	29	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.71%	11.44%	92.98%	68.27%
±2σ	-4.65%	16.80%	97.21%	95.45%
±3σ	-10.01%	22.16%	98.74%	99.73%

Descriptive Statistics

Mean	6.075%
Standard Error	0.112%
Median	4.897%
Mode	3.125%
Standard Deviation	5.363%
Sample Variance	28.766%
Kurtosis	162.02
Skewness	9.24
Range	127.958%
Minimum	0.963%
Maximum	128.921%
Count	2295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.075%	2295	100.00%	6.075%
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 2.14. Further, an Excess Kurtosis of 24.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.57%	13	0.57%	0.57%
-13.57% to -10.18%	8	0.35%	0.92%
-10.18% to -6.80%	55	2.40%	3.31%
-6.80% to -3.42%	304	13.25%	16.56%
-3.42% to -0.03%	829	36.12%	52.68%
-0.03% to 3.35%	755	32.90%	85.58%
3.35% to 6.73%	234	10.20%	95.77%
6.73% to 10.12%	48	2.09%	97.86%
10.12% to 13.50%	21	0.92%	98.78%
Greater than 13.50%	28	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.54%	4.48%	80.04%	68.27%
±2σ	-9.06%	8.99%	95.86%	95.45%
±3σ	-13.57%	13.50%	98.21%	99.73%

Descriptive Statistics

Mean	-0.034%
Standard Error	0.094%
Median	-0.248%
Mode	0.000%
Standard Deviation	4.511%
Sample Variance	20.348%
Kurtosis	24.45
Skewness	2.14
Range	90.447%
Minimum	-25.102%
Maximum	65.345%
Count	2295

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.240%	1055	45.97%	1.489%
Negative	-2.889%	1210	52.72%	-1.523%
Zero	0.000%	30	1.31%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.62. Further, an Excess Kurtosis of 4.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.96%	3	0.57%	0.57%
-24.96% to -18.39%	4	0.76%	1.33%
-18.39% to -11.82%	23	4.36%	5.68%
-11.82% to -5.25%	71	13.45%	19.13%
-5.25% to 1.32%	155	29.36%	48.48%
1.32% to 7.89%	173	32.77%	81.25%
7.89% to 14.46%	73	13.83%	95.08%
14.46% to 21.03%	20	3.79%	98.86%
21.03% to 27.60%	4	0.76%	99.62%
Greater than 27.60%	2	0.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.44%	10.08%	72.73%	68.27%
±2σ	-16.20%	18.84%	95.83%	95.45%
±3σ	-24.96%	27.60%	99.05%	99.73%

Descriptive Statistics

Mean	1.320%
Standard Error	0.381%
Median	1.602%
Mode	-6.882%
Standard Deviation	8.760%
Sample Variance	76.731%
Kurtosis	4.71
Skewness	-0.62
Range	91.172%
Minimum	-52.031%
Maximum	39.141%
Count	528

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.814%	307	58.14%	3.962%
Negative	-6.312%	221	41.86%	-2.642%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.31%
12	1 Year	13.82%
36	3 Years	12.50%
60	5 Years	12.00%
120	10 Years	12.56%
240	20 Years	13.55%
600	50 Years	12.86%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 10.75. Further, an Excess Kurtosis of 156.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.04%	0	0.00%	0.00%
-30.04% to -18.94%	0	0.00%	0.00%
-18.94% to -7.85%	0	0.00%	0.00%
-7.85% to 3.25%	0	0.00%	0.00%
3.25% to 14.34%	355	67.11%	67.11%
14.34% to 25.43%	139	26.28%	93.38%
25.43% to 36.53%	26	4.91%	98.30%
36.53% to 47.62%	2	0.38%	98.68%
47.62% to 58.72%	3	0.57%	99.24%
Greater than 58.72%	4	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-0.45%	29.13%	96.03%	68.27%
±2σ	-15.24%	43.92%	98.68%	95.45%
±3σ	-30.04%	58.72%	99.24%	99.73%

Descriptive Statistics

Mean	14.340%
Standard Error	0.643%
Median	12.000%
Mode	12.000%
Standard Deviation	14.792%
Sample Variance	218.792%
Kurtosis	156.79
Skewness	10.75
Range	254.869%
Minimum	4.500%
Maximum	259.369%
Count	529

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.340%	529	100.00%	14.340%
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 4.16. Further, an Excess Kurtosis of 39.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.09%	0	0.00%	0.00%
-31.09% to -23.38%	1	0.19%	0.19%
-23.38% to -15.67%	8	1.51%	1.70%
-15.67% to -7.96%	71	13.42%	15.12%
-7.96% to -0.25%	215	40.64%	55.77%
-0.25% to 7.46%	154	29.11%	84.88%
7.46% to 15.17%	57	10.78%	95.65%
15.17% to 22.88%	16	3.02%	98.68%
22.88% to 30.59%	4	0.76%	99.43%
Greater than 30.59%	3	0.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.53%	10.03%	82.04%	68.27%
±2σ	-20.81%	20.31%	97.92%	95.45%
±3σ	-31.09%	30.59%	99.43%	99.73%

Descriptive Statistics

Mean	-0.251%
Standard Error	0.447%
Median	-1.335%
Mode	-6.196%
Standard Deviation	10.280%
Sample Variance	105.669%
Kurtosis	39.59
Skewness	4.16
Range	139.964%
Minimum	-30.148%
Maximum	109.816%
Count	529

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.356%	228	43.10%	3.170%
Negative	-6.033%	300	56.71%	-3.421%
Zero	0.000%	1	0.19%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.70. Further, an Excess Kurtosis of 2.02 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.57%	2	1.14%	1.14%
-41.57% to -30.16%	0	0.00%	1.14%
-30.16% to -18.74%	9	5.11%	6.25%
-18.74% to -7.33%	22	12.50%	18.75%
-7.33% to 4.08%	48	27.27%	46.02%
4.08% to 15.50%	56	31.82%	77.84%
15.50% to 26.91%	32	18.18%	96.02%
26.91% to 38.32%	6	3.41%	99.43%
38.32% to 49.74%	1	0.57%	100.00%
Greater than 49.74%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.13%	19.30%	72.16%	68.27%
±2σ	-26.35%	34.52%	96.59%	95.45%
±3σ	-41.57%	49.74%	98.86%	99.73%

Descriptive Statistics

Mean	4.083%
Standard Error	1.147%
Median	5.136%
Mode	-59.675%
Standard Deviation	15.218%
Sample Variance	231.598%
Kurtosis	2.02
Skewness	-0.70
Range	103.764%
Minimum	-59.675%
Maximum	44.089%
Count	176

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.853%	105	59.66%	8.265%
Negative	-10.365%	71	40.34%	-4.181%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	22.00%
12	3 Years	20.78%
20	5 Years	20.45%
40	10 Years	21.53%
80	20 Years	23.55%
200	50 Years	23.17%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 8.02. Further, an Excess Kurtosis of 79.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.70%	0	0.00%	0.00%
-61.70% to -39.27%	0	0.00%	0.00%
-39.27% to -16.84%	0	0.00%	0.00%
-16.84% to 5.59%	0	0.00%	0.00%
5.59% to 28.02%	124	70.06%	70.06%
28.02% to 50.45%	46	25.99%	96.05%
50.45% to 72.88%	2	1.13%	97.18%
72.88% to 95.31%	2	1.13%	98.31%
95.31% to 117.74%	0	0.00%	98.31%
Greater than 117.74%	3	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.89%	57.92%	97.18%	68.27%
±2σ	-31.80%	87.83%	97.74%	95.45%
±3σ	-61.71%	117.74%	98.31%	99.73%

Descriptive Statistics

Mean	28.016%
Standard Error	2.248%
Median	21.432%
Mode	10.049%
Standard Deviation	29.907%
Sample Variance	894.448%
Kurtosis	79.04
Skewness	8.02
Range	339.442%
Minimum	10.049%
Maximum	349.491%
Count	177

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.016%	177	100.00%	28.016%
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 4.05. Further, an Excess Kurtosis of 26.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -59.76%	0	0.00%	0.00%
-59.76% to -45.00%	0	0.00%	0.00%
-45.00% to -30.25%	1	0.56%	0.56%
-30.25% to -15.49%	25	14.12%	14.69%
-15.49% to -0.74%	79	44.63%	59.32%
-0.74% to 14.02%	51	28.81%	88.14%
14.02% to 28.77%	15	8.47%	96.61%
28.77% to 43.52%	4	2.26%	98.87%
43.52% to 58.28%	0	0.00%	98.87%
Greater than 58.28%	2	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.41%	18.93%	86.44%	68.27%
±2σ	-40.08%	38.61%	97.74%	95.45%
±3σ	-59.76%	58.28%	98.87%	99.73%

Descriptive Statistics

Mean	-0.739%
Standard Error	1.479%
Median	-4.337%
Mode	-30.458%
Standard Deviation	19.672%
Sample Variance	386.981%
Kurtosis	26.44
Skewness	4.05
Range	179.490%
Minimum	-30.458%
Maximum	149.032%
Count	177

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.295%	72	40.68%	5.815%
Negative	-11.048%	105	59.32%	-6.554%
Zero	0.000%	0	0.00%	0.000%

CI Deep Analytical Report