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	2.98%	2.29%	2.69%	4.16%	2.71%	3.29%	51.58	54.45	50.21	55.95
Weekly	6.43%	5.31%	6.16%	9.80%	5.96%	7.25%	49.93	56.26	47.04	59.71
Monthly	11.59%	8.46%	11.22%	20.23%	12.41%	15.10%	46.82	60.00	41.35	67.93
Quarterly	21.17%	16.11%	18.04%	35.19%	21.49%	26.15%	42.75	65.71	34.48	81.46
Annual	—	—	—	—	42.98%	52.30%	34.48	81.46	22.44	125.20
Option Time Horizon	—	—	—	—	16.22%	19.74%	45.06	62.34	38.31	73.31

Calculation Notes: Computed at 2026-03-23T16:37 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $53.00 | Strike (K): $55.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.7000 (Bid $2.0000 / Ask $3.4000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.04% | Binomial IV (Annual): 42.98% (CRR binomial tree, American, n=20 steps) | BS IV: 43.51% (European Black-Scholes) | Yahoo IV (Annual): 52.30% → 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
2026-03-20	$0.1500
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 0.40. Further, an Excess Kurtosis of 4.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.78%	6	0.44%	0.44%
-8.78% to -6.55%	13	0.95%	1.38%
-6.55% to -4.32%	41	2.99%	4.37%
-4.32% to -2.08%	199	14.50%	18.88%
-2.08% to 0.15%	463	33.75%	52.62%
0.15% to 2.38%	389	28.35%	80.98%
2.38% to 4.61%	182	13.27%	94.24%
4.61% to 6.84%	52	3.79%	98.03%
6.84% to 9.08%	16	1.17%	99.20%
Greater than 9.08%	11	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.83%	3.12%	74.78%	68.27%
±2σ	-5.80%	6.10%	96.06%	95.45%
±3σ	-8.78%	9.08%	98.76%	99.73%

Descriptive Statistics

Mean	0.149%
Standard Error	0.080%
Median	-0.034%
Mode	2.533%
Standard Deviation	2.976%
Sample Variance	8.857%
Kurtosis	4.05
Skewness	0.40
Range	35.980%
Minimum	-17.699%
Maximum	18.281%
Count	1372

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.360%	680	49.56%	1.170%
Negative	-2.033%	689	50.22%	-1.021%
Zero	0.000%	3	0.22%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.26%
20	1 Month	4.69%
60	1 Quarter	4.43%
250	1 Year	4.34%
750	3 Years	3.76%
1,250	5 Years	4.16%
2,500	10 Years	4.34%
5,000	20 Years	4.34%
12,500	50 Years	4.34%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.65%	0	0.00%	0.00%
-2.65% to -0.93%	0	0.00%	0.00%
-0.93% to 0.79%	0	0.00%	0.00%
0.79% to 2.50%	242	17.63%	17.63%
2.50% to 4.22%	631	45.96%	63.58%
4.22% to 5.94%	294	21.41%	85.00%
5.94% to 7.66%	112	8.16%	93.15%
7.66% to 9.37%	50	3.64%	96.80%
9.37% to 11.09%	16	1.17%	97.96%
Greater than 11.09%	28	2.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.93%	6.51%	83.10%	68.27%
±2σ	-0.36%	8.80%	95.63%	95.45%
±3σ	-2.65%	11.09%	97.96%	99.73%

Descriptive Statistics

Mean	4.221%
Standard Error	0.062%
Median	3.696%
Mode	4.050%
Standard Deviation	2.289%
Sample Variance	5.240%
Kurtosis	14.09
Skewness	2.78
Range	23.082%
Minimum	1.101%
Maximum	24.183%
Count	1373

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.221%	1373	100.00%	4.221%
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 -0.17. Further, an Excess Kurtosis of 4.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.03%	5	0.36%	0.36%
-8.03% to -6.02%	15	1.09%	1.46%
-6.02% to -4.00%	47	3.42%	4.88%
-4.00% to -1.99%	213	15.51%	20.39%
-1.99% to 0.02%	395	28.77%	49.16%
0.02% to 2.04%	438	31.90%	81.06%
2.04% to 4.05%	184	13.40%	94.46%
4.05% to 6.06%	56	4.08%	98.54%
6.06% to 8.08%	10	0.73%	99.27%
Greater than 8.08%	10	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.66%	2.71%	74.07%	68.27%
±2σ	-5.35%	5.39%	95.41%	95.45%
±3σ	-8.03%	8.08%	98.91%	99.73%

Descriptive Statistics

Mean	0.022%
Standard Error	0.072%
Median	0.067%
Mode	0.000%
Standard Deviation	2.685%
Sample Variance	7.211%
Kurtosis	4.10
Skewness	-0.17
Range	32.975%
Minimum	-18.893%
Maximum	14.082%
Count	1373

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.975%	701	51.06%	1.008%
Negative	-2.032%	666	48.51%	-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 0.47. Further, an Excess Kurtosis of 1.60 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.59%	1	0.35%	0.35%
-18.59% to -13.76%	1	0.35%	0.70%
-13.76% to -8.94%	11	3.86%	4.56%
-8.94% to -4.12%	57	20.00%	24.56%
-4.12% to 0.70%	81	28.42%	52.98%
0.70% to 5.52%	70	24.56%	77.54%
5.52% to 10.35%	46	16.14%	93.68%
10.35% to 15.17%	15	5.26%	98.95%
15.17% to 19.99%	1	0.35%	99.30%
Greater than 19.99%	2	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.73%	7.13%	72.63%	68.27%
±2σ	-12.16%	13.56%	96.14%	95.45%
±3σ	-18.59%	19.99%	98.95%	99.73%

Descriptive Statistics

Mean	0.702%
Standard Error	0.381%
Median	0.304%
Mode	0.434%
Standard Deviation	6.429%
Sample Variance	41.334%
Kurtosis	1.60
Skewness	0.47
Range	50.829%
Minimum	-20.215%
Maximum	30.614%
Count	285

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.555%	146	51.23%	2.846%
Negative	-4.427%	138	48.42%	-2.144%
Zero	0.000%	1	0.35%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.03%
12	1 Quarter	8.79%
52	1 Year	10.12%
156	3 Years	8.91%
260	5 Years	9.80%
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 2.31. Further, an Excess Kurtosis of 8.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.44%	0	0.00%	0.00%
-5.44% to -1.46%	0	0.00%	0.00%
-1.46% to 2.52%	0	0.00%	0.00%
2.52% to 6.50%	53	18.53%	18.53%
6.50% to 10.49%	121	42.31%	60.84%
10.49% to 14.47%	70	24.48%	85.31%
14.47% to 18.45%	21	7.34%	92.66%
18.45% to 22.43%	10	3.50%	96.15%
22.43% to 26.41%	7	2.45%	98.60%
Greater than 26.41%	4	1.40%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.18%	15.80%	81.47%	68.27%
±2σ	-0.13%	21.11%	96.15%	95.45%
±3σ	-5.44%	26.41%	98.60%	99.73%

Descriptive Statistics

Mean	10.487%
Standard Error	0.314%
Median	9.245%
Mode	7.576%
Standard Deviation	5.309%
Sample Variance	28.187%
Kurtosis	8.24
Skewness	2.31
Range	37.722%
Minimum	2.830%
Maximum	40.552%
Count	286

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.487%	286	100.00%	10.487%
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 0.10. Further, an Excess Kurtosis of 1.34 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.70%	2	0.70%	0.70%
-18.70% to -14.08%	2	0.70%	1.40%
-14.08% to -9.46%	11	3.85%	5.24%
-9.46% to -4.84%	51	17.83%	23.08%
-4.84% to -0.22%	71	24.83%	47.90%
-0.22% to 4.40%	92	32.17%	80.07%
4.40% to 9.02%	41	14.34%	94.41%
9.02% to 13.64%	13	4.55%	98.95%
13.64% to 18.26%	1	0.35%	99.30%
Greater than 18.26%	2	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.38%	5.94%	71.33%	68.27%
±2σ	-12.54%	12.10%	96.50%	95.45%
±3σ	-18.70%	18.26%	98.60%	99.73%

Descriptive Statistics

Mean	-0.222%
Standard Error	0.364%
Median	-0.039%
Mode	-1.506%
Standard Deviation	6.161%
Sample Variance	37.962%
Kurtosis	1.34
Skewness	0.10
Range	47.340%
Minimum	-21.893%
Maximum	25.447%
Count	286

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.587%	142	49.65%	2.277%
Negative	-4.998%	143	50.00%	-2.499%
Zero	0.000%	1	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of -0.60 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.09%	0	0.00%	0.00%
-32.09% to -23.40%	0	0.00%	0.00%
-23.40% to -14.70%	3	4.62%	4.62%
-14.70% to -6.01%	14	21.54%	26.15%
-6.01% to 2.69%	15	23.08%	49.23%
2.69% to 11.38%	17	26.15%	75.38%
11.38% to 20.07%	12	18.46%	93.85%
20.07% to 28.77%	3	4.62%	98.46%
28.77% to 37.46%	1	1.54%	100.00%
Greater than 37.46%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.91%	14.28%	66.15%	68.27%
±2σ	-20.50%	25.87%	95.38%	95.45%
±3σ	-32.09%	37.46%	100.00%	99.73%

Descriptive Statistics

Mean	2.685%
Standard Error	1.438%
Median	3.714%
Mode	-22.922%
Standard Deviation	11.593%
Sample Variance	134.394%
Kurtosis	-0.60
Skewness	0.08
Range	52.872%
Minimum	-22.922%
Maximum	29.950%
Count	65

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.758%	38	58.46%	6.289%
Negative	-8.676%	27	41.54%	-3.604%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	18.05%
12	1 Year	20.99%
36	3 Years	18.85%
60	5 Years	20.23%
120	10 Years	20.76%
240	20 Years	20.76%
600	50 Years	20.76%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.41. Further, an Excess Kurtosis of 3.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.29%	0	0.00%	0.00%
-2.29% to 4.06%	0	0.00%	0.00%
4.06% to 10.41%	0	0.00%	0.00%
10.41% to 16.76%	14	21.21%	21.21%
16.76% to 23.11%	25	37.88%	59.09%
23.11% to 29.46%	15	22.73%	81.82%
29.46% to 35.80%	6	9.09%	90.91%
35.80% to 42.15%	4	6.06%	96.97%
42.15% to 48.50%	1	1.52%	98.48%
Greater than 48.50%	1	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.64%	31.57%	72.73%	68.27%
±2σ	6.18%	40.04%	96.97%	95.45%
±3σ	-2.29%	48.50%	98.48%	99.73%

Descriptive Statistics

Mean	23.107%
Standard Error	1.042%
Median	22.024%
Mode	10.627%
Standard Deviation	8.465%
Sample Variance	71.649%
Kurtosis	3.62
Skewness	1.41
Range	47.899%
Minimum	10.627%
Maximum	58.526%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.107%	66	100.00%	23.107%
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 0.46. Further, an Excess Kurtosis of -0.28 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.12%	0	0.00%	0.00%
-35.12% to -26.71%	0	0.00%	0.00%
-26.71% to -18.30%	3	4.55%	4.55%
-18.30% to -9.88%	12	18.18%	22.73%
-9.88% to -1.47%	22	33.33%	56.06%
-1.47% to 6.94%	13	19.70%	75.76%
6.94% to 15.36%	12	18.18%	93.94%
15.36% to 23.77%	3	4.55%	98.48%
23.77% to 32.18%	1	1.52%	100.00%
Greater than 32.18%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.69%	9.75%	66.67%	68.27%
±2σ	-23.91%	20.97%	96.97%	95.45%
±3σ	-35.12%	32.18%	100.00%	99.73%

Descriptive Statistics

Mean	-1.470%
Standard Error	1.381%
Median	-2.955%
Mode	-21.379%
Standard Deviation	11.218%
Sample Variance	125.846%
Kurtosis	-0.28
Skewness	0.46
Range	51.383%
Minimum	-21.379%
Maximum	30.004%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.744%	27	40.91%	3.986%
Negative	-9.234%	39	59.09%	-5.456%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.36. Further, an Excess Kurtosis of -0.69 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.40%	0	0.00%	0.00%
-55.40% to -39.53%	0	0.00%	0.00%
-39.53% to -23.65%	2	9.09%	9.09%
-23.65% to -7.78%	1	4.55%	13.64%
-7.78% to 8.10%	9	40.91%	54.55%
8.10% to 23.97%	5	22.73%	77.27%
23.97% to 39.84%	2	9.09%	86.36%
39.84% to 55.72%	3	13.64%	100.00%
55.72% to 71.59%	0	0.00%	100.00%
Greater than 71.59%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.07%	29.26%	68.18%	68.27%
±2σ	-34.24%	50.43%	100.00%	95.45%
±3σ	-55.40%	71.59%	100.00%	99.73%

Descriptive Statistics

Mean	8.095%
Standard Error	4.513%
Median	2.768%
Mode	-27.779%
Standard Deviation	21.166%
Sample Variance	448.000%
Kurtosis	-0.69
Skewness	0.36
Range	74.038%
Minimum	-27.779%
Maximum	46.259%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.204%	12	54.55%	12.657%
Negative	-10.035%	10	45.45%	-4.561%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	34.64%
12	3 Years	34.06%
20	5 Years	35.19%
40	10 Years	38.22%
80	20 Years	38.22%
200	50 Years	38.22%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.70. Further, an Excess Kurtosis of 0.13 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.55%	0	0.00%	0.00%
-4.55% to 7.54%	0	0.00%	0.00%
7.54% to 19.62%	0	0.00%	0.00%
19.62% to 31.70%	6	26.09%	26.09%
31.70% to 43.79%	7	30.43%	56.52%
43.79% to 55.88%	5	21.74%	78.26%
55.88% to 67.96%	3	13.04%	91.30%
67.96% to 80.04%	2	8.70%	100.00%
80.04% to 92.13%	0	0.00%	100.00%
Greater than 92.13%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	27.68%	59.90%	65.22%	68.27%
±2σ	11.56%	76.02%	91.30%	95.45%
±3σ	-4.55%	92.13%	100.00%	99.73%

Descriptive Statistics

Mean	43.790%
Standard Error	3.360%
Median	42.120%
Mode	20.807%
Standard Deviation	16.113%
Sample Variance	259.617%
Kurtosis	0.13
Skewness	0.70
Range	59.233%
Minimum	20.807%
Maximum	80.040%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.790%	23	100.00%	43.790%
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 0.48. Further, an Excess Kurtosis of -0.10 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.69%	0	0.00%	0.00%
-58.69% to -45.16%	0	0.00%	0.00%
-45.16% to -31.64%	0	0.00%	0.00%
-31.64% to -18.11%	5	21.74%	21.74%
-18.11% to -4.58%	6	26.09%	47.83%
-4.58% to 8.95%	8	34.78%	82.61%
8.95% to 22.47%	2	8.70%	91.30%
22.47% to 36.00%	2	8.70%	100.00%
36.00% to 49.53%	0	0.00%	100.00%
Greater than 49.53%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.62%	13.46%	69.57%	68.27%
±2σ	-40.65%	31.49%	91.30%	95.45%
±3σ	-58.69%	49.53%	100.00%	99.73%

Descriptive Statistics

Mean	-4.581%
Standard Error	3.761%
Median	-3.702%
Mode	-30.279%
Standard Deviation	18.036%
Sample Variance	325.315%
Kurtosis	-0.10
Skewness	0.48
Range	65.205%
Minimum	-30.279%
Maximum	34.926%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.018%	10	43.48%	5.225%
Negative	-17.350%	13	56.52%	-9.807%
Zero	0.000%	0	0.00%	0.000%

ASO Deep Analytical Report