ATO - 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	1.45%	1.20%	1.34%	1.77%	1.07%	1.45%	184.81	188.80	182.84	190.82
Weekly	3.03%	2.78%	2.98%	4.03%	2.35%	3.19%	182.45	191.23	178.21	195.78
Monthly	5.67%	5.26%	5.68%	8.45%	4.89%	6.65%	177.87	196.16	169.38	205.99
Quarterly	8.14%	7.82%	7.86%	14.55%	8.48%	11.51%	171.61	203.31	157.67	221.29
Annual	—	—	—	—	16.95%	23.02%	157.67	221.29	133.08	262.17
Option Time Horizon	—	—	—	—	6.08%	8.26%	175.77	198.50	165.40	210.95

Calculation Notes: Computed at 2026-03-01T12:14 UTC | Reference Contract: Call option expiring 2026-04-17 (47 days) | Spot Price (S): $186.79 | Strike (K): $190.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.3500 (Bid $1.9000 / Ask $4.8000) | Risk-Free Rate (r): 3.74% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.97% | Binomial IV (Annual): 16.95% (CRR binomial tree, American, n=20 steps) | BS IV: 17.13% (European Black-Scholes) | Yahoo IV (Annual): 23.02% → 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
2026-02-23	$1.0000
2025-11-24	$1.0000
2025-08-25	$0.8700
2025-05-27	$0.8700
2025-02-25	$0.8700
2024-11-25	$0.8700
2024-08-26	$0.8050
2024-05-24	$0.8050
2024-02-23	$0.8050
2023-11-24	$0.8050
2023-08-18	$0.7400
2023-05-19	$0.7400
2023-02-16	$0.7400
2022-11-25	$0.7400
2022-08-19	$0.6800
2022-05-20	$0.6800
2022-02-17	$0.6800
2021-11-26	$0.6800
2021-08-20	$0.6250
2021-05-21	$0.6250
2021-02-19	$0.6250
2020-11-27	$0.6250
2020-08-21	$0.5750
2020-05-22	$0.5750
2020-02-21	$0.5750
2019-11-22	$0.5750
2019-08-23	$0.5250
2019-05-24	$0.5250
2019-02-22	$0.5250
2018-11-23	$0.5250
2018-08-24	$0.4850
2018-05-18	$0.4850
2018-02-23	$0.4850
2017-11-24	$0.4850
2017-08-17	$0.4500
2017-05-18	$0.4500
2017-02-23	$0.4500
2016-11-23	$0.4500
2016-08-18	$0.4200
2016-05-19	$0.4200
2016-02-18	$0.4200
2015-11-19	$0.4200
2015-08-20	$0.3900
2015-05-21	$0.3900
2015-02-19	$0.3900
2014-11-20	$0.3900
2014-08-21	$0.3700
2014-05-22	$0.3700
2014-02-20	$0.3700
2013-11-21	$0.3700
2013-08-22	$0.3500
2013-05-16	$0.3500
2013-02-28	$0.3500
2012-11-21	$0.3500
2012-08-23	$0.3450
2012-05-23	$0.3450
2012-02-23	$0.3450
2011-11-22	$0.3450
2011-08-23	$0.3400
2011-05-23	$0.3400
2011-02-23	$0.3400
2010-11-23	$0.3400
2010-08-23	$0.3350
2010-05-21	$0.3350
2010-02-23	$0.3350
2009-11-23	$0.3350
2009-08-21	$0.3300
2009-05-21	$0.3300
2009-02-23	$0.3300
2008-11-21	$0.3300
2008-08-21	$0.3250
2008-05-22	$0.3250
2008-02-21	$0.3250
2007-11-21	$0.3250
2007-08-23	$0.3200
2007-05-23	$0.3200
2007-02-22	$0.3200
2006-11-22	$0.3200
2006-08-23	$0.3150
2006-05-23	$0.3150
2006-02-23	$0.3150
2005-11-22	$0.3150
2005-08-23	$0.3100
2005-05-23	$0.3100
2005-02-23	$0.3100
2004-11-22	$0.3100
2004-08-23	$0.3050
2004-05-21	$0.3050
2004-02-23	$0.3050
2003-11-21	$0.3050
2003-08-21	$0.3000
2003-05-22	$0.3000
2003-02-21	$0.3000
2002-11-21	$0.3000
2002-08-22	$0.2950
2002-05-23	$0.2950
2002-02-21	$0.2950
2001-11-21	$0.2950
2001-08-22	$0.2900
2001-05-23	$0.2900
2001-02-22	$0.2900
2000-11-20	$0.2900
2000-08-23	$0.2850
2000-05-23	$0.2850
2000-02-23	$0.2850
1999-11-22	$0.2850
1999-08-23	$0.2750
1999-05-21	$0.2750
1999-02-23	$0.2750
1998-11-23	$0.2750
1998-08-21	$0.2650
1998-05-21	$0.2650
1998-02-23	$0.2650
1997-11-21	$0.2650
1997-05-22	$0.2500
1997-02-21	$0.2500
1996-11-21	$0.2500
1996-08-22	$0.2400
1996-05-23	$0.2400
1996-02-22	$0.2400
1995-11-22	$0.2400
1995-08-23	$0.2300
1995-05-19	$0.2300
1995-02-21	$0.2300
1994-11-18	$0.2300
1994-08-19	$0.2200
1994-05-19	$0.2200
1994-02-18	$0.2200
1993-11-18	$0.2200
1993-08-19	$0.2133
1993-05-19	$0.2133
1993-02-19	$0.2133
1992-11-19	$0.2133
1992-08-19	$0.2067
1992-05-19	$0.2067
1992-02-19	$0.2067
1991-11-19	$0.2067
1991-08-20	$0.2000
1991-05-20	$0.2000
1991-02-19	$0.2000
1990-11-19	$0.2000
1990-08-20	$0.1933
1990-05-21	$0.1933
1990-02-20	$0.1933
1989-11-17	$0.1933
1989-08-21	$0.1867

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.08. Further, an Excess Kurtosis of 10.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.30%	57	0.55%	0.55%
-4.30% to -3.21%	138	1.32%	1.87%
-3.21% to -2.12%	346	3.31%	5.18%
-2.12% to -1.03%	1159	11.10%	16.29%
-1.03% to 0.06%	3924	37.59%	53.88%
0.06% to 1.15%	3088	29.58%	83.46%
1.15% to 2.24%	1207	11.56%	95.03%
2.24% to 3.33%	332	3.18%	98.21%
3.33% to 4.42%	104	1.00%	99.20%
Greater than 4.42%	83	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.40%	1.51%	76.97%	68.27%
±2σ	-2.85%	2.96%	94.95%	95.45%
±3σ	-4.30%	4.42%	98.66%	99.73%

Descriptive Statistics

Mean	0.058%
Standard Error	0.014%
Median	0.000%
Mode	0.000%
Standard Deviation	1.453%
Sample Variance	2.112%
Kurtosis	10.43
Skewness	-0.08
Range	35.008%
Minimum	-19.626%
Maximum	15.382%
Count	10438

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.112%	4932	47.25%	0.525%
Negative	-1.103%	4423	42.37%	-0.467%
Zero	0.000%	1083	10.38%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.51%
20	1 Month	1.64%
60	1 Quarter	1.63%
250	1 Year	1.65%
750	3 Years	1.64%
1,250	5 Years	1.77%
2,500	10 Years	1.80%
5,000	20 Years	1.82%
12,500	50 Years	1.95%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.54. Further, an Excess Kurtosis of 27.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.72%	0	0.00%	0.00%
-1.72% to -0.82%	0	0.00%	0.00%
-0.82% to 0.08%	0	0.00%	0.00%
0.08% to 0.97%	1732	16.59%	16.59%
0.97% to 1.87%	4916	47.09%	63.68%
1.87% to 2.77%	2212	21.19%	84.87%
2.77% to 3.66%	908	8.70%	93.57%
3.66% to 4.56%	359	3.44%	97.01%
4.56% to 5.45%	149	1.43%	98.44%
Greater than 5.45%	163	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.67%	3.06%	84.86%	68.27%
±2σ	-0.52%	4.26%	96.18%	95.45%
±3σ	-1.72%	5.45%	98.44%	99.73%

Descriptive Statistics

Mean	1.869%
Standard Error	0.012%
Median	1.585%
Mode	1.667%
Standard Deviation	1.195%
Sample Variance	1.429%
Kurtosis	27.92
Skewness	3.54
Range	21.869%
Minimum	0.224%
Maximum	22.093%
Count	10439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.869%	10439	100.00%	1.869%
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 0.79. Further, an Excess Kurtosis of 14.75 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%	75	0.72%	0.72%
-4.02% to -3.02%	98	0.94%	1.66%
-3.02% to -2.01%	345	3.30%	4.96%
-2.01% to -1.01%	1257	12.04%	17.00%
-1.01% to -0.01%	2955	28.31%	45.31%
-0.01% to 1.00%	3984	38.16%	83.48%
1.00% to 2.00%	1164	11.15%	94.63%
2.00% to 3.00%	378	3.62%	98.25%
3.00% to 4.01%	119	1.14%	99.39%
Greater than 4.01%	64	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.34%	1.33%	76.59%	68.27%
±2σ	-2.68%	2.67%	95.21%	95.45%
±3σ	-4.02%	4.01%	98.67%	99.73%

Descriptive Statistics

Mean	-0.006%
Standard Error	0.013%
Median	0.000%
Mode	0.000%
Standard Deviation	1.338%
Sample Variance	1.789%
Kurtosis	14.75
Skewness	0.79
Range	33.093%
Minimum	-11.000%
Maximum	22.093%
Count	10439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.049%	4514	43.24%	0.454%
Negative	-1.015%	4730	45.31%	-0.460%
Zero	0.000%	1195	11.45%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.24. Further, an Excess Kurtosis of 6.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.81%	10	0.45%	0.45%
-8.81% to -6.54%	26	1.18%	1.63%
-6.54% to -4.27%	87	3.95%	5.59%
-4.27% to -2.00%	266	12.08%	17.67%
-2.00% to 0.27%	733	33.29%	50.95%
0.27% to 2.54%	699	31.74%	82.70%
2.54% to 4.81%	266	12.08%	94.78%
4.81% to 7.08%	79	3.59%	98.37%
7.08% to 9.36%	21	0.95%	99.32%
Greater than 9.36%	15	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.76%	3.30%	77.34%	68.27%
±2σ	-5.78%	6.33%	95.14%	95.45%
±3σ	-8.81%	9.36%	98.86%	99.73%

Descriptive Statistics

Mean	0.272%
Standard Error	0.065%
Median	0.199%
Mode	0.000%
Standard Deviation	3.028%
Sample Variance	9.171%
Kurtosis	6.97
Skewness	0.24
Range	49.545%
Minimum	-21.818%
Maximum	27.727%
Count	2202

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.317%	1153	52.36%	1.213%
Negative	-2.206%	940	42.69%	-0.942%
Zero	0.000%	109	4.95%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.90%
12	1 Quarter	3.68%
52	1 Year	3.82%
156	3 Years	3.75%
260	5 Years	4.03%
520	10 Years	4.06%
1,040	20 Years	4.11%
2,600	50 Years	4.33%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.37. Further, an Excess Kurtosis of 40.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.94%	0	0.00%	0.00%
-3.94% to -1.85%	0	0.00%	0.00%
-1.85% to 0.23%	0	0.00%	0.00%
0.23% to 2.32%	310	14.07%	14.07%
2.32% to 4.41%	1063	48.25%	62.32%
4.41% to 6.49%	520	23.60%	85.93%
6.49% to 8.58%	183	8.31%	94.24%
8.58% to 10.66%	62	2.81%	97.05%
10.66% to 12.75%	34	1.54%	98.59%
Greater than 12.75%	31	1.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.62%	7.19%	86.56%	68.27%
±2σ	-1.16%	9.97%	96.73%	95.45%
±3σ	-3.94%	12.75%	98.59%	99.73%

Descriptive Statistics

Mean	4.405%
Standard Error	0.059%
Median	3.774%
Mode	3.846%
Standard Deviation	2.781%
Sample Variance	7.734%
Kurtosis	40.80
Skewness	4.37
Range	42.805%
Minimum	0.538%
Maximum	43.343%
Count	2203

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.405%	2203	100.00%	4.405%
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 0.79. Further, an Excess Kurtosis of 7.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.01%	12	0.54%	0.54%
-9.01% to -6.78%	16	0.73%	1.27%
-6.78% to -4.54%	81	3.68%	4.95%
-4.54% to -2.31%	284	12.89%	17.84%
-2.31% to -0.07%	718	32.59%	50.43%
-0.07% to 2.17%	704	31.96%	82.39%
2.17% to 4.40%	258	11.71%	94.10%
4.40% to 6.64%	88	3.99%	98.09%
6.64% to 8.87%	30	1.36%	99.46%
Greater than 8.87%	12	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.05%	2.91%	76.67%	68.27%
±2σ	-6.03%	5.89%	95.28%	95.45%
±3σ	-9.01%	8.87%	98.91%	99.73%

Descriptive Statistics

Mean	-0.071%
Standard Error	0.064%
Median	-0.093%
Mode	0.000%
Standard Deviation	2.981%
Sample Variance	8.884%
Kurtosis	7.72
Skewness	0.79
Range	46.989%
Minimum	-19.082%
Maximum	27.907%
Count	2203

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.355%	953	43.26%	1.019%
Negative	-2.131%	1127	51.16%	-1.090%
Zero	0.000%	123	5.58%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.17. Further, an Excess Kurtosis of 2.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.85%	3	0.59%	0.59%
-15.85% to -11.60%	3	0.59%	1.18%
-11.60% to -7.35%	25	4.93%	6.11%
-7.35% to -3.10%	71	14.00%	20.12%
-3.10% to 1.15%	145	28.60%	48.72%
1.15% to 5.40%	163	32.15%	80.87%
5.40% to 9.64%	65	12.82%	93.69%
9.64% to 13.89%	26	5.13%	98.82%
13.89% to 18.14%	5	0.99%	99.80%
Greater than 18.14%	1	0.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.52%	6.81%	72.98%	68.27%
±2σ	-10.18%	12.48%	95.86%	95.45%
±3σ	-15.85%	18.14%	99.21%	99.73%

Descriptive Statistics

Mean	1.147%
Standard Error	0.252%
Median	1.296%
Mode	0.000%
Standard Deviation	5.665%
Sample Variance	32.095%
Kurtosis	2.68
Skewness	-0.17
Range	57.147%
Minimum	-30.204%
Maximum	26.943%
Count	507

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.662%	299	58.97%	2.749%
Negative	-4.084%	199	39.25%	-1.603%
Zero	0.000%	9	1.77%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	8.10%
12	1 Year	7.90%
36	3 Years	7.74%
60	5 Years	8.45%
120	10 Years	8.39%
240	20 Years	8.48%
600	50 Years	9.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.80. Further, an Excess Kurtosis of 13.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.17%	0	0.00%	0.00%
-6.17% to -2.23%	0	0.00%	0.00%
-2.23% to 1.71%	0	0.00%	0.00%
1.71% to 5.65%	92	18.11%	18.11%
5.65% to 9.60%	221	43.50%	61.61%
9.60% to 13.54%	122	24.02%	85.63%
13.54% to 17.48%	43	8.46%	94.09%
17.48% to 21.43%	14	2.76%	96.85%
21.43% to 25.37%	9	1.77%	98.62%
Greater than 25.37%	7	1.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.34%	14.85%	82.68%	68.27%
±2σ	-0.92%	20.11%	96.26%	95.45%
±3σ	-6.17%	25.37%	98.62%	99.73%

Descriptive Statistics

Mean	9.597%
Standard Error	0.233%
Median	8.427%
Mode	5.882%
Standard Deviation	5.257%
Sample Variance	27.633%
Kurtosis	13.47
Skewness	2.80
Range	44.152%
Minimum	2.555%
Maximum	46.707%
Count	508

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.597%	508	100.00%	9.597%
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 7.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.46%	1	0.20%	0.20%
-17.46% to -13.21%	3	0.59%	0.79%
-13.21% to -8.95%	20	3.94%	4.72%
-8.95% to -4.69%	76	14.96%	19.69%
-4.69% to -0.43%	170	33.46%	53.15%
-0.43% to 3.83%	140	27.56%	80.71%
3.83% to 8.08%	64	12.60%	93.31%
8.08% to 12.34%	26	5.12%	98.43%
12.34% to 16.60%	5	0.98%	99.41%
Greater than 16.60%	3	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.11%	5.24%	74.02%	68.27%
±2σ	-11.79%	10.92%	96.06%	95.45%
±3σ	-17.46%	16.60%	99.21%	99.73%

Descriptive Statistics

Mean	-0.432%
Standard Error	0.252%
Median	-0.775%
Mode	0.000%
Standard Deviation	5.677%
Sample Variance	32.230%
Kurtosis	7.45
Skewness	1.17
Range	64.091%
Minimum	-20.816%
Maximum	43.275%
Count	508

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.558%	208	40.95%	1.866%
Negative	-4.053%	288	56.69%	-2.298%
Zero	0.000%	12	2.36%	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 0.55 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.11%	1	0.59%	0.59%
-21.11% to -15.00%	1	0.59%	1.18%
-15.00% to -8.90%	11	6.51%	7.69%
-8.90% to -2.79%	25	14.79%	22.49%
-2.79% to 3.31%	43	25.44%	47.93%
3.31% to 9.41%	51	30.18%	78.11%
9.41% to 15.52%	28	16.57%	94.67%
15.52% to 21.62%	8	4.73%	99.41%
21.62% to 27.73%	0	0.00%	99.41%
Greater than 27.73%	1	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.83%	11.45%	71.01%	68.27%
±2σ	-12.97%	19.59%	95.86%	95.45%
±3σ	-21.11%	27.73%	98.82%	99.73%

Descriptive Statistics

Mean	3.310%
Standard Error	0.626%
Median	3.769%
Mode	-21.881%
Standard Deviation	8.139%
Sample Variance	66.238%
Kurtosis	0.55
Skewness	-0.07
Range	54.104%
Minimum	-21.881%
Maximum	32.223%
Count	169

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.507%	117	69.23%	5.197%
Negative	-6.254%	51	30.18%	-1.887%
Zero	0.000%	1	0.59%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	13.05%
12	3 Years	13.12%
20	5 Years	14.55%
40	10 Years	14.34%
80	20 Years	14.10%
200	50 Years	15.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.03. Further, an Excess Kurtosis of 5.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.04%	0	0.00%	0.00%
-7.04% to -1.17%	0	0.00%	0.00%
-1.17% to 4.70%	1	0.59%	0.59%
4.70% to 10.56%	32	18.82%	19.41%
10.56% to 16.43%	73	42.94%	62.35%
16.43% to 22.29%	39	22.94%	85.29%
22.29% to 28.16%	14	8.24%	93.53%
28.16% to 34.02%	4	2.35%	95.88%
34.02% to 39.89%	3	1.76%	97.65%
Greater than 39.89%	4	2.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.61%	24.25%	81.76%	68.27%
±2σ	0.79%	32.07%	95.29%	95.45%
±3σ	-7.04%	39.89%	97.65%	99.73%

Descriptive Statistics

Mean	16.427%
Standard Error	0.600%
Median	14.866%
Mode	17.391%
Standard Deviation	7.821%
Sample Variance	61.168%
Kurtosis	5.97
Skewness	2.03
Range	51.385%
Minimum	4.005%
Maximum	55.390%
Count	170

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.427%	170	100.00%	16.427%
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 1.02 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.12%	0	0.00%	0.00%
-25.12% to -19.22%	1	0.59%	0.59%
-19.22% to -13.33%	5	2.94%	3.53%
-13.33% to -7.44%	33	19.41%	22.94%
-7.44% to -1.54%	57	33.53%	56.47%
-1.54% to 4.35%	36	21.18%	77.65%
4.35% to 10.24%	24	14.12%	91.76%
10.24% to 16.13%	10	5.88%	97.65%
16.13% to 22.03%	3	1.76%	99.41%
Greater than 22.03%	1	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.40%	6.31%	71.76%	68.27%
±2σ	-17.26%	14.17%	95.88%	95.45%
±3σ	-25.12%	22.03%	99.41%	99.73%

Descriptive Statistics

Mean	-1.545%
Standard Error	0.603%
Median	-2.493%
Mode	-10.526%
Standard Deviation	7.857%
Sample Variance	61.740%
Kurtosis	1.02
Skewness	0.67
Range	53.030%
Minimum	-23.030%
Maximum	30.000%
Count	170

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.679%	62	36.47%	2.436%
Negative	-6.324%	107	62.94%	-3.980%
Zero	0.000%	1	0.59%	0.000%

ATO Deep Analytical Report