MVIS - 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	6.13%	6.35%	5.19%	8.41%	9.66%	9.65%	0.62	0.76	0.57	0.83
Weekly	16.44%	19.21%	13.50%	19.75%	21.27%	21.23%	0.55	0.85	0.45	1.05
Monthly	27.71%	41.09%	24.80%	40.25%	44.27%	44.20%	0.44	1.07	0.28	1.66
Quarterly	64.22%	99.90%	44.15%	78.01%	76.67%	76.56%	0.32	1.48	0.15	3.18
Annual	—	—	—	—	153.35%	153.13%	0.15	3.18	0.03	14.73
Option Time Horizon	—	—	—	—	57.88%	57.80%	0.38	1.22	0.22	2.18

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $0.69 | 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): 153.35% (CRR binomial tree, American, n=20 steps) | BS IV: 154.89% (European Black-Scholes) | Yahoo IV (Annual): 153.13% → 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 4.16. Further, an Excess Kurtosis of 77.66 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.28%	27	0.36%	0.36%
-18.28% to -13.68%	33	0.44%	0.81%
-13.68% to -9.08%	157	2.11%	2.92%
-9.08% to -4.48%	895	12.03%	14.95%
-4.48% to 0.12%	3075	41.34%	56.29%
0.12% to 4.71%	2229	29.97%	86.26%
4.71% to 9.31%	662	8.90%	95.16%
9.31% to 13.91%	218	2.93%	98.09%
13.91% to 18.51%	78	1.05%	99.14%
Greater than 18.51%	64	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.02%	6.25%	81.33%	68.27%
±2σ	-12.15%	12.38%	96.15%	95.45%
±3σ	-18.28%	18.51%	98.78%	99.73%

Descriptive Statistics

Mean	0.116%
Standard Error	0.071%
Median	-0.145%
Mode	0.000%
Standard Deviation	6.132%
Sample Variance	37.597%
Kurtosis	77.66
Skewness	4.16
Range	203.448%
Minimum	-53.448%
Maximum	150.000%
Count	7438

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.531%	3255	43.76%	1.983%
Negative	-3.718%	3735	50.22%	-1.867%
Zero	0.000%	448	6.02%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	9.53%
20	1 Month	10.67%
60	1 Quarter	7.92%
250	1 Year	7.70%
750	3 Years	8.06%
1,250	5 Years	8.41%
2,500	10 Years	8.85%
5,000	20 Years	8.09%
12,500	50 Years	7.82%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 9.75. Further, an Excess Kurtosis of 256.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.10%	0	0.00%	0.00%
-11.10% to -6.34%	0	0.00%	0.00%
-6.34% to -1.58%	0	0.00%	0.00%
-1.58% to 3.18%	597	8.03%	8.03%
3.18% to 7.94%	4148	55.76%	63.79%
7.94% to 12.70%	1787	24.02%	87.81%
12.70% to 17.46%	548	7.37%	95.17%
17.46% to 22.22%	186	2.50%	97.67%
22.22% to 26.98%	80	1.08%	98.75%
Greater than 26.98%	93	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.60%	14.29%	90.99%	68.27%
±2σ	-4.75%	20.63%	97.16%	95.45%
±3σ	-11.10%	26.98%	98.75%	99.73%

Descriptive Statistics

Mean	7.942%
Standard Error	0.074%
Median	6.494%
Mode	5.263%
Standard Deviation	6.346%
Sample Variance	40.270%
Kurtosis	256.12
Skewness	9.75
Range	234.488%
Minimum	0.806%
Maximum	235.294%
Count	7439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.942%	7439	100.00%	7.942%
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 6.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.93%	49	0.66%	0.66%
-14.93% to -11.04%	96	1.29%	1.95%
-11.04% to -7.15%	246	3.31%	5.26%
-7.15% to -3.26%	849	11.41%	16.67%
-3.26% to 0.63%	2442	32.83%	49.50%
0.63% to 4.52%	2479	33.32%	82.82%
4.52% to 8.41%	901	12.11%	94.93%
8.41% to 12.30%	253	3.40%	98.33%
12.30% to 16.19%	75	1.01%	99.34%
Greater than 16.19%	49	0.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.56%	5.81%	77.01%	68.27%
±2σ	-9.74%	11.00%	94.97%	95.45%
±3σ	-14.93%	16.19%	98.68%	99.73%

Descriptive Statistics

Mean	0.629%
Standard Error	0.060%
Median	0.671%
Mode	0.000%
Standard Deviation	5.186%
Sample Variance	26.892%
Kurtosis	6.60
Skewness	-0.22
Range	89.178%
Minimum	-52.124%
Maximum	37.054%
Count	7439

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.947%	4055	54.51%	2.152%
Negative	-3.774%	3002	40.35%	-1.523%
Zero	0.000%	382	5.13%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.75. Further, an Excess Kurtosis of 109.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.59%	1	0.06%	0.06%
-48.59% to -36.26%	3	0.19%	0.26%
-36.26% to -23.93%	30	1.95%	2.20%
-23.93% to -11.61%	156	10.12%	12.32%
-11.61% to 0.72%	693	44.94%	57.26%
0.72% to 13.05%	476	30.87%	88.13%
13.05% to 25.38%	128	8.30%	96.43%
25.38% to 37.70%	29	1.88%	98.31%
37.70% to 50.03%	10	0.65%	98.96%
Greater than 50.03%	16	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.72%	17.16%	85.34%	68.27%
±2σ	-32.15%	33.60%	97.28%	95.45%
±3σ	-48.59%	50.03%	98.90%	99.73%

Descriptive Statistics

Mean	0.722%
Standard Error	0.419%
Median	-1.020%
Mode	0.000%
Standard Deviation	16.437%
Sample Variance	270.191%
Kurtosis	109.12
Skewness	6.75
Range	374.690%
Minimum	-51.613%
Maximum	323.077%
Count	1542

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.461%	682	44.23%	5.069%
Negative	-8.194%	818	53.05%	-4.347%
Zero	0.000%	42	2.72%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	25.47%
12	1 Quarter	17.84%
52	1 Year	16.70%
156	3 Years	18.38%
260	5 Years	19.75%
520	10 Years	21.38%
1,040	20 Years	19.19%
2,600	50 Years	18.49%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.80. Further, an Excess Kurtosis of 104.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.92%	0	0.00%	0.00%
-36.92% to -22.51%	0	0.00%	0.00%
-22.51% to -8.10%	0	0.00%	0.00%
-8.10% to 6.31%	52	3.37%	3.37%
6.31% to 20.72%	962	62.35%	65.72%
20.72% to 35.12%	379	24.56%	90.28%
35.12% to 49.53%	90	5.83%	96.11%
49.53% to 63.94%	34	2.20%	98.31%
63.94% to 78.35%	9	0.58%	98.90%
Greater than 78.35%	17	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.50%	39.93%	92.81%	68.27%
±2σ	-17.71%	59.14%	97.54%	95.45%
±3σ	-36.92%	78.35%	98.90%	99.73%

Descriptive Statistics

Mean	20.716%
Standard Error	0.489%
Median	16.505%
Mode	14.286%
Standard Deviation	19.212%
Sample Variance	369.083%
Kurtosis	104.38
Skewness	7.80
Range	371.809%
Minimum	3.191%
Maximum	375.000%
Count	1543

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.716%	1543	100.00%	20.716%
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 0.98. Further, an Excess Kurtosis of 9.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.87%	6	0.39%	0.39%
-38.87% to -28.75%	14	0.91%	1.30%
-28.75% to -18.62%	53	3.43%	4.73%
-18.62% to -8.50%	179	11.60%	16.33%
-8.50% to 1.63%	545	35.32%	51.65%
1.63% to 11.75%	508	32.92%	84.58%
11.75% to 21.88%	173	11.21%	95.79%
21.88% to 32.00%	31	2.01%	97.80%
32.00% to 42.13%	19	1.23%	99.03%
Greater than 42.13%	15	0.97%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.87%	15.13%	78.87%	68.27%
±2σ	-25.37%	28.63%	95.46%	95.45%
±3σ	-38.87%	42.13%	98.64%	99.73%

Descriptive Statistics

Mean	1.629%
Standard Error	0.344%
Median	1.227%
Mode	0.000%
Standard Deviation	13.500%
Sample Variance	182.250%
Kurtosis	9.11
Skewness	0.98
Range	183.031%
Minimum	-76.364%
Maximum	106.667%
Count	1543

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.098%	833	53.99%	5.452%
Negative	-8.870%	665	43.10%	-3.823%
Zero	0.000%	45	2.92%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.97. Further, an Excess Kurtosis of 6.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -81.19%	0	0.00%	0.00%
-81.19% to -60.41%	1	0.28%	0.28%
-60.41% to -39.63%	3	0.85%	1.13%
-39.63% to -18.84%	56	15.77%	16.90%
-18.84% to 1.94%	151	42.54%	59.44%
1.94% to 22.72%	91	25.63%	85.07%
22.72% to 43.51%	28	7.89%	92.96%
43.51% to 64.29%	14	3.94%	96.90%
64.29% to 85.07%	5	1.41%	98.31%
Greater than 85.07%	6	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.77%	29.65%	80.00%	68.27%
±2σ	-53.48%	57.36%	95.49%	95.45%
±3σ	-81.19%	85.07%	98.31%	99.73%

Descriptive Statistics

Mean	1.939%
Standard Error	1.471%
Median	-2.860%
Mode	0.000%
Standard Deviation	27.711%
Sample Variance	767.897%
Kurtosis	6.50
Skewness	1.97
Range	212.967%
Minimum	-61.538%
Maximum	151.429%
Count	355

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.977%	158	44.51%	10.226%
Negative	-15.165%	194	54.65%	-8.287%
Zero	0.000%	3	0.84%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	31.54%
12	1 Year	31.02%
36	3 Years	39.70%
60	5 Years	40.25%
120	10 Years	49.51%
240	20 Years	43.09%
600	50 Years	41.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.66. Further, an Excess Kurtosis of 19.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.34%	0	0.00%	0.00%
-72.34% to -41.52%	0	0.00%	0.00%
-41.52% to -10.71%	0	0.00%	0.00%
-10.71% to 20.11%	31	8.71%	8.71%
20.11% to 50.93%	210	58.99%	67.70%
50.93% to 81.75%	73	20.51%	88.20%
81.75% to 112.57%	20	5.62%	93.82%
112.57% to 143.39%	11	3.09%	96.91%
143.39% to 174.21%	3	0.84%	97.75%
Greater than 174.21%	8	2.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.84%	92.03%	90.73%	68.27%
±2σ	-31.25%	133.12%	95.51%	95.45%
±3σ	-72.35%	174.21%	97.75%	99.73%

Descriptive Statistics

Mean	50.934%
Standard Error	2.178%
Median	39.591%
Mode	66.667%
Standard Deviation	41.093%
Sample Variance	1688.644%
Kurtosis	19.75
Skewness	3.66
Range	367.958%
Minimum	10.989%
Maximum	378.947%
Count	356

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.934%	356	100.00%	50.934%
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 0.88. Further, an Excess Kurtosis of 4.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -69.50%	0	0.00%	0.00%
-69.50% to -50.90%	4	1.12%	1.12%
-50.90% to -32.30%	15	4.21%	5.34%
-32.30% to -13.71%	46	12.92%	18.26%
-13.71% to 4.89%	127	35.67%	53.93%
4.89% to 23.49%	99	27.81%	81.74%
23.49% to 42.09%	40	11.24%	92.98%
42.09% to 60.69%	18	5.06%	98.03%
60.69% to 79.28%	4	1.12%	99.16%
Greater than 79.28%	3	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.91%	29.69%	74.44%	68.27%
±2σ	-44.70%	54.49%	94.66%	95.45%
±3σ	-69.50%	79.28%	99.16%	99.73%

Descriptive Statistics

Mean	4.892%
Standard Error	1.314%
Median	3.151%
Mode	0.000%
Standard Deviation	24.797%
Sample Variance	614.909%
Kurtosis	4.34
Skewness	0.88
Range	217.143%
Minimum	-57.143%
Maximum	160.000%
Count	356

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.641%	200	56.18%	11.596%
Negative	-15.701%	152	42.70%	-6.704%
Zero	0.000%	4	1.12%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.46. Further, an Excess Kurtosis of 27.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -185.69%	0	0.00%	0.00%
-185.69% to -137.53%	0	0.00%	0.00%
-137.53% to -89.37%	0	0.00%	0.00%
-89.37% to -41.21%	10	8.47%	8.47%
-41.21% to 6.96%	64	54.24%	62.71%
6.96% to 55.12%	29	24.58%	87.29%
55.12% to 103.28%	11	9.32%	96.61%
103.28% to 151.44%	2	1.69%	98.31%
151.44% to 199.60%	0	0.00%	98.31%
Greater than 199.60%	2	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-57.26%	71.17%	91.53%	68.27%
±2σ	-121.48%	135.39%	97.46%	95.45%
±3σ	-185.69%	199.60%	98.31%	99.73%

Descriptive Statistics

Mean	6.955%
Standard Error	5.912%
Median	-5.914%
Mode	-46.154%
Standard Deviation	64.216%
Sample Variance	4123.725%
Kurtosis	27.77
Skewness	4.46
Range	547.279%
Minimum	-70.136%
Maximum	477.143%
Count	118

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	49.069%	50	42.37%	20.792%
Negative	-24.011%	68	57.63%	-13.837%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	47.98%
12	3 Years	79.97%
20	5 Years	78.01%
40	10 Years	100.98%
80	20 Years	82.81%
200	50 Years	76.67%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.07. Further, an Excess Kurtosis of 22.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -190.92%	0	0.00%	0.00%
-190.92% to -115.99%	0	0.00%	0.00%
-115.99% to -41.06%	0	0.00%	0.00%
-41.06% to 33.87%	6	5.04%	5.04%
33.87% to 108.80%	79	66.39%	71.43%
108.80% to 183.72%	20	16.81%	88.24%
183.72% to 258.65%	7	5.88%	94.12%
258.65% to 333.58%	4	3.36%	97.48%
333.58% to 408.51%	1	0.84%	98.32%
Greater than 408.51%	2	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.89%	208.70%	92.44%	68.27%
±2σ	-91.01%	308.60%	94.96%	95.45%
±3σ	-190.92%	408.51%	98.32%	99.73%

Descriptive Statistics

Mean	108.796%
Standard Error	9.158%
Median	85.938%
Mode	26.429%
Standard Deviation	99.904%
Sample Variance	9980.781%
Kurtosis	22.58
Skewness	4.07
Range	781.466%
Minimum	26.429%
Maximum	807.895%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	108.796%	119	100.00%	108.796%
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 1.34. Further, an Excess Kurtosis of 4.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -119.58%	0	0.00%	0.00%
-119.58% to -86.46%	0	0.00%	0.00%
-86.46% to -53.35%	3	2.52%	2.52%
-53.35% to -20.23%	20	16.81%	19.33%
-20.23% to 12.88%	46	38.66%	57.98%
12.88% to 45.99%	29	24.37%	82.35%
45.99% to 79.11%	11	9.24%	91.60%
79.11% to 112.22%	8	6.72%	98.32%
112.22% to 145.34%	1	0.84%	99.16%
Greater than 145.34%	1	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-31.27%	57.03%	77.31%	68.27%
±2σ	-75.43%	101.19%	95.80%	95.45%
±3σ	-119.58%	145.34%	99.16%	99.73%

Descriptive Statistics

Mean	12.880%
Standard Error	4.048%
Median	7.044%
Mode	-78.218%
Standard Deviation	44.153%
Sample Variance	1949.505%
Kurtosis	4.92
Skewness	1.34
Range	316.097%
Minimum	-78.218%
Maximum	237.879%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.828%	68	57.14%	22.759%
Negative	-23.513%	50	42.02%	-9.879%
Zero	0.000%	1	0.84%	0.000%

MVIS Deep Analytical Report