ASO - 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	2.97%	2.30%	2.69%	4.20%	2.91%	3.15%	57.09	60.52	55.46	62.30
Weekly	6.45%	5.34%	6.20%	9.85%	6.40%	6.92%	55.13	62.67	51.71	66.81
Monthly	11.52%	8.56%	11.18%	20.21%	13.33%	14.41%	51.44	67.16	45.02	76.74
Quarterly	21.00%	17.00%	17.94%	34.64%	23.09%	24.96%	46.66	74.05	37.04	93.28
Annual	—	—	—	—	46.19%	49.93%	37.04	93.28	23.34	148.04
Option Time Horizon	—	—	—	—	17.76%	19.20%	49.21	70.21	41.20	83.86

Calculation Notes: Computed at 2026-02-22T14:21 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $58.78 | Strike (K): $60.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.7500 (Bid $3.5000 / Ask $4.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.88% | Binomial IV (Annual): 46.19% (CRR binomial tree, American, n=20 steps) | BS IV: 46.48% (European Black-Scholes) | Yahoo IV (Annual): 49.93% → 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
2025-12-18	$0.1300
2025-09-11	$0.1300
2025-06-18	$0.1300
2025-03-25	$0.1300
2024-12-18	$0.1100
2024-09-19	$0.1100
2024-06-20	$0.1100
2024-03-25	$0.1100
2023-12-12	$0.0900
2023-09-12	$0.0900
2023-06-14	$0.0900
2023-03-22	$0.0900
2022-12-19	$0.0750
2022-09-14	$0.0750
2022-06-15	$0.0750
2022-03-16	$0.0750

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.44. Further, an Excess Kurtosis of 4.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.76%	5	0.37%	0.37%
-8.76% to -6.53%	13	0.96%	1.33%
-6.53% to -4.30%	41	3.03%	4.37%
-4.30% to -2.07%	199	14.73%	19.10%
-2.07% to 0.16%	455	33.68%	52.78%
0.16% to 2.39%	379	28.05%	80.83%
2.39% to 4.62%	180	13.32%	94.15%
4.62% to 6.84%	52	3.85%	98.00%
6.84% to 9.07%	16	1.18%	99.19%
Greater than 9.07%	11	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.81%	3.13%	74.69%	68.27%
±2σ	-5.78%	6.10%	96.00%	95.45%
±3σ	-8.76%	9.07%	98.82%	99.73%

Descriptive Statistics

Mean	0.158%
Standard Error	0.081%
Median	-0.037%
Mode	2.533%
Standard Deviation	2.971%
Sample Variance	8.826%
Kurtosis	4.01
Skewness	0.44
Range	35.980%
Minimum	-17.699%
Maximum	18.281%
Count	1351

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.373%	669	49.52%	1.175%
Negative	-2.024%	679	50.26%	-1.017%
Zero	0.000%	3	0.22%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.03%
20	1 Month	4.07%
60	1 Quarter	4.27%
250	1 Year	4.32%
750	3 Years	3.73%
1,250	5 Years	4.20%
2,500	10 Years	4.33%
5,000	20 Years	4.33%
12,500	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 2.78. Further, an Excess Kurtosis of 14.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.68%	0	0.00%	0.00%
-2.68% to -0.95%	0	0.00%	0.00%
-0.95% to 0.77%	0	0.00%	0.00%
0.77% to 2.49%	234	17.31%	17.31%
2.49% to 4.21%	629	46.52%	63.83%
4.21% to 5.94%	284	21.01%	84.84%
5.94% to 7.66%	113	8.36%	93.20%
7.66% to 9.38%	50	3.70%	96.89%
9.38% to 11.11%	14	1.04%	97.93%
Greater than 11.11%	28	2.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.92%	6.51%	83.06%	68.27%
±2σ	-0.38%	8.81%	95.71%	95.45%
±3σ	-2.68%	11.11%	97.93%	99.73%

Descriptive Statistics

Mean	4.215%
Standard Error	0.062%
Median	3.687%
Mode	4.050%
Standard Deviation	2.297%
Sample Variance	5.276%
Kurtosis	14.10
Skewness	2.78
Range	23.082%
Minimum	1.101%
Maximum	24.183%
Count	1352

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.215%	1352	100.00%	4.215%
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 -0.19. Further, an Excess Kurtosis of 4.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.04%	5	0.37%	0.37%
-8.04% to -6.02%	15	1.11%	1.48%
-6.02% to -4.01%	46	3.40%	4.88%
-4.01% to -1.99%	209	15.46%	20.34%
-1.99% to 0.02%	388	28.70%	49.04%
0.02% to 2.04%	433	32.03%	81.07%
2.04% to 4.05%	181	13.39%	94.45%
4.05% to 6.07%	56	4.14%	98.59%
6.07% to 8.08%	10	0.74%	99.33%
Greater than 8.08%	9	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.66%	2.71%	74.19%	68.27%
±2σ	-5.35%	5.39%	95.41%	95.45%
±3σ	-8.04%	8.08%	98.96%	99.73%

Descriptive Statistics

Mean	0.022%
Standard Error	0.073%
Median	0.080%
Mode	0.000%
Standard Deviation	2.686%
Sample Variance	7.214%
Kurtosis	4.13
Skewness	-0.19
Range	32.975%
Minimum	-18.893%
Maximum	14.082%
Count	1352

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.970%	692	51.18%	1.008%
Negative	-2.039%	654	48.37%	-0.986%
Zero	0.000%	6	0.44%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.45. Further, an Excess Kurtosis of 1.58 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.61%	1	0.36%	0.36%
-18.61% to -13.77%	1	0.36%	0.71%
-13.77% to -8.93%	11	3.91%	4.63%
-8.93% to -4.09%	56	19.93%	24.56%
-4.09% to 0.75%	80	28.47%	53.02%
0.75% to 5.59%	69	24.56%	77.58%
5.59% to 10.43%	46	16.37%	93.95%
10.43% to 15.27%	14	4.98%	98.93%
15.27% to 20.11%	1	0.36%	99.29%
Greater than 20.11%	2	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.70%	7.20%	72.60%	68.27%
±2σ	-12.15%	13.65%	96.09%	95.45%
±3σ	-18.61%	20.11%	98.93%	99.73%

Descriptive Statistics

Mean	0.749%
Standard Error	0.385%
Median	0.306%
Mode	0.434%
Standard Deviation	6.452%
Sample Variance	41.623%
Kurtosis	1.58
Skewness	0.45
Range	50.829%
Minimum	-20.215%
Maximum	30.614%
Count	281

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.579%	145	51.60%	2.879%
Negative	-4.432%	135	48.04%	-2.129%
Zero	0.000%	1	0.36%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.62%
12	1 Quarter	8.39%
52	1 Year	10.18%
156	3 Years	8.87%
260	5 Years	9.85%
520	10 Years	10.04%
1,040	20 Years	10.04%
2,600	50 Years	10.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.30. Further, an Excess Kurtosis of 8.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.53%	0	0.00%	0.00%
-5.53% to -1.52%	0	0.00%	0.00%
-1.52% to 2.49%	0	0.00%	0.00%
2.49% to 6.49%	52	18.44%	18.44%
6.49% to 10.50%	120	42.55%	60.99%
10.50% to 14.50%	69	24.47%	85.46%
14.50% to 18.51%	20	7.09%	92.55%
18.51% to 22.51%	10	3.55%	96.10%
22.51% to 26.52%	7	2.48%	98.58%
Greater than 26.52%	4	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.16%	15.84%	81.91%	68.27%
±2σ	-0.19%	21.18%	96.10%	95.45%
±3σ	-5.53%	26.52%	98.58%	99.73%

Descriptive Statistics

Mean	10.497%
Standard Error	0.318%
Median	9.245%
Mode	7.576%
Standard Deviation	5.341%
Sample Variance	28.522%
Kurtosis	8.12
Skewness	2.30
Range	37.722%
Minimum	2.830%
Maximum	40.552%
Count	282

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.497%	282	100.00%	10.497%
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 0.11. Further, an Excess Kurtosis of 1.30 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.82%	2	0.71%	0.71%
-18.82% to -14.18%	2	0.71%	1.42%
-14.18% to -9.53%	11	3.90%	5.32%
-9.53% to -4.88%	51	18.09%	23.40%
-4.88% to -0.23%	69	24.47%	47.87%
-0.23% to 4.42%	90	31.91%	79.79%
4.42% to 9.07%	41	14.54%	94.33%
9.07% to 13.71%	13	4.61%	98.94%
13.71% to 18.36%	1	0.35%	99.29%
Greater than 18.36%	2	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.43%	5.97%	70.92%	68.27%
±2σ	-12.63%	12.17%	96.81%	95.45%
±3σ	-18.83%	18.36%	98.58%	99.73%

Descriptive Statistics

Mean	-0.231%
Standard Error	0.369%
Median	-0.039%
Mode	-1.506%
Standard Deviation	6.198%
Sample Variance	38.417%
Kurtosis	1.30
Skewness	0.11
Range	47.340%
Minimum	-21.893%
Maximum	25.447%
Count	282

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.614%	140	49.65%	2.291%
Negative	-5.043%	141	50.00%	-2.522%
Zero	0.000%	1	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.06. Further, an Excess Kurtosis of -0.54 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.69%	0	0.00%	0.00%
-31.69% to -23.05%	0	0.00%	0.00%
-23.05% to -14.40%	3	4.69%	4.69%
-14.40% to -5.76%	13	20.31%	25.00%
-5.76% to 2.88%	15	23.44%	48.44%
2.88% to 11.52%	18	28.12%	76.56%
11.52% to 20.16%	11	17.19%	93.75%
20.16% to 28.80%	3	4.69%	98.44%
28.80% to 37.45%	1	1.56%	100.00%
Greater than 37.45%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.64%	14.40%	65.62%	68.27%
±2σ	-20.16%	25.92%	95.31%	95.45%
±3σ	-31.69%	37.45%	100.00%	99.73%

Descriptive Statistics

Mean	2.880%
Standard Error	1.440%
Median	3.754%
Mode	-22.922%
Standard Deviation	11.522%
Sample Variance	132.755%
Kurtosis	-0.54
Skewness	0.06
Range	52.872%
Minimum	-22.922%
Maximum	29.950%
Count	64

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.701%	38	59.38%	6.354%
Negative	-8.552%	26	40.62%	-3.474%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.76%
12	1 Year	20.45%
36	3 Years	18.68%
60	5 Years	20.21%
120	10 Years	20.73%
240	20 Years	20.73%
600	50 Years	20.73%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.39. Further, an Excess Kurtosis of 3.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.63%	0	0.00%	0.00%
-2.63% to 3.79%	0	0.00%	0.00%
3.79% to 10.21%	0	0.00%	0.00%
10.21% to 16.63%	13	20.00%	20.00%
16.63% to 23.05%	26	40.00%	60.00%
23.05% to 29.47%	14	21.54%	81.54%
29.47% to 35.90%	7	10.77%	92.31%
35.90% to 42.32%	3	4.62%	96.92%
42.32% to 48.74%	1	1.54%	98.46%
Greater than 48.74%	1	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.49%	31.62%	72.31%	68.27%
±2σ	5.93%	40.18%	96.92%	95.45%
±3σ	-2.63%	48.74%	98.46%	99.73%

Descriptive Statistics

Mean	23.053%
Standard Error	1.062%
Median	22.023%
Mode	10.627%
Standard Deviation	8.562%
Sample Variance	73.314%
Kurtosis	3.49
Skewness	1.39
Range	47.899%
Minimum	10.627%
Maximum	58.526%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.053%	65	100.00%	23.053%
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 0.49. Further, an Excess Kurtosis of -0.20 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.17%	0	0.00%	0.00%
-35.17% to -26.78%	0	0.00%	0.00%
-26.78% to -18.40%	2	3.08%	3.08%
-18.40% to -10.01%	13	20.00%	23.08%
-10.01% to -1.63%	21	32.31%	55.38%
-1.63% to 6.76%	14	21.54%	76.92%
6.76% to 15.14%	10	15.38%	92.31%
15.14% to 23.53%	4	6.15%	98.46%
23.53% to 31.91%	1	1.54%	100.00%
Greater than 31.91%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.81%	9.55%	67.69%	68.27%
±2σ	-23.99%	20.73%	96.92%	95.45%
±3σ	-35.17%	31.91%	100.00%	99.73%

Descriptive Statistics

Mean	-1.629%
Standard Error	1.387%
Median	-3.045%
Mode	-21.379%
Standard Deviation	11.180%
Sample Variance	124.982%
Kurtosis	-0.20
Skewness	0.49
Range	51.383%
Minimum	-21.379%
Maximum	30.004%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.698%	26	40.00%	3.879%
Negative	-9.180%	39	60.00%	-5.508%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.30. Further, an Excess Kurtosis of -0.65 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.40%	0	0.00%	0.00%
-54.40% to -38.66%	0	0.00%	0.00%
-38.66% to -22.91%	2	9.09%	9.09%
-22.91% to -7.16%	1	4.55%	13.64%
-7.16% to 8.59%	9	40.91%	54.55%
8.59% to 24.34%	5	22.73%	77.27%
24.34% to 40.08%	2	9.09%	86.36%
40.08% to 55.83%	3	13.64%	100.00%
55.83% to 71.58%	0	0.00%	100.00%
Greater than 71.58%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.41%	29.58%	68.18%	68.27%
±2σ	-33.41%	50.58%	100.00%	95.45%
±3σ	-54.40%	71.58%	100.00%	99.73%

Descriptive Statistics

Mean	8.587%
Standard Error	4.477%
Median	4.953%
Mode	-27.779%
Standard Deviation	20.997%
Sample Variance	440.885%
Kurtosis	-0.65
Skewness	0.30
Range	74.038%
Minimum	-27.779%
Maximum	46.259%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.946%	13	59.09%	12.968%
Negative	-10.709%	9	40.91%	-4.381%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.91%
12	3 Years	33.15%
20	5 Years	34.64%
40	10 Years	37.73%
80	20 Years	37.73%
200	50 Years	37.73%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.46. Further, an Excess Kurtosis of 0.11 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.79%	0	0.00%	0.00%
-7.79% to 4.96%	0	0.00%	0.00%
4.96% to 17.71%	1	4.35%	4.35%
17.71% to 30.46%	5	21.74%	26.09%
30.46% to 43.21%	6	26.09%	52.17%
43.21% to 55.96%	6	26.09%	78.26%
55.96% to 68.71%	3	13.04%	91.30%
68.71% to 81.46%	2	8.70%	100.00%
81.46% to 94.21%	0	0.00%	100.00%
Greater than 94.21%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	26.21%	60.21%	65.22%	68.27%
±2σ	9.21%	77.21%	95.65%	95.45%
±3σ	-7.79%	94.21%	100.00%	99.73%

Descriptive Statistics

Mean	43.210%
Standard Error	3.545%
Median	42.120%
Mode	12.606%
Standard Deviation	17.000%
Sample Variance	288.997%
Kurtosis	0.11
Skewness	0.46
Range	67.434%
Minimum	12.606%
Maximum	80.040%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.210%	23	100.00%	43.210%
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 0.56. Further, an Excess Kurtosis of 0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.87%	0	0.00%	0.00%
-58.87% to -45.41%	0	0.00%	0.00%
-45.41% to -31.95%	0	0.00%	0.00%
-31.95% to -18.50%	5	21.74%	21.74%
-18.50% to -5.04%	7	30.43%	52.17%
-5.04% to 8.42%	7	30.43%	82.61%
8.42% to 21.88%	2	8.70%	91.30%
21.88% to 35.33%	2	8.70%	100.00%
35.33% to 48.79%	0	0.00%	100.00%
Greater than 48.79%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.98%	12.90%	69.57%	68.27%
±2σ	-40.93%	30.85%	91.30%	95.45%
±3σ	-58.87%	48.79%	100.00%	99.73%

Descriptive Statistics

Mean	-5.039%
Standard Error	3.741%
Median	-6.550%
Mode	-30.279%
Standard Deviation	17.943%
Sample Variance	321.936%
Kurtosis	0.03
Skewness	0.56
Range	65.205%
Minimum	-30.279%
Maximum	34.926%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.911%	9	39.13%	5.052%
Negative	-16.579%	14	60.87%	-10.092%
Zero	0.000%	0	0.00%	0.000%

ASO Deep Analytical Report