SENS - 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	5.85%	5.48%	4.93%	7.71%	6.57%	6.58%	6.27	7.15	5.88	7.64
Weekly	13.87%	17.55%	12.37%	17.94%	14.45%	14.49%	5.80	7.74	5.02	8.95
Monthly	30.49%	48.47%	25.61%	39.81%	30.09%	30.16%	4.96	9.05	3.67	12.23
Quarterly	92.96%	157.48%	39.41%	74.99%	52.11%	52.25%	3.98	11.28	2.36	19.00
Annual	—	—	—	—	104.22%	104.49%	2.36	19.00	0.83	53.86
Option Time Horizon	—	—	—	—	39.34%	39.44%	4.52	9.93	3.05	14.71

Calculation Notes: Computed at 2026-03-23T16:38 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $6.70 | Strike (K): $7.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.7750 (Bid $0.7000 / Ask $0.8500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 104.22% (CRR binomial tree, American, n=20 steps) | BS IV: 105.29% (European Black-Scholes) | Yahoo IV (Annual): 104.49% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.28. Further, an Excess Kurtosis of 36.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.49%	5	0.20%	0.20%
-17.49% to -13.10%	13	0.52%	0.71%
-13.10% to -8.71%	69	2.74%	3.46%
-8.71% to -4.33%	282	11.20%	14.65%
-4.33% to 0.06%	1061	42.14%	56.79%
0.06% to 4.45%	726	28.83%	85.62%
4.45% to 8.84%	253	10.05%	95.67%
8.84% to 13.23%	62	2.46%	98.13%
13.23% to 17.62%	25	0.99%	99.13%
Greater than 17.62%	22	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.79%	5.92%	82.17%	68.27%
±2σ	-11.64%	11.77%	96.51%	95.45%
±3σ	-17.49%	17.62%	98.93%	99.73%

Descriptive Statistics

Mean	0.064%
Standard Error	0.117%
Median	-0.363%
Mode	0.000%
Standard Deviation	5.852%
Sample Variance	34.242%
Kurtosis	36.19
Skewness	3.28
Range	114.397%
Minimum	-33.699%
Maximum	80.698%
Count	2518

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.337%	1088	43.21%	1.874%
Negative	-3.455%	1319	52.38%	-1.810%
Zero	0.000%	111	4.41%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.05%
20	1 Month	8.13%
60	1 Quarter	7.37%
250	1 Year	6.83%
750	3 Years	7.61%
1,250	5 Years	7.71%
2,500	10 Years	7.60%
5,000	20 Years	7.61%
12,500	50 Years	7.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.40. Further, an Excess Kurtosis of 61.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.75%	0	0.00%	0.00%
-8.75% to -4.64%	0	0.00%	0.00%
-4.64% to -0.53%	0	0.00%	0.00%
-0.53% to 3.58%	297	11.79%	11.79%
3.58% to 7.69%	1303	51.73%	63.52%
7.69% to 11.80%	590	23.42%	86.94%
11.80% to 15.91%	197	7.82%	94.76%
15.91% to 20.02%	68	2.70%	97.46%
20.02% to 24.13%	29	1.15%	98.61%
Greater than 24.13%	35	1.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.21%	13.17%	88.21%	68.27%
±2σ	-3.27%	18.65%	96.63%	95.45%
±3σ	-8.75%	24.13%	98.61%	99.73%

Descriptive Statistics

Mean	7.690%
Standard Error	0.109%
Median	6.442%
Mode	7.143%
Standard Deviation	5.479%
Sample Variance	30.023%
Kurtosis	61.38
Skewness	5.40
Range	100.634%
Minimum	0.717%
Maximum	101.351%
Count	2519

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.690%	2519	100.00%	7.690%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.56. Further, an Excess Kurtosis of 7.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.24%	18	0.71%	0.71%
-14.24% to -10.55%	26	1.03%	1.75%
-10.55% to -6.85%	88	3.49%	5.24%
-6.85% to -3.15%	319	12.66%	17.90%
-3.15% to 0.54%	791	31.40%	49.31%
0.54% to 4.24%	837	33.23%	82.53%
4.24% to 7.94%	312	12.39%	94.92%
7.94% to 11.63%	89	3.53%	98.45%
11.63% to 15.33%	27	1.07%	99.52%
Greater than 15.33%	12	0.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.39%	5.47%	76.06%	68.27%
±2σ	-9.32%	10.40%	95.28%	95.45%
±3σ	-14.24%	15.33%	98.81%	99.73%

Descriptive Statistics

Mean	0.543%
Standard Error	0.098%
Median	0.599%
Mode	0.000%
Standard Deviation	4.929%
Sample Variance	24.296%
Kurtosis	7.18
Skewness	-0.56
Range	77.331%
Minimum	-43.860%
Maximum	33.471%
Count	2519

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.709%	1378	54.70%	2.029%
Negative	-3.656%	1024	40.65%	-1.486%
Zero	0.000%	117	4.64%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.60. Further, an Excess Kurtosis of 17.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.21%	2	0.38%	0.38%
-41.21% to -30.81%	2	0.38%	0.76%
-30.81% to -20.41%	8	1.53%	2.29%
-20.41% to -10.01%	66	12.62%	14.91%
-10.01% to 0.39%	209	39.96%	54.88%
0.39% to 10.79%	170	32.50%	87.38%
10.79% to 21.19%	44	8.41%	95.79%
21.19% to 31.58%	11	2.10%	97.90%
31.58% to 41.98%	3	0.57%	98.47%
Greater than 41.98%	8	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.48%	14.25%	83.37%	68.27%
±2σ	-27.34%	28.12%	96.56%	95.45%
±3σ	-41.21%	41.98%	98.09%	99.73%

Descriptive Statistics

Mean	0.388%
Standard Error	0.606%
Median	-1.047%
Mode	0.000%
Standard Deviation	13.865%
Sample Variance	192.227%
Kurtosis	17.24
Skewness	2.60
Range	163.903%
Minimum	-42.973%
Maximum	120.930%
Count	523

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.225%	237	45.31%	4.633%
Negative	-7.958%	279	53.35%	-4.245%
Zero	0.000%	7	1.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	18.47%
12	1 Quarter	16.86%
52	1 Year	15.97%
156	3 Years	17.84%
260	5 Years	17.94%
520	10 Years	17.81%
1,040	20 Years	17.83%
2,600	50 Years	17.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.77. Further, an Excess Kurtosis of 32.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.85%	0	0.00%	0.00%
-32.85% to -19.69%	0	0.00%	0.00%
-19.69% to -6.53%	0	0.00%	0.00%
-6.53% to 6.63%	23	4.39%	4.39%
6.63% to 19.80%	338	64.50%	68.89%
19.80% to 32.96%	105	20.04%	88.93%
32.96% to 46.12%	36	6.87%	95.80%
46.12% to 59.28%	8	1.53%	97.33%
59.28% to 72.44%	4	0.76%	98.09%
Greater than 72.44%	10	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.25%	37.35%	92.37%	68.27%
±2σ	-15.30%	54.89%	96.56%	95.45%
±3σ	-32.85%	72.44%	98.09%	99.73%

Descriptive Statistics

Mean	19.797%
Standard Error	0.767%
Median	15.127%
Mode	7.692%
Standard Deviation	17.549%
Sample Variance	307.966%
Kurtosis	32.81
Skewness	4.77
Range	186.331%
Minimum	3.273%
Maximum	189.604%
Count	524

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.797%	524	100.00%	19.797%
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 0.72. Further, an Excess Kurtosis of 7.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.62%	5	0.95%	0.95%
-35.62% to -26.35%	4	0.76%	1.72%
-26.35% to -17.07%	18	3.44%	5.15%
-17.07% to -7.80%	55	10.50%	15.65%
-7.80% to 1.47%	182	34.73%	50.38%
1.47% to 10.75%	173	33.02%	83.40%
10.75% to 20.02%	61	11.64%	95.04%
20.02% to 29.30%	18	3.44%	98.47%
29.30% to 38.57%	4	0.76%	99.24%
Greater than 38.57%	4	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.89%	13.84%	79.01%	68.27%
±2σ	-23.26%	26.20%	95.99%	95.45%
±3σ	-35.62%	38.57%	98.28%	99.73%

Descriptive Statistics

Mean	1.474%
Standard Error	0.540%
Median	1.268%
Mode	0.000%
Standard Deviation	12.365%
Sample Variance	152.897%
Kurtosis	7.93
Skewness	0.72
Range	143.469%
Minimum	-54.737%
Maximum	88.732%
Count	524

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.189%	285	54.39%	4.998%
Negative	-7.925%	233	44.47%	-3.524%
Zero	0.000%	6	1.15%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.58. Further, an Excess Kurtosis of 10.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -89.89%	0	0.00%	0.00%
-89.89% to -67.02%	0	0.00%	0.00%
-67.02% to -44.16%	2	1.65%	1.65%
-44.16% to -21.29%	14	11.57%	13.22%
-21.29% to 1.58%	60	49.59%	62.81%
1.58% to 24.45%	31	25.62%	88.43%
24.45% to 47.31%	8	6.61%	95.04%
47.31% to 70.18%	1	0.83%	95.87%
70.18% to 93.05%	3	2.48%	98.35%
Greater than 93.05%	2	1.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.91%	32.07%	85.12%	68.27%
±2σ	-59.40%	62.56%	95.04%	95.45%
±3σ	-89.89%	93.05%	98.35%	99.73%

Descriptive Statistics

Mean	1.579%
Standard Error	2.772%
Median	-5.217%
Mode	-54.714%
Standard Deviation	30.490%
Sample Variance	929.635%
Kurtosis	10.58
Skewness	2.58
Range	226.503%
Minimum	-54.714%
Maximum	171.789%
Count	121

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.399%	48	39.67%	10.472%
Negative	-14.741%	73	60.33%	-8.893%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	38.12%
12	1 Year	33.33%
36	3 Years	39.84%
60	5 Years	39.81%
120	10 Years	41.42%
240	20 Years	41.29%
600	50 Years	41.29%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.67. Further, an Excess Kurtosis of 17.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -94.76%	0	0.00%	0.00%
-94.76% to -58.41%	0	0.00%	0.00%
-58.41% to -22.06%	0	0.00%	0.00%
-22.06% to 14.29%	3	2.46%	2.46%
14.29% to 50.65%	86	70.49%	72.95%
50.65% to 87.00%	21	17.21%	90.16%
87.00% to 123.35%	4	3.28%	93.44%
123.35% to 159.70%	2	1.64%	95.08%
159.70% to 196.06%	3	2.46%	97.54%
Greater than 196.06%	3	2.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.18%	99.12%	92.62%	68.27%
±2σ	-46.29%	147.59%	95.08%	95.45%
±3σ	-94.76%	196.06%	97.54%	99.73%

Descriptive Statistics

Mean	50.646%
Standard Error	4.388%
Median	37.027%
Mode	42.857%
Standard Deviation	48.470%
Sample Variance	2349.389%
Kurtosis	17.52
Skewness	3.67
Range	361.622%
Minimum	7.692%
Maximum	369.314%
Count	122

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.646%	122	100.00%	50.646%
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 0.90. Further, an Excess Kurtosis of 4.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -71.42%	0	0.00%	0.00%
-71.42% to -52.21%	2	1.64%	1.64%
-52.21% to -33.00%	4	3.28%	4.92%
-33.00% to -13.80%	19	15.57%	20.49%
-13.80% to 5.41%	35	28.69%	49.18%
5.41% to 24.62%	46	37.70%	86.89%
24.62% to 43.82%	11	9.02%	95.90%
43.82% to 63.03%	1	0.82%	96.72%
63.03% to 82.24%	2	1.64%	98.36%
Greater than 82.24%	2	1.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.20%	31.02%	79.51%	68.27%
±2σ	-45.81%	56.63%	93.44%	95.45%
±3σ	-71.42%	82.24%	98.36%	99.73%

Descriptive Statistics

Mean	5.411%
Standard Error	2.319%
Median	6.150%
Mode	0.000%
Standard Deviation	25.609%
Sample Variance	655.838%
Kurtosis	4.27
Skewness	0.90
Range	188.532%
Minimum	-64.557%
Maximum	123.975%
Count	122

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.860%	73	59.84%	11.883%
Negative	-17.167%	46	37.70%	-6.473%
Zero	0.000%	3	2.46%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.91. Further, an Excess Kurtosis of 27.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -269.94%	0	0.00%	0.00%
-269.94% to -200.22%	0	0.00%	0.00%
-200.22% to -130.50%	0	0.00%	0.00%
-130.50% to -60.78%	0	0.00%	0.00%
-60.78% to 8.93%	30	73.17%	73.17%
8.93% to 78.65%	9	21.95%	95.12%
78.65% to 148.37%	0	0.00%	95.12%
148.37% to 218.08%	1	2.44%	97.56%
218.08% to 287.80%	0	0.00%	97.56%
Greater than 287.80%	1	2.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-84.02%	101.89%	95.12%	68.27%
±2σ	-176.98%	194.84%	97.56%	95.45%
±3σ	-269.94%	287.80%	97.56%	99.73%

Descriptive Statistics

Mean	8.933%
Standard Error	14.517%
Median	-8.527%
Mode	-52.361%
Standard Deviation	92.956%
Sample Variance	8640.828%
Kurtosis	27.04
Skewness	4.91
Range	587.750%
Minimum	-52.361%
Maximum	535.389%
Count	41

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	65.008%	15	36.59%	23.783%
Negative	-23.418%	26	63.41%	-14.851%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	45.51%
12	3 Years	76.10%
20	5 Years	74.99%
40	10 Years	90.83%
80	20 Years	89.43%
200	50 Years	89.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.83. Further, an Excess Kurtosis of 26.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -355.03%	0	0.00%	0.00%
-355.03% to -236.92%	0	0.00%	0.00%
-236.92% to -118.81%	0	0.00%	0.00%
-118.81% to -0.70%	0	0.00%	0.00%
-0.70% to 117.42%	32	76.19%	76.19%
117.42% to 235.53%	7	16.67%	92.86%
235.53% to 353.64%	1	2.38%	95.24%
353.64% to 471.75%	1	2.38%	97.62%
471.75% to 589.86%	0	0.00%	97.62%
Greater than 589.86%	1	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-40.07%	274.90%	95.24%	68.27%
±2σ	-197.55%	432.38%	97.62%	95.45%
±3σ	-355.03%	589.86%	97.62%	99.73%

Descriptive Statistics

Mean	117.415%
Standard Error	24.300%
Median	76.136%
Mode	7.692%
Standard Deviation	157.481%
Sample Variance	24800.406%
Kurtosis	26.74
Skewness	4.83
Range	1006.594%
Minimum	7.692%
Maximum	1014.286%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	117.415%	42	100.00%	117.415%
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 0.22. Further, an Excess Kurtosis of 0.80 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -103.79%	0	0.00%	0.00%
-103.79% to -74.24%	1	2.38%	2.38%
-74.24% to -44.68%	1	2.38%	4.76%
-44.68% to -15.13%	5	11.90%	16.67%
-15.13% to 14.43%	18	42.86%	59.52%
14.43% to 43.98%	10	23.81%	83.33%
43.98% to 73.53%	3	7.14%	90.48%
73.53% to 103.09%	3	7.14%	97.62%
103.09% to 132.64%	1	2.38%	100.00%
Greater than 132.64%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.98%	53.83%	76.19%	68.27%
±2σ	-64.39%	93.24%	92.86%	95.45%
±3σ	-103.79%	132.64%	100.00%	99.73%

Descriptive Statistics

Mean	14.425%
Standard Error	6.080%
Median	9.128%
Mode	-84.388%
Standard Deviation	39.406%
Sample Variance	1552.805%
Kurtosis	0.80
Skewness	0.22
Range	196.100%
Minimum	-84.388%
Maximum	111.712%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	33.636%	28	66.67%	22.424%
Negative	-23.998%	14	33.33%	-7.999%
Zero	0.000%	0	0.00%	0.000%

SENS Deep Analytical Report