AMAT - 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	3.03%	2.35%	2.59%	3.57%	3.69%	3.71%	349.62	376.41	336.95	390.56
Weekly	6.69%	5.88%	6.67%	8.62%	8.13%	8.17%	334.46	393.48	308.36	426.78
Monthly	13.25%	13.55%	13.08%	18.24%	16.91%	17.01%	306.32	429.63	258.65	508.80
Quarterly	24.62%	24.45%	23.07%	31.30%	29.30%	29.47%	270.64	486.26	201.91	651.78
Annual	—	—	—	—	58.59%	58.94%	201.91	651.78	112.38	1171.05
Option Time Horizon	—	—	—	—	22.12%	22.25%	290.79	452.56	233.09	564.59

Calculation Notes: Computed at 2026-03-23T16:32 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $362.77 | Strike (K): $370.00 (first OTM call ≥ spot) | Observed Mid-Price: $29.5750 (Bid $28.8000 / Ask $30.3500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.52% | Binomial IV (Annual): 58.59% (CRR binomial tree, American, n=20 steps) | BS IV: 58.79% (European Black-Scholes) | Yahoo IV (Annual): 58.94% → 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
2026-02-19	$0.4600
2025-11-20	$0.4600
2025-08-21	$0.4600
2025-05-22	$0.4600
2025-02-20	$0.4000
2024-11-21	$0.4000
2024-08-22	$0.4000
2024-05-22	$0.4000
2024-02-21	$0.3200
2023-11-22	$0.3200
2023-08-23	$0.3200
2023-05-24	$0.3200
2023-02-22	$0.2600
2022-11-23	$0.2600
2022-08-24	$0.2600
2022-05-25	$0.2600
2022-02-22	$0.2400
2021-11-24	$0.2400
2021-08-25	$0.2400
2021-05-26	$0.2400
2021-02-24	$0.2200
2020-11-18	$0.2200
2020-08-19	$0.2200
2020-05-20	$0.2200
2020-02-18	$0.2100
2019-11-20	$0.2100
2019-08-21	$0.2100
2019-05-22	$0.2100
2019-02-20	$0.2000
2018-11-21	$0.2000
2018-08-22	$0.2000
2018-05-23	$0.2000
2018-02-20	$0.1000
2017-11-22	$0.1000
2017-08-22	$0.1000
2017-05-23	$0.1000
2017-02-17	$0.1000
2016-11-22	$0.1000
2016-08-23	$0.1000
2016-05-24	$0.1000
2016-02-23	$0.1000
2015-11-17	$0.1000
2015-08-18	$0.1000
2015-05-19	$0.1000
2015-02-13	$0.1000
2014-11-18	$0.1000
2014-08-19	$0.1000
2014-05-20	$0.1000
2014-02-14	$0.1000
2013-11-19	$0.1000
2013-08-20	$0.1000
2013-05-21	$0.1000
2013-02-15	$0.0900
2012-11-19	$0.0900
2012-08-21	$0.0900
2012-05-22	$0.0900
2012-02-21	$0.0800
2011-11-21	$0.0800
2011-08-29	$0.0800
2011-05-27	$0.0800
2011-02-28	$0.0700
2010-11-22	$0.0700
2010-08-23	$0.0700
2010-05-24	$0.0700
2010-02-22	$0.0600
2009-11-09	$0.0600
2009-08-11	$0.0600
2009-05-12	$0.0600
2009-02-10	$0.0600
2008-11-10	$0.0600
2008-08-12	$0.0600
2008-05-13	$0.0600
2008-02-12	$0.0600
2007-11-13	$0.0600
2007-08-14	$0.0600
2007-05-15	$0.0600
2007-02-13	$0.0500
2006-11-14	$0.0500
2006-08-15	$0.0500
2006-05-16	$0.0500
2006-02-14	$0.0300
2005-11-15	$0.0300
2005-08-15	$0.0300
2005-05-16	$0.0300

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of 3.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.98%	59	0.51%	0.51%
-8.98% to -6.71%	136	1.18%	1.69%
-6.71% to -4.43%	455	3.95%	5.64%
-4.43% to -2.16%	1409	12.23%	17.87%
-2.16% to 0.12%	4066	35.29%	53.16%
0.12% to 2.40%	3349	29.07%	82.23%
2.40% to 4.67%	1364	11.84%	94.07%
4.67% to 6.95%	435	3.78%	97.85%
6.95% to 9.22%	165	1.43%	99.28%
Greater than 9.22%	83	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.91%	3.15%	75.77%	68.27%
±2σ	-5.95%	6.19%	94.51%	95.45%
±3σ	-8.98%	9.22%	98.77%	99.73%

Descriptive Statistics

Mean	0.120%
Standard Error	0.028%
Median	0.000%
Mode	0.000%
Standard Deviation	3.034%
Sample Variance	9.203%
Kurtosis	3.99
Skewness	0.29
Range	47.407%
Minimum	-21.774%
Maximum	25.633%
Count	11521

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.367%	5550	48.17%	1.140%
Negative	-2.207%	5325	46.22%	-1.020%
Zero	0.000%	646	5.61%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.07%
20	1 Month	4.56%
60	1 Quarter	4.47%
250	1 Year	3.78%
750	3 Years	3.37%
1,250	5 Years	3.57%
2,500	10 Years	3.34%
5,000	20 Years	3.13%
12,500	50 Years	3.87%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.15. Further, an Excess Kurtosis of 8.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.45%	0	0.00%	0.00%
-3.45% to -1.69%	0	0.00%	0.00%
-1.69% to 0.08%	0	0.00%	0.00%
0.08% to 1.84%	2330	20.22%	20.22%
1.84% to 3.60%	4865	42.22%	62.45%
3.60% to 5.36%	2393	20.77%	83.21%
5.36% to 7.12%	1051	9.12%	92.34%
7.12% to 8.88%	474	4.11%	96.45%
8.88% to 10.65%	202	1.75%	98.20%
Greater than 10.65%	207	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.25%	5.95%	81.20%	68.27%
±2σ	-1.10%	8.30%	95.50%	95.45%
±3σ	-3.45%	10.65%	98.20%	99.73%

Descriptive Statistics

Mean	3.600%
Standard Error	0.022%
Median	2.985%
Mode	2.500%
Standard Deviation	2.349%
Sample Variance	5.517%
Kurtosis	8.04
Skewness	2.15
Range	27.367%
Minimum	0.357%
Maximum	27.724%
Count	11522

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.600%	11522	100.00%	3.600%
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 Fairly Symmetrical with a Skewness factor of 0.09. Further, an Excess Kurtosis of 3.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.66%	84	0.73%	0.73%
-7.66% to -5.72%	148	1.28%	2.01%
-5.72% to -3.78%	418	3.63%	5.64%
-3.78% to -1.84%	1357	11.78%	17.42%
-1.84% to 0.10%	4204	36.49%	53.91%
0.10% to 2.04%	3324	28.85%	82.75%
2.04% to 3.98%	1325	11.50%	94.25%
3.98% to 5.92%	416	3.61%	97.86%
5.92% to 7.86%	155	1.35%	99.21%
Greater than 7.86%	91	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.49%	2.69%	76.31%	68.27%
±2σ	-5.08%	5.27%	94.24%	95.45%
±3σ	-7.66%	7.86%	98.48%	99.73%

Descriptive Statistics

Mean	0.099%
Standard Error	0.024%
Median	0.000%
Mode	0.000%
Standard Deviation	2.587%
Sample Variance	6.695%
Kurtosis	3.82
Skewness	0.09
Range	42.935%
Minimum	-21.285%
Maximum	21.650%
Count	11522

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.026%	5429	47.12%	0.955%
Negative	-1.961%	5027	43.63%	-0.856%
Zero	0.000%	1066	9.25%	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 2.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.50%	12	0.50%	0.50%
-19.50% to -14.48%	28	1.17%	1.67%
-14.48% to -9.46%	99	4.12%	5.79%
-9.46% to -4.44%	330	13.75%	19.54%
-4.44% to 0.58%	749	31.21%	50.75%
0.58% to 5.60%	746	31.08%	81.83%
5.60% to 10.62%	297	12.38%	94.21%
10.62% to 15.64%	88	3.67%	97.88%
15.64% to 20.66%	33	1.38%	99.25%
Greater than 20.66%	18	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.11%	7.28%	73.29%	68.27%
±2σ	-12.80%	13.97%	94.83%	95.45%
±3σ	-19.50%	20.66%	98.75%	99.73%

Descriptive Statistics

Mean	0.583%
Standard Error	0.137%
Median	0.461%
Mode	0.000%
Standard Deviation	6.693%
Sample Variance	44.790%
Kurtosis	2.79
Skewness	0.07
Range	81.252%
Minimum	-48.947%
Maximum	32.305%
Count	2400

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.219%	1271	52.96%	2.764%
Negative	-4.847%	1080	45.00%	-2.181%
Zero	0.000%	49	2.04%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.30%
12	1 Quarter	10.85%
52	1 Year	9.15%
156	3 Years	8.23%
260	5 Years	8.62%
520	10 Years	8.06%
1,040	20 Years	7.31%
2,600	50 Years	9.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.22. Further, an Excess Kurtosis of 11.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.99%	0	0.00%	0.00%
-7.99% to -3.58%	0	0.00%	0.00%
-3.58% to 0.83%	0	0.00%	0.00%
0.83% to 5.25%	501	20.87%	20.87%
5.25% to 9.66%	968	40.32%	61.18%
9.66% to 14.07%	521	21.70%	82.88%
14.07% to 18.48%	235	9.79%	92.67%
18.48% to 22.89%	96	4.00%	96.67%
22.89% to 27.31%	37	1.54%	98.21%
Greater than 27.31%	43	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.77%	15.54%	79.43%	68.27%
±2σ	-2.11%	21.42%	95.71%	95.45%
±3σ	-7.99%	27.31%	98.21%	99.73%

Descriptive Statistics

Mean	9.658%
Standard Error	0.120%
Median	8.204%
Mode	6.667%
Standard Deviation	5.883%
Sample Variance	34.606%
Kurtosis	11.06
Skewness	2.22
Range	75.989%
Minimum	1.094%
Maximum	77.083%
Count	2401

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.658%	2401	100.00%	9.658%
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 1.08. Further, an Excess Kurtosis of 8.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.93%	6	0.25%	0.25%
-19.93% to -14.93%	26	1.08%	1.33%
-14.93% to -9.93%	80	3.33%	4.66%
-9.93% to -4.93%	322	13.41%	18.08%
-4.93% to 0.07%	848	35.32%	53.39%
0.07% to 5.08%	696	28.99%	82.38%
5.08% to 10.08%	278	11.58%	93.96%
10.08% to 15.08%	92	3.83%	97.79%
15.08% to 20.08%	30	1.25%	99.04%
Greater than 20.08%	23	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.59%	6.74%	75.30%	68.27%
±2σ	-13.26%	13.41%	95.04%	95.45%
±3σ	-19.93%	20.08%	98.79%	99.73%

Descriptive Statistics

Mean	0.075%
Standard Error	0.136%
Median	-0.226%
Mode	0.000%
Standard Deviation	6.668%
Sample Variance	44.457%
Kurtosis	8.51
Skewness	1.08
Range	99.477%
Minimum	-24.219%
Maximum	75.258%
Count	2401

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.210%	1128	46.98%	2.448%
Negative	-4.674%	1219	50.77%	-2.373%
Zero	0.000%	54	2.25%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.40. Further, an Excess Kurtosis of 0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.33%	1	0.18%	0.18%
-37.33% to -27.40%	3	0.54%	0.72%
-27.40% to -17.46%	24	4.35%	5.07%
-17.46% to -7.52%	88	15.94%	21.01%
-7.52% to 2.42%	177	32.07%	53.08%
2.42% to 12.35%	146	26.45%	79.53%
12.35% to 22.29%	73	13.22%	92.75%
22.29% to 32.23%	23	4.17%	96.92%
32.23% to 42.17%	14	2.54%	99.46%
Greater than 42.17%	3	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.83%	15.67%	73.01%	68.27%
±2σ	-24.08%	28.92%	94.20%	95.45%
±3σ	-37.33%	42.17%	99.28%	99.73%

Descriptive Statistics

Mean	2.416%
Standard Error	0.564%
Median	1.544%
Mode	0.000%
Standard Deviation	13.250%
Sample Variance	175.570%
Kurtosis	0.77
Skewness	0.40
Range	95.031%
Minimum	-47.008%
Maximum	48.023%
Count	552

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.952%	295	53.44%	6.387%
Negative	-8.632%	254	46.01%	-3.972%
Zero	0.000%	3	0.54%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	27.45%
12	1 Year	21.73%
36	3 Years	18.43%
60	5 Years	18.24%
120	10 Years	17.50%
240	20 Years	15.70%
600	50 Years	20.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.78. Further, an Excess Kurtosis of 51.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.09%	0	0.00%	0.00%
-18.09% to -7.93%	0	0.00%	0.00%
-7.93% to 2.23%	0	0.00%	0.00%
2.23% to 12.39%	85	15.37%	15.37%
12.39% to 22.55%	243	43.94%	59.31%
22.55% to 32.72%	148	26.76%	86.08%
32.72% to 42.88%	44	7.96%	94.03%
42.88% to 53.04%	20	3.62%	97.65%
53.04% to 63.20%	7	1.27%	98.92%
Greater than 63.20%	6	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.00%	36.10%	84.09%	68.27%
±2σ	-4.54%	49.65%	96.56%	95.45%
±3σ	-18.09%	63.20%	98.92%	99.73%

Descriptive Statistics

Mean	22.554%
Standard Error	0.576%
Median	19.431%
Mode	19.048%
Standard Deviation	13.549%
Sample Variance	183.581%
Kurtosis	51.23
Skewness	4.78
Range	191.772%
Minimum	6.006%
Maximum	197.778%
Count	553

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.554%	553	100.00%	22.554%
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 0.89. Further, an Excess Kurtosis of 4.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.62%	0	0.00%	0.00%
-39.62% to -29.81%	3	0.54%	0.54%
-29.81% to -20.00%	25	4.52%	5.06%
-20.00% to -10.20%	88	15.91%	20.98%
-10.20% to -0.39%	172	31.10%	52.08%
-0.39% to 9.42%	160	28.93%	81.01%
9.42% to 19.23%	68	12.30%	93.31%
19.23% to 29.04%	27	4.88%	98.19%
29.04% to 38.84%	6	1.08%	99.28%
Greater than 38.84%	4	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.46%	12.69%	74.50%	68.27%
±2σ	-26.54%	25.77%	95.48%	95.45%
±3σ	-39.62%	38.84%	99.28%	99.73%

Descriptive Statistics

Mean	-0.387%
Standard Error	0.556%
Median	-1.060%
Mode	0.000%
Standard Deviation	13.077%
Sample Variance	171.006%
Kurtosis	4.19
Skewness	0.89
Range	120.855%
Minimum	-32.146%
Maximum	88.709%
Count	553

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.189%	259	46.84%	4.772%
Negative	-9.805%	291	52.62%	-5.160%
Zero	0.000%	3	0.54%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.65. Further, an Excess Kurtosis of 0.74 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -66.37%	0	0.00%	0.00%
-66.37% to -47.91%	1	0.54%	0.54%
-47.91% to -29.44%	7	3.80%	4.35%
-29.44% to -10.98%	33	17.93%	22.28%
-10.98% to 7.48%	60	32.61%	54.89%
7.48% to 25.95%	47	25.54%	80.43%
25.95% to 44.41%	20	10.87%	91.30%
44.41% to 62.88%	9	4.89%	96.20%
62.88% to 81.34%	5	2.72%	98.91%
Greater than 81.34%	2	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.13%	32.10%	74.46%	68.27%
±2σ	-41.75%	56.72%	94.02%	95.45%
±3σ	-66.37%	81.34%	98.91%	99.73%

Descriptive Statistics

Mean	7.484%
Standard Error	1.815%
Median	5.476%
Mode	-4.545%
Standard Deviation	24.619%
Sample Variance	606.102%
Kurtosis	0.74
Skewness	0.65
Range	136.401%
Minimum	-49.640%
Maximum	86.761%
Count	184

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.394%	109	59.24%	13.266%
Negative	-14.185%	75	40.76%	-5.782%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	44.53%
12	3 Years	34.09%
20	5 Years	31.30%
40	10 Years	32.28%
80	20 Years	27.88%
200	50 Years	35.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.04. Further, an Excess Kurtosis of 8.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.89%	0	0.00%	0.00%
-29.89% to -11.55%	0	0.00%	0.00%
-11.55% to 6.78%	0	0.00%	0.00%
6.78% to 25.12%	41	22.16%	22.16%
25.12% to 43.45%	73	39.46%	61.62%
43.45% to 61.79%	39	21.08%	82.70%
61.79% to 80.12%	17	9.19%	91.89%
80.12% to 98.46%	10	5.41%	97.30%
98.46% to 116.79%	3	1.62%	98.92%
Greater than 116.79%	2	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.00%	67.90%	78.38%	68.27%
±2σ	-5.44%	92.35%	96.76%	95.45%
±3σ	-29.89%	116.79%	98.92%	99.73%

Descriptive Statistics

Mean	43.452%
Standard Error	1.797%
Median	37.727%
Mode	24.211%
Standard Deviation	24.447%
Sample Variance	597.638%
Kurtosis	8.09
Skewness	2.04
Range	187.534%
Minimum	10.244%
Maximum	197.778%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.452%	185	100.00%	43.452%
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 0.97. Further, an Excess Kurtosis of 1.97 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -70.84%	0	0.00%	0.00%
-70.84% to -53.54%	0	0.00%	0.00%
-53.54% to -36.23%	8	4.32%	4.32%
-36.23% to -18.93%	31	16.76%	21.08%
-18.93% to -1.62%	63	34.05%	55.14%
-1.62% to 15.68%	50	27.03%	82.16%
15.68% to 32.98%	16	8.65%	90.81%
32.98% to 50.29%	12	6.49%	97.30%
50.29% to 67.59%	3	1.62%	98.92%
Greater than 67.59%	2	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.70%	21.45%	75.14%	68.27%
±2σ	-47.77%	44.52%	95.68%	95.45%
±3σ	-70.84%	67.59%	98.92%	99.73%

Descriptive Statistics

Mean	-1.625%
Standard Error	1.696%
Median	-4.615%
Mode	4.762%
Standard Deviation	23.073%
Sample Variance	532.345%
Kurtosis	1.97
Skewness	0.97
Range	143.472%
Minimum	-46.329%
Maximum	97.143%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.991%	77	41.62%	7.904%
Negative	-16.324%	108	58.38%	-9.530%
Zero	0.000%	0	0.00%	0.000%

AMAT Deep Analytical Report