GPRO - 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	4.22%	3.73%	3.75%	5.46%	10.47%	10.43%	0.59	0.72	0.53	0.80
Weekly	9.47%	10.96%	9.72%	12.82%	23.05%	22.97%	0.52	0.82	0.41	1.03
Monthly	18.84%	26.05%	18.22%	30.39%	47.98%	47.81%	0.40	1.05	0.25	1.70
Quarterly	34.27%	56.07%	42.45%	60.15%	83.10%	82.81%	0.28	1.50	0.12	3.44
Annual	—	—	—	—	166.21%	165.63%	0.12	3.44	0.02	18.11
Option Time Horizon	—	—	—	—	62.73%	62.51%	0.35	1.22	0.19	2.29

Calculation Notes: Computed at 2026-03-23T16:36 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $0.65 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.0750 (Bid $0.0500 / Ask $0.1000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 166.21% (CRR binomial tree, American, n=20 steps) | BS IV: 167.91% (European Black-Scholes) | Yahoo IV (Annual): 165.63% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.75. Further, an Excess Kurtosis of 9.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.70%	22	0.75%	0.75%
-12.70% to -9.53%	25	0.85%	1.59%
-9.53% to -6.37%	94	3.19%	4.78%
-6.37% to -3.21%	317	10.74%	15.52%
-3.21% to -0.04%	1015	34.40%	49.92%
-0.04% to 3.12%	1032	34.97%	84.89%
3.12% to 6.28%	304	10.30%	95.19%
6.28% to 9.45%	80	2.71%	97.90%
9.45% to 12.61%	30	1.02%	98.92%
Greater than 12.61%	32	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.26%	4.17%	80.24%	68.27%
±2σ	-8.48%	8.39%	95.15%	95.45%
±3σ	-12.70%	12.61%	98.17%	99.73%

Descriptive Statistics

Mean	-0.043%
Standard Error	0.078%
Median	0.000%
Mode	0.000%
Standard Deviation	4.218%
Sample Variance	17.789%
Kurtosis	9.70
Skewness	0.75
Range	67.195%
Minimum	-26.103%
Maximum	41.092%
Count	2951

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.973%	1393	47.20%	1.403%
Negative	-2.896%	1474	49.95%	-1.447%
Zero	0.000%	84	2.85%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	8.35%
20	1 Month	10.52%
60	1 Quarter	8.06%
250	1 Year	9.33%
750	3 Years	6.30%
1,250	5 Years	5.46%
2,500	10 Years	5.38%
5,000	20 Years	5.53%
12,500	50 Years	5.53%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.13. Further, an Excess Kurtosis of 34.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.77%	0	0.00%	0.00%
-5.77% to -2.98%	0	0.00%	0.00%
-2.98% to -0.18%	0	0.00%	0.00%
-0.18% to 2.62%	387	13.11%	13.11%
2.62% to 5.41%	1524	51.63%	64.74%
5.41% to 8.21%	627	21.24%	85.98%
8.21% to 11.00%	227	7.69%	93.67%
11.00% to 13.80%	98	3.32%	96.99%
13.80% to 16.59%	45	1.52%	98.51%
Greater than 16.59%	44	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.68%	9.14%	88.18%	68.27%
±2σ	-2.04%	12.86%	96.14%	95.45%
±3σ	-5.77%	16.59%	98.51%	99.73%

Descriptive Statistics

Mean	5.411%
Standard Error	0.069%
Median	4.450%
Mode	3.448%
Standard Deviation	3.727%
Sample Variance	13.892%
Kurtosis	34.99
Skewness	4.13
Range	61.328%
Minimum	1.001%
Maximum	62.329%
Count	2952

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.411%	2952	100.00%	5.411%
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 0.68. Further, an Excess Kurtosis of 15.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.00%	19	0.64%	0.64%
-11.00% to -8.18%	31	1.05%	1.69%
-8.18% to -5.36%	79	2.68%	4.37%
-5.36% to -2.55%	348	11.79%	16.16%
-2.55% to 0.27%	1042	35.30%	51.46%
0.27% to 3.08%	958	32.45%	83.91%
3.08% to 5.90%	329	11.14%	95.05%
5.90% to 8.72%	84	2.85%	97.90%
8.72% to 11.53%	42	1.42%	99.32%
Greater than 11.53%	20	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.49%	4.02%	78.93%	68.27%
±2σ	-7.24%	7.78%	95.02%	95.45%
±3σ	-11.00%	11.53%	98.68%	99.73%

Descriptive Statistics

Mean	0.269%
Standard Error	0.069%
Median	0.179%
Mode	0.000%
Standard Deviation	3.755%
Sample Variance	14.102%
Kurtosis	15.27
Skewness	0.68
Range	77.332%
Minimum	-27.007%
Maximum	50.325%
Count	2952

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.770%	1520	51.49%	1.426%
Negative	-2.508%	1362	46.14%	-1.157%
Zero	0.000%	70	2.37%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.82. Further, an Excess Kurtosis of 4.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.65%	1	0.16%	0.16%
-28.65% to -21.55%	7	1.14%	1.31%
-21.55% to -14.44%	24	3.92%	5.23%
-14.44% to -7.34%	75	12.25%	17.48%
-7.34% to -0.23%	217	35.46%	52.94%
-0.23% to 6.87%	191	31.21%	84.15%
6.87% to 13.97%	61	9.97%	94.12%
13.97% to 21.08%	22	3.59%	97.71%
21.08% to 28.18%	7	1.14%	98.86%
Greater than 28.18%	7	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.71%	9.24%	77.45%	68.27%
±2σ	-19.18%	18.71%	95.59%	95.45%
±3σ	-28.65%	28.18%	98.69%	99.73%

Descriptive Statistics

Mean	-0.234%
Standard Error	0.383%
Median	-0.871%
Mode	0.000%
Standard Deviation	9.472%
Sample Variance	89.723%
Kurtosis	4.65
Skewness	0.82
Range	93.534%
Minimum	-39.640%
Maximum	53.894%
Count	612

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.206%	272	44.44%	3.203%
Negative	-6.354%	331	54.09%	-3.437%
Zero	0.000%	9	1.47%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	28.59%
12	1 Quarter	18.86%
52	1 Year	23.67%
156	3 Years	14.97%
260	5 Years	12.82%
520	10 Years	12.70%
1,040	20 Years	13.06%
2,600	50 Years	13.06%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.04. Further, an Excess Kurtosis of 30.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.65%	0	0.00%	0.00%
-18.65% to -10.43%	0	0.00%	0.00%
-10.43% to -2.21%	0	0.00%	0.00%
-2.21% to 6.01%	72	11.75%	11.75%
6.01% to 14.23%	322	52.53%	64.27%
14.23% to 22.45%	133	21.70%	85.97%
22.45% to 30.67%	50	8.16%	94.13%
30.67% to 38.89%	15	2.45%	96.57%
38.89% to 47.11%	10	1.63%	98.21%
Greater than 47.11%	11	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.27%	25.19%	90.21%	68.27%
±2σ	-7.69%	36.15%	95.76%	95.45%
±3σ	-18.65%	47.11%	98.21%	99.73%

Descriptive Statistics

Mean	14.230%
Standard Error	0.443%
Median	10.909%
Mode	5.133%
Standard Deviation	10.961%
Sample Variance	120.154%
Kurtosis	30.65
Skewness	4.04
Range	133.447%
Minimum	3.553%
Maximum	137.000%
Count	613

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.230%	613	100.00%	14.230%
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 1.01. Further, an Excess Kurtosis of 6.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.92%	6	0.98%	0.98%
-27.92% to -20.63%	2	0.33%	1.31%
-20.63% to -13.34%	21	3.43%	4.73%
-13.34% to -6.05%	72	11.75%	16.48%
-6.05% to 1.23%	232	37.85%	54.32%
1.23% to 8.52%	181	29.53%	83.85%
8.52% to 15.81%	61	9.95%	93.80%
15.81% to 23.10%	26	4.24%	98.04%
23.10% to 30.39%	4	0.65%	98.69%
Greater than 30.39%	8	1.31%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.48%	10.95%	78.30%	68.27%
±2σ	-18.20%	20.67%	95.92%	95.45%
±3σ	-27.92%	30.39%	97.72%	99.73%

Descriptive Statistics

Mean	1.234%
Standard Error	0.392%
Median	0.730%
Mode	0.000%
Standard Deviation	9.717%
Sample Variance	94.419%
Kurtosis	6.88
Skewness	1.01
Range	106.848%
Minimum	-33.714%
Maximum	73.134%
Count	613

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.517%	325	53.02%	3.985%
Negative	-6.023%	280	45.68%	-2.751%
Zero	0.000%	8	1.30%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.29. Further, an Excess Kurtosis of 3.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -57.77%	0	0.00%	0.00%
-57.77% to -43.65%	0	0.00%	0.00%
-43.65% to -29.52%	4	2.84%	2.84%
-29.52% to -15.39%	29	20.57%	23.40%
-15.39% to -1.27%	47	33.33%	56.74%
-1.27% to 12.86%	33	23.40%	80.14%
12.86% to 26.98%	19	13.48%	93.62%
26.98% to 41.11%	5	3.55%	97.16%
41.11% to 55.24%	2	1.42%	98.58%
Greater than 55.24%	2	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.10%	17.57%	76.60%	68.27%
±2σ	-38.94%	36.40%	97.16%	95.45%
±3σ	-57.77%	55.24%	98.58%	99.73%

Descriptive Statistics

Mean	-1.268%
Standard Error	1.586%
Median	-3.522%
Mode	-36.424%
Standard Deviation	18.835%
Sample Variance	354.747%
Kurtosis	3.18
Skewness	1.29
Range	117.312%
Minimum	-36.424%
Maximum	80.888%
Count	141

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.775%	55	39.01%	6.543%
Negative	-12.807%	86	60.99%	-7.811%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	42.53%
12	1 Year	62.48%
36	3 Years	36.77%
60	5 Years	30.39%
120	10 Years	29.47%
240	20 Years	30.09%
600	50 Years	30.09%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.97. Further, an Excess Kurtosis of 25.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.30%	0	0.00%	0.00%
-42.30% to -22.77%	0	0.00%	0.00%
-22.77% to -3.23%	0	0.00%	0.00%
-3.23% to 16.30%	17	11.97%	11.97%
16.30% to 35.84%	75	52.82%	64.79%
35.84% to 55.38%	34	23.94%	88.73%
55.38% to 74.91%	8	5.63%	94.37%
74.91% to 94.45%	3	2.11%	96.48%
94.45% to 113.98%	3	2.11%	98.59%
Greater than 113.98%	2	1.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.79%	61.89%	89.44%	68.27%
±2σ	-16.25%	87.94%	96.48%	95.45%
±3σ	-42.30%	113.98%	98.59%	99.73%

Descriptive Statistics

Mean	35.841%
Standard Error	2.186%
Median	29.494%
Mode	31.250%
Standard Deviation	26.048%
Sample Variance	678.497%
Kurtosis	25.03
Skewness	3.97
Range	228.429%
Minimum	7.741%
Maximum	236.170%
Count	142

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.841%	142	100.00%	35.841%
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 -0.04. Further, an Excess Kurtosis of -0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.28%	0	0.00%	0.00%
-50.28% to -36.62%	2	1.41%	1.41%
-36.62% to -22.96%	8	5.63%	7.04%
-22.96% to -9.29%	25	17.61%	24.65%
-9.29% to 4.37%	38	26.76%	51.41%
4.37% to 18.03%	37	26.06%	77.46%
18.03% to 31.69%	24	16.90%	94.37%
31.69% to 45.36%	7	4.93%	99.30%
45.36% to 59.02%	1	0.70%	100.00%
Greater than 59.02%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.85%	22.59%	69.01%	68.27%
±2σ	-32.07%	40.80%	95.77%	95.45%
±3σ	-50.28%	59.02%	100.00%	99.73%

Descriptive Statistics

Mean	4.368%
Standard Error	1.529%
Median	3.949%
Mode	-14.130%
Standard Deviation	18.217%
Sample Variance	331.870%
Kurtosis	-0.08
Skewness	-0.04
Range	96.886%
Minimum	-43.436%
Maximum	53.450%
Count	142

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.458%	89	62.68%	9.688%
Negative	-14.253%	53	37.32%	-5.320%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.21. Further, an Excess Kurtosis of 2.95 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -106.09%	0	0.00%	0.00%
-106.09% to -80.39%	0	0.00%	0.00%
-80.39% to -54.69%	1	2.13%	2.13%
-54.69% to -28.99%	9	19.15%	21.28%
-28.99% to -3.29%	16	34.04%	55.32%
-3.29% to 22.41%	13	27.66%	82.98%
22.41% to 48.10%	3	6.38%	89.36%
48.10% to 73.80%	4	8.51%	97.87%
73.80% to 99.50%	0	0.00%	97.87%
Greater than 99.50%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-37.56%	30.97%	72.34%	68.27%
±2σ	-71.83%	65.24%	97.87%	95.45%
±3σ	-106.09%	99.50%	97.87%	99.73%

Descriptive Statistics

Mean	-3.294%
Standard Error	4.998%
Median	-7.495%
Mode	-59.742%
Standard Deviation	34.266%
Sample Variance	1174.149%
Kurtosis	2.95
Skewness	1.21
Range	183.700%
Minimum	-59.742%
Maximum	123.958%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.463%	19	40.43%	11.102%
Negative	-25.060%	27	57.45%	-14.396%
Zero	0.000%	1	2.13%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	139.85%
12	3 Years	76.46%
20	5 Years	60.15%
40	10 Years	53.38%
80	20 Years	55.12%
200	50 Years	55.12%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.61. Further, an Excess Kurtosis of 9.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -91.27%	0	0.00%	0.00%
-91.27% to -49.21%	0	0.00%	0.00%
-49.21% to -7.16%	0	0.00%	0.00%
-7.16% to 34.89%	6	12.50%	12.50%
34.89% to 76.94%	25	52.08%	64.58%
76.94% to 119.00%	10	20.83%	85.42%
119.00% to 161.05%	1	2.08%	87.50%
161.05% to 203.10%	5	10.42%	97.92%
203.10% to 245.16%	0	0.00%	97.92%
Greater than 245.16%	1	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	20.87%	133.01%	85.42%	68.27%
±2σ	-35.20%	189.08%	97.92%	95.45%
±3σ	-91.27%	245.16%	97.92%	99.73%

Descriptive Statistics

Mean	76.945%
Standard Error	8.093%
Median	55.569%
Mode	16.798%
Standard Deviation	56.070%
Sample Variance	3143.870%
Kurtosis	9.37
Skewness	2.61
Range	322.091%
Minimum	16.798%
Maximum	338.889%
Count	48

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	76.945%	48	100.00%	76.945%
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 1.49 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -112.42%	0	0.00%	0.00%
-112.42% to -80.58%	0	0.00%	0.00%
-80.58% to -48.73%	1	2.08%	2.08%
-48.73% to -16.89%	8	16.67%	18.75%
-16.89% to 14.95%	20	41.67%	60.42%
14.95% to 46.79%	10	20.83%	81.25%
46.79% to 78.63%	6	12.50%	93.75%
78.63% to 110.47%	1	2.08%	95.83%
110.47% to 142.31%	1	2.08%	97.92%
Greater than 142.31%	1	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.51%	57.40%	70.83%	68.27%
±2σ	-69.96%	99.86%	95.83%	95.45%
±3σ	-112.42%	142.31%	97.92%	99.73%

Descriptive Statistics

Mean	14.949%
Standard Error	6.128%
Median	6.575%
Mode	-55.039%
Standard Deviation	42.455%
Sample Variance	1802.437%
Kurtosis	1.49
Skewness	1.08
Range	207.039%
Minimum	-55.039%
Maximum	152.000%
Count	48

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.297%	27	56.25%	23.230%
Negative	-19.874%	20	41.67%	-8.281%
Zero	0.000%	1	2.08%	0.000%

GPRO Deep Analytical Report