INVZ - 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	5.36%	4.69%	4.71%	8.12%	11.49%	11.42%	0.60	0.76	0.54	0.85
Weekly	12.27%	13.01%	11.65%	19.05%	25.29%	25.13%	0.53	0.87	0.41	1.12
Monthly	28.18%	34.98%	26.69%	43.27%	52.65%	52.32%	0.40	1.15	0.24	1.94
Quarterly	54.49%	119.18%	57.76%	88.29%	91.19%	90.63%	0.27	1.69	0.11	4.20
Annual	—	—	—	—	182.38%	181.25%	0.11	4.20	0.02	26.04
Option Time Horizon	—	—	—	—	68.84%	68.41%	0.34	1.35	0.17	2.69

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $0.68 | Strike (K): $1.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1000 (Bid $0.0500 / Ask $0.1500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 182.38% (CRR binomial tree, American, n=20 steps) | BS IV: 183.15% (European Black-Scholes) | Yahoo IV (Annual): 181.25% → 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 1.03. Further, an Excess Kurtosis of 4.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.12%	2	0.14%	0.14%
-16.12% to -12.10%	7	0.49%	0.63%
-12.10% to -8.09%	36	2.52%	3.15%
-8.09% to -4.07%	223	15.63%	18.78%
-4.07% to -0.05%	514	36.02%	54.80%
-0.05% to 3.97%	418	29.29%	84.09%
3.97% to 7.99%	132	9.25%	93.34%
7.99% to 12.01%	54	3.78%	97.13%
12.01% to 16.03%	19	1.33%	98.46%
Greater than 16.03%	22	1.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.41%	5.31%	77.22%	68.27%
±2σ	-10.76%	10.67%	95.30%	95.45%
±3σ	-16.12%	16.03%	98.32%	99.73%

Descriptive Statistics

Mean	-0.048%
Standard Error	0.142%
Median	-0.508%
Mode	0.000%
Standard Deviation	5.358%
Sample Variance	28.709%
Kurtosis	4.70
Skewness	1.03
Range	61.068%
Minimum	-28.025%
Maximum	33.043%
Count	1427

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.361%	606	42.47%	1.852%
Negative	-3.463%	783	54.87%	-1.900%
Zero	0.000%	38	2.66%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.63%
20	1 Month	7.44%
60	1 Quarter	7.83%
250	1 Year	8.80%
750	3 Years	8.87%
1,250	5 Years	8.12%
2,500	10 Years	7.59%
5,000	20 Years	7.59%
12,500	50 Years	7.59%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.18. Further, an Excess Kurtosis of 9.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.45%	0	0.00%	0.00%
-6.45% to -2.94%	0	0.00%	0.00%
-2.94% to 0.58%	36	2.52%	2.52%
0.58% to 4.10%	178	12.46%	14.99%
4.10% to 7.62%	652	45.66%	60.64%
7.62% to 11.13%	336	23.53%	84.17%
11.13% to 14.65%	135	9.45%	93.63%
14.65% to 18.16%	46	3.22%	96.85%
18.16% to 21.68%	19	1.33%	98.18%
Greater than 21.68%	26	1.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.93%	12.30%	80.53%	68.27%
±2σ	-1.76%	16.99%	96.15%	95.45%
±3σ	-6.45%	21.68%	98.18%	99.73%

Descriptive Statistics

Mean	7.615%
Standard Error	0.124%
Median	6.719%
Mode	5.263%
Standard Deviation	4.689%
Sample Variance	21.990%
Kurtosis	9.62
Skewness	2.18
Range	48.012%
Minimum	0.101%
Maximum	48.113%
Count	1428

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.615%	1428	100.00%	7.615%
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 0.03. Further, an Excess Kurtosis of 2.56 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.37%	9	0.63%	0.63%
-13.37% to -9.84%	23	1.61%	2.24%
-9.84% to -6.30%	59	4.13%	6.37%
-6.30% to -2.77%	166	11.62%	18.00%
-2.77% to 0.76%	459	32.14%	50.14%
0.76% to 4.29%	448	31.37%	81.51%
4.29% to 7.82%	180	12.61%	94.12%
7.82% to 11.35%	57	3.99%	98.11%
11.35% to 14.88%	22	1.54%	99.65%
Greater than 14.88%	5	0.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.95%	5.46%	74.79%	68.27%
±2σ	-8.66%	10.17%	94.12%	95.45%
±3σ	-13.37%	14.88%	99.02%	99.73%

Descriptive Statistics

Mean	0.755%
Standard Error	0.125%
Median	0.724%
Mode	0.000%
Standard Deviation	4.707%
Sample Variance	22.160%
Kurtosis	2.56
Skewness	0.03
Range	47.431%
Minimum	-21.168%
Maximum	26.263%
Count	1428

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.652%	827	57.91%	2.115%
Negative	-3.511%	553	38.73%	-1.360%
Zero	0.000%	48	3.36%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.34. Further, an Excess Kurtosis of 4.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.01%	0	0.00%	0.00%
-37.01% to -27.81%	1	0.34%	0.34%
-27.81% to -18.60%	8	2.68%	3.02%
-18.60% to -9.40%	44	14.77%	17.79%
-9.40% to -0.20%	122	40.94%	58.72%
-0.20% to 9.00%	76	25.50%	84.23%
9.00% to 18.21%	22	7.38%	91.61%
18.21% to 27.41%	15	5.03%	96.64%
27.41% to 36.61%	7	2.35%	98.99%
Greater than 36.61%	3	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.47%	12.07%	75.17%	68.27%
±2σ	-24.74%	24.34%	94.97%	95.45%
±3σ	-37.01%	36.61%	98.99%	99.73%

Descriptive Statistics

Mean	-0.198%
Standard Error	0.711%
Median	-1.642%
Mode	-12.500%
Standard Deviation	12.270%
Sample Variance	150.563%
Kurtosis	4.07
Skewness	1.34
Range	103.189%
Minimum	-34.844%
Maximum	68.345%
Count	298

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.928%	116	38.93%	4.254%
Negative	-7.371%	180	60.40%	-4.452%
Zero	0.000%	2	0.67%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.30%
12	1 Quarter	17.22%
52	1 Year	20.28%
156	3 Years	20.71%
260	5 Years	19.05%
520	10 Years	17.65%
1,040	20 Years	17.65%
2,600	50 Years	17.65%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.27. Further, an Excess Kurtosis of 9.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.29%	0	0.00%	0.00%
-19.29% to -9.53%	0	0.00%	0.00%
-9.53% to 0.23%	1	0.33%	0.33%
0.23% to 9.98%	40	13.38%	13.71%
9.98% to 19.74%	141	47.16%	60.87%
19.74% to 29.50%	70	23.41%	84.28%
29.50% to 39.26%	30	10.03%	94.31%
39.26% to 49.02%	7	2.34%	96.66%
49.02% to 58.78%	3	1.00%	97.66%
Greater than 58.78%	7	2.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.73%	32.75%	82.61%	68.27%
±2σ	-6.28%	45.77%	95.65%	95.45%
±3σ	-19.29%	58.78%	97.66%	99.73%

Descriptive Statistics

Mean	19.743%
Standard Error	0.752%
Median	16.949%
Mode	1.227%
Standard Deviation	13.011%
Sample Variance	169.285%
Kurtosis	9.98
Skewness	2.27
Range	109.232%
Minimum	0.101%
Maximum	109.333%
Count	299

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.743%	299	100.00%	19.743%
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 4.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.60%	1	0.33%	0.33%
-32.60% to -23.87%	5	1.67%	2.01%
-23.87% to -15.13%	14	4.68%	6.69%
-15.13% to -6.39%	29	9.70%	16.39%
-6.39% to 2.35%	106	35.45%	51.84%
2.35% to 11.08%	89	29.77%	81.61%
11.08% to 19.82%	37	12.37%	93.98%
19.82% to 28.56%	15	5.02%	99.00%
28.56% to 37.30%	1	0.33%	99.33%
Greater than 37.30%	2	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.30%	14.00%	76.59%	68.27%
±2σ	-20.95%	25.65%	94.65%	95.45%
±3σ	-32.60%	37.30%	99.00%	99.73%

Descriptive Statistics

Mean	2.347%
Standard Error	0.674%
Median	2.062%
Mode	0.000%
Standard Deviation	11.650%
Sample Variance	135.715%
Kurtosis	4.23
Skewness	0.49
Range	108.494%
Minimum	-40.171%
Maximum	68.323%
Count	299

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.703%	185	61.87%	5.385%
Negative	-8.488%	107	35.79%	-3.038%
Zero	0.000%	7	2.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.60. Further, an Excess Kurtosis of 4.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.99%	0	0.00%	0.00%
-84.99% to -63.85%	0	0.00%	0.00%
-63.85% to -42.72%	2	2.94%	2.94%
-42.72% to -21.59%	11	16.18%	19.12%
-21.59% to -0.46%	27	39.71%	58.82%
-0.46% to 20.67%	15	22.06%	80.88%
20.67% to 41.81%	7	10.29%	91.18%
41.81% to 62.94%	4	5.88%	97.06%
62.94% to 84.07%	1	1.47%	98.53%
Greater than 84.07%	1	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-28.63%	27.72%	79.41%	68.27%
±2σ	-56.81%	55.89%	97.06%	95.45%
±3σ	-84.99%	84.07%	98.53%	99.73%

Descriptive Statistics

Mean	-0.458%
Standard Error	3.417%
Median	-6.604%
Mode	-52.323%
Standard Deviation	28.176%
Sample Variance	793.911%
Kurtosis	4.67
Skewness	1.60
Range	173.376%
Minimum	-52.323%
Maximum	121.053%
Count	68

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.796%	26	38.23%	9.863%
Negative	-16.710%	42	61.77%	-10.321%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	37.89%
12	1 Year	47.20%
36	3 Years	49.26%
60	5 Years	43.27%
120	10 Years	40.76%
240	20 Years	40.76%
600	50 Years	40.76%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.24. Further, an Excess Kurtosis of 8.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -52.92%	0	0.00%	0.00%
-52.92% to -26.68%	0	0.00%	0.00%
-26.68% to -0.44%	0	0.00%	0.00%
-0.44% to 25.79%	7	10.14%	10.14%
25.79% to 52.03%	34	49.28%	59.42%
52.03% to 78.27%	19	27.54%	86.96%
78.27% to 104.50%	5	7.25%	94.20%
104.50% to 130.74%	1	1.45%	95.65%
130.74% to 156.98%	2	2.90%	98.55%
Greater than 156.98%	1	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.05%	87.01%	82.61%	68.27%
±2σ	-17.93%	122.00%	95.65%	95.45%
±3σ	-52.92%	156.98%	98.55%	99.73%

Descriptive Statistics

Mean	52.031%
Standard Error	4.211%
Median	46.218%
Mode	2.156%
Standard Deviation	34.983%
Sample Variance	1223.801%
Kurtosis	8.30
Skewness	2.24
Range	221.373%
Minimum	2.156%
Maximum	223.529%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.031%	69	100.00%	52.031%
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 0.61. Further, an Excess Kurtosis of 1.44 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.63%	0	0.00%	0.00%
-72.63% to -52.62%	1	1.45%	1.45%
-52.62% to -32.60%	1	1.45%	2.90%
-32.60% to -12.58%	12	17.39%	20.29%
-12.58% to 7.43%	22	31.88%	52.17%
7.43% to 27.45%	20	28.99%	81.16%
27.45% to 47.47%	10	14.49%	95.65%
47.47% to 67.48%	1	1.45%	97.10%
67.48% to 87.50%	1	1.45%	98.55%
Greater than 87.50%	1	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.25%	34.12%	68.12%	68.27%
±2σ	-45.94%	60.81%	95.65%	95.45%
±3σ	-72.63%	87.50%	98.55%	99.73%

Descriptive Statistics

Mean	7.435%
Standard Error	3.213%
Median	6.494%
Mode	-54.167%
Standard Deviation	26.689%
Sample Variance	712.312%
Kurtosis	1.44
Skewness	0.61
Range	151.731%
Minimum	-54.167%
Maximum	97.564%
Count	69

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.038%	42	60.87%	14.023%
Negative	-16.837%	27	39.13%	-6.588%
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 1.57. Further, an Excess Kurtosis of 2.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -163.06%	0	0.00%	0.00%
-163.06% to -122.19%	0	0.00%	0.00%
-122.19% to -81.33%	0	0.00%	0.00%
-81.33% to -40.46%	5	21.74%	21.74%
-40.46% to 0.41%	10	43.48%	65.22%
0.41% to 41.27%	5	21.74%	86.96%
41.27% to 82.14%	1	4.35%	91.30%
82.14% to 123.00%	1	4.35%	95.65%
123.00% to 163.87%	1	4.35%	100.00%
Greater than 163.87%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-54.08%	54.89%	73.91%	68.27%
±2σ	-108.57%	109.38%	91.30%	95.45%
±3σ	-163.06%	163.87%	100.00%	99.73%

Descriptive Statistics

Mean	0.405%
Standard Error	11.362%
Median	-13.000%
Mode	-63.415%
Standard Deviation	54.488%
Sample Variance	2968.944%
Kurtosis	2.69
Skewness	1.57
Range	221.748%
Minimum	-63.415%
Maximum	158.333%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	55.984%	8	34.78%	19.473%
Negative	-31.325%	14	60.87%	-19.068%
Zero	0.000%	1	4.35%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	92.29%
12	3 Years	111.30%
20	5 Years	88.29%
40	10 Years	82.54%
80	20 Years	82.54%
200	50 Years	82.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.02. Further, an Excess Kurtosis of 11.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -236.54%	0	0.00%	0.00%
-236.54% to -147.15%	0	0.00%	0.00%
-147.15% to -57.77%	0	0.00%	0.00%
-57.77% to 31.62%	2	8.33%	8.33%
31.62% to 121.00%	15	62.50%	70.83%
121.00% to 210.38%	4	16.67%	87.50%
210.38% to 299.77%	2	8.33%	95.83%
299.77% to 389.15%	0	0.00%	95.83%
389.15% to 478.54%	0	0.00%	95.83%
Greater than 478.54%	1	4.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.82%	240.18%	91.67%	68.27%
±2σ	-117.36%	359.36%	95.83%	95.45%
±3σ	-236.54%	478.54%	95.83%	99.73%

Descriptive Statistics

Mean	121.000%
Standard Error	24.327%
Median	89.520%
Mode	4.061%
Standard Deviation	119.179%
Sample Variance	14203.740%
Kurtosis	11.30
Skewness	3.02
Range	593.717%
Minimum	4.061%
Maximum	597.778%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	121.000%	24	100.00%	121.000%
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 0.87. Further, an Excess Kurtosis of 0.55 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -148.70%	0	0.00%	0.00%
-148.70% to -105.39%	0	0.00%	0.00%
-105.39% to -62.07%	0	0.00%	0.00%
-62.07% to -18.75%	6	25.00%	25.00%
-18.75% to 24.57%	7	29.17%	54.17%
24.57% to 67.89%	6	25.00%	79.17%
67.89% to 111.20%	3	12.50%	91.67%
111.20% to 154.52%	1	4.17%	95.83%
154.52% to 197.84%	1	4.17%	100.00%
Greater than 197.84%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.19%	82.33%	70.83%	68.27%
±2σ	-90.95%	140.08%	95.83%	95.45%
±3σ	-148.70%	197.84%	100.00%	99.73%

Descriptive Statistics

Mean	24.568%
Standard Error	11.790%
Median	14.478%
Mode	-61.290%
Standard Deviation	57.757%
Sample Variance	3335.904%
Kurtosis	0.55
Skewness	0.87
Range	233.290%
Minimum	-61.290%
Maximum	172.000%
Count	24

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.123%	16	66.67%	34.749%
Negative	-30.542%	8	33.33%	-10.181%
Zero	0.000%	0	0.00%	0.000%

INVZ Deep Analytical Report