RUN - 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	5.00%	3.88%	4.24%	7.78%	6.03%	6.07%	11.47	12.94	10.80	13.75
Weekly	11.34%	11.54%	11.73%	18.46%	13.27%	13.37%	10.67	13.91	9.35	15.89
Monthly	23.16%	25.07%	22.73%	38.18%	27.62%	27.82%	9.24	16.06	7.01	21.17
Quarterly	42.78%	48.04%	40.31%	65.48%	47.84%	48.19%	7.55	19.66	4.68	31.72
Annual	—	—	—	—	95.67%	96.39%	4.68	31.72	1.80	82.57
Option Time Horizon	—	—	—	—	36.11%	36.38%	8.49	17.48	5.92	25.09

Calculation Notes: Computed at 2026-03-23T16:36 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $12.19 | Strike (K): $13.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.4700 (Bid $1.3300 / Ask $1.6100) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 95.67% (CRR binomial tree, American, n=20 steps) | BS IV: 96.74% (European Black-Scholes) | Yahoo IV (Annual): 96.39% → 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 Fairly Symmetrical with a Skewness factor of 0.03. Further, an Excess Kurtosis of 7.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.87%	17	0.64%	0.64%
-14.87% to -11.12%	16	0.60%	1.24%
-11.12% to -7.37%	96	3.59%	4.83%
-7.37% to -3.62%	333	12.47%	17.30%
-3.62% to 0.13%	884	33.10%	50.39%
0.13% to 3.88%	867	32.46%	82.85%
3.88% to 7.63%	320	11.98%	94.83%
7.63% to 11.38%	94	3.52%	98.35%
11.38% to 15.13%	17	0.64%	98.99%
Greater than 15.13%	27	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.87%	5.13%	76.75%	68.27%
±2σ	-9.87%	10.13%	95.54%	95.45%
±3σ	-14.87%	15.13%	98.35%	99.73%

Descriptive Statistics

Mean	0.131%
Standard Error	0.097%
Median	0.080%
Mode	0.000%
Standard Deviation	4.999%
Sample Variance	24.987%
Kurtosis	7.35
Skewness	0.03
Range	72.865%
Minimum	-40.041%
Maximum	32.824%
Count	2671

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.594%	1349	50.51%	1.815%
Negative	-3.463%	1299	48.63%	-1.684%
Zero	0.000%	23	0.86%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.85%
20	1 Month	8.95%
60	1 Quarter	7.94%
250	1 Year	9.05%
750	3 Years	8.00%
1,250	5 Years	7.78%
2,500	10 Years	6.68%
5,000	20 Years	6.79%
12,500	50 Years	6.79%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.11. Further, an Excess Kurtosis of 20.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.03%	0	0.00%	0.00%
-5.03% to -2.12%	0	0.00%	0.00%
-2.12% to 0.80%	0	0.00%	0.00%
0.80% to 3.71%	489	18.30%	18.30%
3.71% to 6.62%	1113	41.65%	59.96%
6.62% to 9.53%	656	24.55%	84.51%
9.53% to 12.45%	250	9.36%	93.86%
12.45% to 15.36%	89	3.33%	97.19%
15.36% to 18.27%	35	1.31%	98.50%
Greater than 18.27%	40	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.74%	10.51%	83.20%	68.27%
±2σ	-1.15%	14.39%	96.59%	95.45%
±3σ	-5.03%	18.27%	98.50%	99.73%

Descriptive Statistics

Mean	6.621%
Standard Error	0.075%
Median	5.793%
Mode	4.564%
Standard Deviation	3.884%
Sample Variance	15.087%
Kurtosis	20.00
Skewness	3.11
Range	49.116%
Minimum	1.165%
Maximum	50.281%
Count	2672

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.621%	2672	100.00%	6.621%
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 5.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.57%	14	0.52%	0.52%
-12.57% to -9.39%	25	0.94%	1.46%
-9.39% to -6.21%	96	3.59%	5.05%
-6.21% to -3.03%	371	13.88%	18.94%
-3.03% to 0.15%	884	33.08%	52.02%
0.15% to 3.33%	804	30.09%	82.11%
3.33% to 6.51%	321	12.01%	94.12%
6.51% to 9.69%	106	3.97%	98.09%
9.69% to 12.87%	33	1.24%	99.33%
Greater than 12.87%	18	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.09%	4.39%	74.78%	68.27%
±2σ	-8.33%	8.63%	94.80%	95.45%
±3σ	-12.57%	12.87%	98.80%	99.73%

Descriptive Statistics

Mean	0.154%
Standard Error	0.082%
Median	0.000%
Mode	0.000%
Standard Deviation	4.240%
Sample Variance	17.978%
Kurtosis	5.51
Skewness	0.49
Range	65.015%
Minimum	-24.713%
Maximum	40.302%
Count	2672

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.257%	1317	49.29%	1.605%
Negative	-2.936%	1321	49.44%	-1.452%
Zero	0.000%	34	1.27%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of 2.93 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.35%	6	1.08%	1.08%
-33.35% to -24.84%	4	0.72%	1.81%
-24.84% to -16.33%	15	2.71%	4.51%
-16.33% to -7.83%	78	14.08%	18.59%
-7.83% to 0.68%	180	32.49%	51.08%
0.68% to 9.19%	173	31.23%	82.31%
9.19% to 17.69%	72	13.00%	95.31%
17.69% to 26.20%	10	1.81%	97.11%
26.20% to 34.71%	10	1.81%	98.92%
Greater than 34.71%	6	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.66%	12.02%	76.90%	68.27%
±2σ	-22.00%	23.36%	94.77%	95.45%
±3σ	-33.35%	34.71%	97.83%	99.73%

Descriptive Statistics

Mean	0.680%
Standard Error	0.482%
Median	0.444%
Mode	0.000%
Standard Deviation	11.342%
Sample Variance	128.637%
Kurtosis	2.93
Skewness	0.29
Range	100.498%
Minimum	-43.478%
Maximum	57.020%
Count	554

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.639%	285	51.44%	4.444%
Negative	-7.871%	265	47.83%	-3.765%
Zero	0.000%	4	0.72%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	21.66%
12	1 Quarter	17.82%
52	1 Year	21.32%
156	3 Years	19.16%
260	5 Years	18.46%
520	10 Years	15.69%
1,040	20 Years	15.93%
2,600	50 Years	15.93%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.94. Further, an Excess Kurtosis of 14.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.12%	0	0.00%	0.00%
-17.12% to -8.46%	0	0.00%	0.00%
-8.46% to 0.20%	0	0.00%	0.00%
0.20% to 8.86%	92	16.58%	16.58%
8.86% to 17.52%	262	47.21%	63.78%
17.52% to 26.18%	121	21.80%	85.59%
26.18% to 34.84%	48	8.65%	94.23%
34.84% to 43.49%	15	2.70%	96.94%
43.49% to 52.15%	6	1.08%	98.02%
Greater than 52.15%	11	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.97%	29.06%	84.68%	68.27%
±2σ	-5.57%	40.61%	95.50%	95.45%
±3σ	-17.12%	52.15%	98.02%	99.73%

Descriptive Statistics

Mean	17.518%
Standard Error	0.490%
Median	14.667%
Mode	7.212%
Standard Deviation	11.545%
Sample Variance	133.283%
Kurtosis	14.84
Skewness	2.94
Range	110.653%
Minimum	2.513%
Maximum	113.166%
Count	555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.518%	555	100.00%	17.518%
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 1.61. Further, an Excess Kurtosis of 8.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.47%	1	0.18%	0.18%
-34.47% to -25.67%	4	0.72%	0.90%
-25.67% to -16.87%	16	2.88%	3.78%
-16.87% to -8.07%	75	13.51%	17.30%
-8.07% to 0.72%	214	38.56%	55.86%
0.72% to 9.52%	157	28.29%	84.14%
9.52% to 18.32%	61	10.99%	95.14%
18.32% to 27.12%	15	2.70%	97.84%
27.12% to 35.91%	4	0.72%	98.56%
Greater than 35.91%	8	1.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.01%	12.46%	78.38%	68.27%
±2σ	-22.73%	24.19%	95.68%	95.45%
±3σ	-34.46%	35.91%	98.38%	99.73%

Descriptive Statistics

Mean	0.725%
Standard Error	0.498%
Median	-0.147%
Mode	0.000%
Standard Deviation	11.730%
Sample Variance	137.585%
Kurtosis	8.61
Skewness	1.61
Range	123.802%
Minimum	-36.131%
Maximum	87.671%
Count	555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.095%	267	48.11%	4.375%
Negative	-7.159%	283	50.99%	-3.650%
Zero	0.000%	5	0.90%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 1.19 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.00%	0	0.00%	0.00%
-67.00% to -49.63%	0	0.00%	0.00%
-49.63% to -32.27%	4	3.15%	3.15%
-32.27% to -14.90%	30	23.62%	26.77%
-14.90% to 2.47%	34	26.77%	53.54%
2.47% to 19.84%	35	27.56%	81.10%
19.84% to 37.20%	13	10.24%	91.34%
37.20% to 54.57%	8	6.30%	97.64%
54.57% to 71.94%	1	0.79%	98.43%
Greater than 71.94%	2	1.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.69%	25.63%	76.38%	68.27%
±2σ	-43.84%	48.78%	95.28%	95.45%
±3σ	-67.00%	71.94%	98.43%	99.73%

Descriptive Statistics

Mean	2.469%
Standard Error	2.055%
Median	-0.377%
Mode	-47.777%
Standard Deviation	23.157%
Sample Variance	536.260%
Kurtosis	1.19
Skewness	0.86
Range	133.832%
Minimum	-47.777%
Maximum	86.055%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.630%	62	48.82%	10.071%
Negative	-14.853%	65	51.18%	-7.602%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	32.08%
12	1 Year	43.86%
36	3 Years	39.73%
60	5 Years	38.18%
120	10 Years	34.44%
240	20 Years	35.29%
600	50 Years	35.29%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.02. Further, an Excess Kurtosis of 6.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.43%	0	0.00%	0.00%
-31.43% to -12.63%	0	0.00%	0.00%
-12.63% to 6.17%	0	0.00%	0.00%
6.17% to 24.97%	29	22.66%	22.66%
24.97% to 43.77%	46	35.94%	58.59%
43.77% to 62.57%	30	23.44%	82.03%
62.57% to 81.37%	14	10.94%	92.97%
81.37% to 100.17%	5	3.91%	96.88%
100.17% to 118.97%	1	0.78%	97.66%
Greater than 118.97%	3	2.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.70%	68.84%	79.69%	68.27%
±2σ	-6.37%	93.90%	96.09%	95.45%
±3σ	-31.43%	118.97%	97.66%	99.73%

Descriptive Statistics

Mean	43.768%
Standard Error	2.216%
Median	39.216%
Mode	11.488%
Standard Deviation	25.067%
Sample Variance	628.353%
Kurtosis	6.57
Skewness	2.02
Range	164.581%
Minimum	11.488%
Maximum	176.069%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.768%	128	100.00%	43.768%
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 0.66. Further, an Excess Kurtosis of 1.42 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.36%	0	0.00%	0.00%
-65.36% to -48.32%	0	0.00%	0.00%
-48.32% to -31.27%	7	5.47%	5.47%
-31.27% to -14.23%	23	17.97%	23.44%
-14.23% to 2.82%	40	31.25%	54.69%
2.82% to 19.86%	28	21.88%	76.56%
19.86% to 36.91%	22	17.19%	93.75%
36.91% to 53.95%	5	3.91%	97.66%
53.95% to 71.00%	1	0.78%	98.44%
Greater than 71.00%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.91%	25.54%	68.75%	68.27%
±2σ	-42.64%	48.27%	95.31%	95.45%
±3σ	-65.36%	71.00%	98.44%	99.73%

Descriptive Statistics

Mean	2.817%
Standard Error	2.009%
Median	1.381%
Mode	-46.252%
Standard Deviation	22.727%
Sample Variance	516.525%
Kurtosis	1.42
Skewness	0.66
Range	138.925%
Minimum	-46.252%
Maximum	92.673%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.154%	68	53.12%	10.176%
Negative	-15.697%	60	46.88%	-7.358%
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 1.35. Further, an Excess Kurtosis of 2.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -119.98%	0	0.00%	0.00%
-119.98% to -87.89%	0	0.00%	0.00%
-87.89% to -55.80%	0	0.00%	0.00%
-55.80% to -23.72%	10	23.81%	23.81%
-23.72% to 8.37%	13	30.95%	54.76%
8.37% to 40.46%	9	21.43%	76.19%
40.46% to 72.55%	8	19.05%	95.24%
72.55% to 104.63%	1	2.38%	97.62%
104.63% to 136.72%	0	0.00%	97.62%
Greater than 136.72%	1	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.41%	51.15%	78.57%	68.27%
±2σ	-77.20%	93.94%	95.24%	95.45%
±3σ	-119.98%	136.72%	97.62%	99.73%

Descriptive Statistics

Mean	8.371%
Standard Error	6.602%
Median	1.058%
Mode	-55.045%
Standard Deviation	42.783%
Sample Variance	1830.366%
Kurtosis	2.82
Skewness	1.35
Range	216.556%
Minimum	-55.045%
Maximum	161.511%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.426%	22	52.38%	20.128%
Negative	-25.989%	19	45.24%	-11.757%
Zero	0.000%	1	2.38%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	82.76%
12	3 Years	71.66%
20	5 Years	65.48%
40	10 Years	64.66%
80	20 Years	65.54%
200	50 Years	65.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.26. Further, an Excess Kurtosis of 1.87 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.68%	0	0.00%	0.00%
-54.68% to -18.65%	0	0.00%	0.00%
-18.65% to 17.38%	0	0.00%	0.00%
17.38% to 53.41%	10	23.26%	23.26%
53.41% to 89.44%	15	34.88%	58.14%
89.44% to 125.47%	9	20.93%	79.07%
125.47% to 161.50%	5	11.63%	90.70%
161.50% to 197.53%	2	4.65%	95.35%
197.53% to 233.56%	1	2.33%	97.67%
Greater than 233.56%	1	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	41.40%	137.48%	72.09%	68.27%
±2σ	-6.64%	185.52%	95.35%	95.45%
±3σ	-54.68%	233.56%	97.67%	99.73%

Descriptive Statistics

Mean	89.442%
Standard Error	7.326%
Median	84.014%
Mode	27.444%
Standard Deviation	48.040%
Sample Variance	2307.835%
Kurtosis	1.87
Skewness	1.26
Range	219.941%
Minimum	27.444%
Maximum	247.385%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	89.442%	43	100.00%	89.442%
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 0.75. Further, an Excess Kurtosis of 0.63 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -113.24%	0	0.00%	0.00%
-113.24% to -83.01%	0	0.00%	0.00%
-83.01% to -52.78%	1	2.33%	2.33%
-52.78% to -22.55%	11	25.58%	27.91%
-22.55% to 7.68%	11	25.58%	53.49%
7.68% to 37.91%	11	25.58%	79.07%
37.91% to 68.14%	6	13.95%	93.02%
68.14% to 98.37%	2	4.65%	97.67%
98.37% to 128.60%	1	2.33%	100.00%
Greater than 128.60%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-32.63%	47.99%	72.09%	68.27%
±2σ	-72.94%	88.29%	95.35%	95.45%
±3σ	-113.24%	128.60%	100.00%	99.73%

Descriptive Statistics

Mean	7.679%
Standard Error	6.147%
Median	-0.576%
Mode	-63.505%
Standard Deviation	40.307%
Sample Variance	1624.649%
Kurtosis	0.63
Skewness	0.75
Range	189.459%
Minimum	-63.505%
Maximum	125.954%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	42.418%	20	46.51%	19.729%
Negative	-22.530%	23	53.49%	-12.051%
Zero	0.000%	0	0.00%	0.000%

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