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%	1.78%	1.02%	1.29%	179.13	182.83	177.30	184.71
Weekly	3.03%	2.78%	2.98%	4.05%	2.25%	2.84%	176.94	185.09	173.00	189.31
Monthly	5.66%	5.25%	5.67%	8.58%	4.69%	5.90%	172.68	189.66	164.77	198.76
Quarterly	8.14%	7.84%	7.86%	14.28%	8.12%	10.22%	166.85	196.28	153.84	212.88
Annual	—	—	—	—	16.24%	20.45%	153.84	212.88	130.78	250.43
Option Time Horizon	—	—	—	—	6.25%	7.86%	170.01	192.64	159.71	205.05

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $180.97 | Strike (K): $185.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.0000 (Bid $2.0000 / Ask $4.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 2.02% | Binomial IV (Annual): 16.24% (CRR binomial tree, American, n=20 steps) | BS IV: 16.31% (European Black-Scholes) | Yahoo IV (Annual): 20.45% → 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
2025-11-24	$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 10.42 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%	345	3.31%	5.18%
-2.12% to -1.03%	1159	11.13%	16.31%
-1.03% to 0.06%	3915	37.58%	53.89%
0.06% to 1.15%	3079	29.56%	83.45%
1.15% to 2.24%	1205	11.57%	95.02%
2.24% to 3.33%	332	3.19%	98.20%
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%	76.94%	68.27%
±2σ	-2.85%	2.97%	94.96%	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	1.454%
Sample Variance	2.115%
Kurtosis	10.42
Skewness	-0.08
Range	35.008%
Minimum	-19.626%
Maximum	15.382%
Count	10417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.113%	4920	47.23%	0.526%
Negative	-1.104%	4414	42.37%	-0.468%
Zero	0.000%	1083	10.40%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.41%
20	1 Month	1.76%
60	1 Quarter	1.61%
250	1 Year	1.66%
750	3 Years	1.67%
1,250	5 Years	1.78%
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 27.88 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 0.07%	0	0.00%	0.00%
0.07% to 0.97%	1725	16.56%	16.56%
0.97% to 1.87%	4906	47.09%	63.65%
1.87% to 2.77%	2214	21.25%	84.90%
2.77% to 3.66%	902	8.66%	93.56%
3.66% to 4.56%	359	3.45%	97.01%
4.56% to 5.46%	151	1.45%	98.45%
Greater than 5.46%	161	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.67%	3.06%	84.83%	68.27%
±2σ	-0.52%	4.26%	96.17%	95.45%
±3σ	-1.72%	5.46%	98.45%	99.73%

Descriptive Statistics

Mean	1.869%
Standard Error	0.012%
Median	1.586%
Mode	1.667%
Standard Deviation	1.196%
Sample Variance	1.431%
Kurtosis	27.88
Skewness	3.54
Range	21.869%
Minimum	0.224%
Maximum	22.093%
Count	10418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.869%	10418	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 14.74 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	3.31%	4.97%
-2.01% to -1.01%	1254	12.04%	17.01%
-1.01% to -0.01%	2945	28.27%	45.28%
-0.01% to 1.00%	3979	38.19%	83.47%
1.00% to 2.00%	1162	11.15%	94.62%
2.00% to 3.00%	377	3.62%	98.24%
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%	76.55%	68.27%
±2σ	-2.68%	2.67%	95.20%	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	1.791%
Kurtosis	14.74
Skewness	0.79
Range	33.093%
Minimum	-11.000%
Maximum	22.093%
Count	10418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.049%	4506	43.25%	0.454%
Negative	-1.016%	4717	45.28%	-0.460%
Zero	0.000%	1195	11.47%	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%	1.64%
-6.54% to -4.27%	87	3.96%	5.60%
-4.27% to -2.00%	264	12.01%	17.61%
-2.00% to 0.27%	733	33.35%	50.96%
0.27% to 2.54%	698	31.76%	82.71%
2.54% to 4.82%	265	12.06%	94.77%
4.82% to 7.09%	79	3.59%	98.36%
7.09% to 9.36%	21	0.96%	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%	77.39%	68.27%
±2σ	-5.79%	6.33%	95.18%	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	3.029%
Sample Variance	9.177%
Kurtosis	6.97
Skewness	0.24
Range	49.545%
Minimum	-21.818%
Maximum	27.727%
Count	2198

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.317%	1151	52.37%	1.213%
Negative	-2.206%	938	42.67%	-0.941%
Zero	0.000%	109	4.96%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.77%
12	1 Quarter	3.25%
52	1 Year	3.82%
156	3 Years	3.80%
260	5 Years	4.05%
520	10 Years	4.05%
1,040	20 Years	4.10%
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 40.72 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 -1.86%	0	0.00%	0.00%
-1.86% to 0.23%	0	0.00%	0.00%
0.23% to 2.32%	311	14.14%	14.14%
2.32% to 4.41%	1059	48.16%	62.30%
4.41% to 6.49%	519	23.60%	85.90%
6.49% to 8.58%	183	8.32%	94.22%
8.58% to 10.67%	62	2.82%	97.04%
10.67% to 12.75%	34	1.55%	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%	86.54%	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	2.783%
Sample Variance	7.747%
Kurtosis	40.72
Skewness	4.37
Range	42.805%
Minimum	0.538%
Maximum	43.343%
Count	2199

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.405%	2199	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 7.73 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	0.55%	0.55%
-9.01% to -6.78%	16	0.73%	1.27%
-6.78% to -4.54%	81	3.68%	4.96%
-4.54% to -2.31%	283	12.87%	17.83%
-2.31% to -0.07%	716	32.56%	50.39%
-0.07% to 2.17%	704	32.01%	82.40%
2.17% to 4.40%	257	11.69%	94.09%
4.40% to 6.64%	88	4.00%	98.09%
6.64% to 8.87%	30	1.36%	99.45%
Greater than 8.87%	12	0.55%	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%	95.27%	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	8.887%
Kurtosis	7.73
Skewness	0.79
Range	46.989%
Minimum	-19.082%
Maximum	27.907%
Count	2199

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.353%	952	43.29%	1.019%
Negative	-2.132%	1124	51.11%	-1.090%
Zero	0.000%	123	5.59%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.19. Further, an Excess Kurtosis of 2.71 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.82%	3	0.59%	0.59%
-15.82% to -11.58%	3	0.59%	1.19%
-11.58% to -7.34%	25	4.94%	6.13%
-7.34% to -3.10%	71	14.03%	20.16%
-3.10% to 1.15%	144	28.46%	48.62%
1.15% to 5.39%	163	32.21%	80.83%
5.39% to 9.63%	66	13.04%	93.87%
9.63% to 13.88%	24	4.74%	98.62%
13.88% to 18.12%	6	1.19%	99.80%
Greater than 18.12%	1	0.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.51%	6.80%	72.92%	68.27%
±2σ	-10.17%	12.46%	95.65%	95.45%
±3σ	-15.82%	18.12%	99.21%	99.73%

Descriptive Statistics

Mean	1.148%
Standard Error	0.251%
Median	1.301%
Mode	0.000%
Standard Deviation	5.657%
Sample Variance	31.998%
Kurtosis	2.71
Skewness	-0.19
Range	57.147%
Minimum	-30.204%
Maximum	26.943%
Count	506

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.651%	299	59.09%	2.748%
Negative	-4.090%	198	39.13%	-1.600%
Zero	0.000%	9	1.78%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	7.11%
12	1 Year	7.68%
36	3 Years	7.75%
60	5 Years	8.58%
120	10 Years	8.39%
240	20 Years	8.46%
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 13.52 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 5.66%	91	17.95%	17.95%
5.66% to 9.60%	221	43.59%	61.54%
9.60% to 13.54%	123	24.26%	85.80%
13.54% to 17.48%	42	8.28%	94.08%
17.48% to 21.42%	14	2.76%	96.84%
21.42% to 25.36%	9	1.78%	98.62%
Greater than 25.36%	7	1.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.34%	14.85%	82.64%	68.27%
±2σ	-0.91%	20.11%	96.25%	95.45%
±3σ	-6.17%	25.36%	98.62%	99.73%

Descriptive Statistics

Mean	9.597%
Standard Error	0.233%
Median	8.451%
Mode	5.882%
Standard Deviation	5.255%
Sample Variance	27.612%
Kurtosis	13.52
Skewness	2.80
Range	44.152%
Minimum	2.555%
Maximum	46.707%
Count	507

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.597%	507	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 1.19. Further, an Excess Kurtosis of 7.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.45%	1	0.20%	0.20%
-17.45% to -13.20%	3	0.59%	0.79%
-13.20% to -8.94%	19	3.75%	4.54%
-8.94% to -4.69%	77	15.19%	19.72%
-4.69% to -0.43%	170	33.53%	53.25%
-0.43% to 3.82%	139	27.42%	80.67%
3.82% to 8.07%	64	12.62%	93.29%
8.07% to 12.33%	26	5.13%	98.42%
12.33% to 16.58%	5	0.99%	99.41%
Greater than 16.58%	3	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.10%	5.24%	73.77%	68.27%
±2σ	-11.78%	10.91%	96.06%	95.45%
±3σ	-17.45%	16.58%	99.21%	99.73%

Descriptive Statistics

Mean	-0.433%
Standard Error	0.252%
Median	-0.775%
Mode	0.000%
Standard Deviation	5.672%
Sample Variance	32.170%
Kurtosis	7.50
Skewness	1.19
Range	64.091%
Minimum	-20.816%
Maximum	43.275%
Count	507

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.566%	207	40.83%	1.864%
Negative	-4.043%	288	56.80%	-2.297%
Zero	0.000%	12	2.37%	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 -21.10%	1	0.59%	0.59%
-21.10% to -15.00%	1	0.59%	1.18%
-15.00% to -8.90%	11	6.51%	7.69%
-8.90% to -2.80%	25	14.79%	22.49%
-2.80% to 3.31%	43	25.44%	47.93%
3.31% to 9.41%	51	30.18%	78.11%
9.41% to 15.51%	28	16.57%	94.67%
15.51% to 21.61%	8	4.73%	99.41%
21.61% to 27.72%	0	0.00%	99.41%
Greater than 27.72%	1	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.83%	11.44%	71.01%	68.27%
±2σ	-12.97%	19.58%	95.86%	95.45%
±3σ	-21.10%	27.72%	98.82%	99.73%

Descriptive Statistics

Mean	3.307%
Standard Error	0.626%
Median	3.769%
Mode	-21.881%
Standard Deviation	8.137%
Sample Variance	66.210%
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	7.504%	117	69.23%	5.195%
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	11.69%
12	3 Years	12.67%
20	5 Years	14.28%
40	10 Years	14.20%
80	20 Years	14.03%
200	50 Years	15.08%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.11%	0	0.00%	0.00%
-7.11% to -1.24%	0	0.00%	0.00%
-1.24% to 4.64%	1	0.59%	0.59%
4.64% to 10.52%	33	19.41%	20.00%
10.52% to 16.39%	72	42.35%	62.35%
16.39% to 22.27%	39	22.94%	85.29%
22.27% to 28.15%	14	8.24%	93.53%
28.15% to 34.03%	4	2.35%	95.88%
34.03% to 39.90%	3	1.76%	97.65%
Greater than 39.90%	4	2.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.56%	24.23%	82.35%	68.27%
±2σ	0.72%	32.07%	95.29%	95.45%
±3σ	-7.11%	39.90%	97.65%	99.73%

Descriptive Statistics

Mean	16.395%
Standard Error	0.601%
Median	14.820%
Mode	17.391%
Standard Deviation	7.836%
Sample Variance	61.401%
Kurtosis	5.94
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	16.395%	170	100.00%	16.395%
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 1.03 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.11%	0	0.00%	0.00%
-25.11% to -19.22%	1	0.59%	0.59%
-19.22% to -13.33%	5	2.94%	3.53%
-13.33% to -7.43%	33	19.41%	22.94%
-7.43% 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 22.02%	3	1.76%	99.41%
Greater than 22.02%	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	-17.25%	14.17%	95.88%	95.45%
±3σ	-25.11%	22.02%	99.41%	99.73%

Descriptive Statistics

Mean	-1.543%
Standard Error	0.603%
Median	-2.492%
Mode	-10.526%
Standard Deviation	7.856%
Sample Variance	61.712%
Kurtosis	1.03
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	-6.321%	107	62.94%	-3.979%
Zero	0.000%	1	0.59%	0.000%

ATO Deep Analytical Report