RNG - 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	3.37%	2.43%	2.84%	4.80%	5.93%	4.30%	35.81	40.32	33.74	42.78
Weekly	7.29%	6.69%	7.31%	11.48%	13.06%	9.47%	33.34	43.30	29.26	49.34
Monthly	13.04%	12.53%	13.01%	24.19%	27.20%	19.71%	28.95	49.87	22.05	65.46
Quarterly	23.30%	22.98%	27.39%	41.81%	47.11%	34.14%	23.72	60.86	14.81	97.47
Annual	—	—	—	—	94.21%	68.29%	14.81	97.47	5.77	250.06
Option Time Horizon	—	—	—	—	35.56%	25.77%	26.63	54.22	18.66	77.37

Calculation Notes: Computed at 2026-03-23T16:39 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $37.99 | Strike (K): $40.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.1500 (Bid $2.8000 / Ask $3.5000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 80.00% | Binomial IV (Annual): 94.21% (CRR binomial tree, American, n=20 steps) | BS IV: 101.93% (European Black-Scholes) | Yahoo IV (Annual): 68.29% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2026-03-09	$0.0750

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.88. Further, an Excess Kurtosis of 11.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.03%	13	0.41%	0.41%
-10.03% to -7.50%	29	0.92%	1.34%
-7.50% to -4.97%	125	3.98%	5.32%
-4.97% to -2.45%	348	11.09%	16.41%
-2.45% to 0.08%	1083	34.51%	50.92%
0.08% to 2.60%	1021	32.54%	83.46%
2.60% to 5.13%	369	11.76%	95.22%
5.13% to 7.66%	99	3.15%	98.37%
7.66% to 10.18%	29	0.92%	99.30%
Greater than 10.18%	22	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.29%	3.45%	77.76%	68.27%
±2σ	-6.66%	6.81%	95.32%	95.45%
±3σ	-10.02%	10.18%	98.88%	99.73%

Descriptive Statistics

Mean	0.079%
Standard Error	0.060%
Median	0.046%
Mode	0.000%
Standard Deviation	3.368%
Sample Variance	11.343%
Kurtosis	11.41
Skewness	0.88
Range	57.824%
Minimum	-23.425%
Maximum	34.399%
Count	3138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.373%	1578	50.29%	1.193%
Negative	-2.294%	1523	48.53%	-1.113%
Zero	0.000%	37	1.18%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.14%
20	1 Month	5.51%
60	1 Quarter	5.67%
250	1 Year	4.23%
750	3 Years	4.17%
1,250	5 Years	4.80%
2,500	10 Years	4.39%
5,000	20 Years	4.38%
12,500	50 Years	4.38%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.23. Further, an Excess Kurtosis of 8.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.03%	0	0.00%	0.00%
-3.03% to -1.21%	0	0.00%	0.00%
-1.21% to 0.61%	0	0.00%	0.00%
0.61% to 2.44%	624	19.88%	19.88%
2.44% to 4.26%	1296	41.29%	61.17%
4.26% to 6.08%	705	22.46%	83.63%
6.08% to 7.90%	286	9.11%	92.74%
7.90% to 9.72%	127	4.05%	96.78%
9.72% to 11.54%	48	1.53%	98.31%
Greater than 11.54%	53	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.83%	6.69%	80.89%	68.27%
±2σ	-0.60%	9.12%	95.70%	95.45%
±3σ	-3.03%	11.54%	98.31%	99.73%

Descriptive Statistics

Mean	4.258%
Standard Error	0.043%
Median	3.663%
Mode	2.558%
Standard Deviation	2.429%
Sample Variance	5.899%
Kurtosis	8.64
Skewness	2.23
Range	22.177%
Minimum	0.648%
Maximum	22.825%
Count	3139

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.258%	3139	100.00%	4.258%
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 0.31. Further, an Excess Kurtosis of 2.74 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.45%	16	0.51%	0.51%
-8.45% to -6.32%	32	1.02%	1.53%
-6.32% to -4.18%	116	3.70%	5.22%
-4.18% to -2.05%	408	13.00%	18.22%
-2.05% to 0.08%	1078	34.34%	52.56%
0.08% to 2.21%	911	29.02%	81.59%
2.21% to 4.34%	384	12.23%	93.82%
4.34% to 6.48%	126	4.01%	97.83%
6.48% to 8.61%	44	1.40%	99.24%
Greater than 8.61%	24	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.76%	2.92%	74.86%	68.27%
±2σ	-5.61%	5.77%	94.42%	95.45%
±3σ	-8.45%	8.61%	98.73%	99.73%

Descriptive Statistics

Mean	0.080%
Standard Error	0.051%
Median	-0.046%
Mode	0.000%
Standard Deviation	2.843%
Sample Variance	8.085%
Kurtosis	2.74
Skewness	0.31
Range	31.443%
Minimum	-13.629%
Maximum	17.814%
Count	3139

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.222%	1518	48.36%	1.075%
Negative	-1.965%	1589	50.62%	-0.995%
Zero	0.000%	32	1.02%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.23. Further, an Excess Kurtosis of 3.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.49%	3	0.46%	0.46%
-21.49% to -16.02%	9	1.38%	1.84%
-16.02% to -10.55%	27	4.15%	5.99%
-10.55% to -5.09%	84	12.90%	18.89%
-5.09% to 0.38%	204	31.34%	50.23%
0.38% to 5.85%	207	31.80%	82.03%
5.85% to 11.31%	83	12.75%	94.78%
11.31% to 16.78%	23	3.53%	98.31%
16.78% to 22.25%	8	1.23%	99.54%
Greater than 22.25%	3	0.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.91%	7.67%	75.58%	68.27%
±2σ	-14.20%	14.96%	94.93%	95.45%
±3σ	-21.49%	22.25%	99.08%	99.73%

Descriptive Statistics

Mean	0.380%
Standard Error	0.286%
Median	0.363%
Mode	-2.863%
Standard Deviation	7.289%
Sample Variance	53.136%
Kurtosis	3.14
Skewness	0.23
Range	71.538%
Minimum	-33.664%
Maximum	37.874%
Count	651

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.385%	346	53.15%	2.862%
Negative	-5.297%	305	46.85%	-2.482%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.24%
12	1 Quarter	14.10%
52	1 Year	10.39%
156	3 Years	10.01%
260	5 Years	11.48%
520	10 Years	10.44%
1,040	20 Years	10.35%
2,600	50 Years	10.35%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.39. Further, an Excess Kurtosis of 9.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.10%	0	0.00%	0.00%
-9.10% to -4.08%	0	0.00%	0.00%
-4.08% to 0.93%	0	0.00%	0.00%
0.93% to 5.95%	127	19.48%	19.48%
5.95% to 10.96%	277	42.48%	61.96%
10.96% to 15.98%	151	23.16%	85.12%
15.98% to 21.00%	50	7.67%	92.79%
21.00% to 26.01%	24	3.68%	96.47%
26.01% to 31.03%	13	1.99%	98.47%
Greater than 31.03%	10	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.28%	17.65%	84.05%	68.27%
±2σ	-2.41%	24.34%	95.40%	95.45%
±3σ	-9.10%	31.03%	98.47%	99.73%

Descriptive Statistics

Mean	10.965%
Standard Error	0.262%
Median	9.191%
Mode	3.111%
Standard Deviation	6.688%
Sample Variance	44.727%
Kurtosis	9.05
Skewness	2.39
Range	54.595%
Minimum	2.573%
Maximum	57.168%
Count	652

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.965%	652	100.00%	10.965%
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 4.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.69%	3	0.46%	0.46%
-21.69% to -16.21%	3	0.46%	0.92%
-16.21% to -10.72%	24	3.68%	4.60%
-10.72% to -5.24%	93	14.26%	18.87%
-5.24% to 0.25%	228	34.97%	53.83%
0.25% to 5.73%	187	28.68%	82.52%
5.73% to 11.22%	62	9.51%	92.02%
11.22% to 16.70%	37	5.67%	97.70%
16.70% to 22.19%	9	1.38%	99.08%
Greater than 22.19%	6	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.06%	7.56%	76.69%	68.27%
±2σ	-14.38%	14.87%	95.55%	95.45%
±3σ	-21.69%	22.19%	98.62%	99.73%

Descriptive Statistics

Mean	0.248%
Standard Error	0.286%
Median	-0.281%
Mode	-8.512%
Standard Deviation	7.313%
Sample Variance	53.481%
Kurtosis	4.91
Skewness	0.90
Range	79.662%
Minimum	-27.345%
Maximum	52.317%
Count	652

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.811%	309	47.39%	2.754%
Negative	-4.791%	341	52.30%	-2.506%
Zero	0.000%	2	0.31%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.22. Further, an Excess Kurtosis of -0.24 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.77%	0	0.00%	0.00%
-37.77% to -28.00%	0	0.00%	0.00%
-28.00% to -18.22%	7	4.67%	4.67%
-18.22% to -8.44%	28	18.67%	23.33%
-8.44% to 1.33%	40	26.67%	50.00%
1.33% to 11.11%	39	26.00%	76.00%
11.11% to 20.89%	23	15.33%	91.33%
20.89% to 30.66%	12	8.00%	99.33%
30.66% to 40.44%	0	0.00%	99.33%
Greater than 40.44%	1	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.70%	14.37%	67.33%	68.27%
±2σ	-24.74%	27.40%	95.33%	95.45%
±3σ	-37.77%	40.44%	99.33%	99.73%

Descriptive Statistics

Mean	1.333%
Standard Error	1.064%
Median	1.157%
Mode	7.073%
Standard Deviation	13.035%
Sample Variance	169.899%
Kurtosis	-0.24
Skewness	0.22
Range	68.200%
Minimum	-27.609%
Maximum	40.591%
Count	150

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.522%	77	51.33%	5.915%
Negative	-9.414%	73	48.67%	-4.582%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	34.15%
12	1 Year	21.60%
36	3 Years	21.76%
60	5 Years	24.19%
120	10 Years	22.26%
240	20 Years	22.06%
600	50 Years	22.06%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.70. Further, an Excess Kurtosis of 4.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.32%	0	0.00%	0.00%
-12.32% to -2.92%	0	0.00%	0.00%
-2.92% to 6.48%	0	0.00%	0.00%
6.48% to 15.88%	34	22.52%	22.52%
15.88% to 25.27%	57	37.75%	60.26%
25.27% to 34.67%	31	20.53%	80.79%
34.67% to 44.07%	17	11.26%	92.05%
44.07% to 53.47%	9	5.96%	98.01%
53.47% to 62.87%	1	0.66%	98.68%
Greater than 62.87%	2	1.32%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.74%	37.81%	75.50%	68.27%
±2σ	0.21%	50.34%	94.70%	95.45%
±3σ	-12.32%	62.87%	98.68%	99.73%

Descriptive Statistics

Mean	25.274%
Standard Error	1.020%
Median	21.934%
Mode	6.999%
Standard Deviation	12.532%
Sample Variance	157.050%
Kurtosis	4.71
Skewness	1.70
Range	83.286%
Minimum	6.999%
Maximum	90.285%
Count	151

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.274%	151	100.00%	25.274%
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 0.45. Further, an Excess Kurtosis of 0.09 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.61%	0	0.00%	0.00%
-38.61% to -28.85%	1	0.66%	0.66%
-28.85% to -19.09%	6	3.97%	4.64%
-19.09% to -9.33%	30	19.87%	24.50%
-9.33% to 0.42%	43	28.48%	52.98%
0.42% to 10.18%	37	24.50%	77.48%
10.18% to 19.94%	23	15.23%	92.72%
19.94% to 29.70%	7	4.64%	97.35%
29.70% to 39.45%	4	2.65%	100.00%
Greater than 39.45%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.59%	13.43%	68.21%	68.27%
±2σ	-25.60%	26.44%	96.03%	95.45%
±3σ	-38.61%	39.45%	100.00%	99.73%

Descriptive Statistics

Mean	0.423%
Standard Error	1.059%
Median	-0.694%
Mode	-28.999%
Standard Deviation	13.010%
Sample Variance	169.267%
Kurtosis	0.09
Skewness	0.45
Range	68.374%
Minimum	-28.999%
Maximum	39.375%
Count	151

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.958%	74	49.01%	5.370%
Negative	-9.701%	77	50.99%	-4.947%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.23. Further, an Excess Kurtosis of -0.36 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.72%	0	0.00%	0.00%
-65.72% to -48.24%	1	2.00%	2.00%
-48.24% to -30.77%	2	4.00%	6.00%
-30.77% to -13.30%	8	16.00%	22.00%
-13.30% to 4.18%	13	26.00%	48.00%
4.18% to 21.65%	14	28.00%	76.00%
21.65% to 39.13%	9	18.00%	94.00%
39.13% to 56.60%	3	6.00%	100.00%
56.60% to 74.08%	0	0.00%	100.00%
Greater than 74.08%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.12%	27.48%	72.00%	68.27%
±2σ	-42.42%	50.78%	98.00%	95.45%
±3σ	-65.72%	74.07%	100.00%	99.73%

Descriptive Statistics

Mean	4.178%
Standard Error	3.295%
Median	7.159%
Mode	-51.924%
Standard Deviation	23.299%
Sample Variance	542.832%
Kurtosis	-0.36
Skewness	-0.23
Range	101.997%
Minimum	-51.924%
Maximum	50.073%
Count	50

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.255%	28	56.00%	11.903%
Negative	-17.557%	22	44.00%	-7.725%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	36.86%
12	3 Years	38.54%
20	5 Years	41.81%
40	10 Years	38.73%
80	20 Years	37.78%
200	50 Years	37.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.14. Further, an Excess Kurtosis of 0.65 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.50%	0	0.00%	0.00%
-21.50% to -4.26%	0	0.00%	0.00%
-4.26% to 12.97%	0	0.00%	0.00%
12.97% to 30.21%	13	25.49%	25.49%
30.21% to 47.44%	20	39.22%	64.71%
47.44% to 64.68%	7	13.73%	78.43%
64.68% to 81.91%	5	9.80%	88.24%
81.91% to 99.15%	4	7.84%	96.08%
99.15% to 116.38%	2	3.92%	100.00%
Greater than 116.38%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	24.46%	70.42%	74.51%	68.27%
±2σ	1.48%	93.40%	96.08%	95.45%
±3σ	-21.50%	116.38%	100.00%	99.73%

Descriptive Statistics

Mean	47.443%
Standard Error	3.218%
Median	40.492%
Mode	19.818%
Standard Deviation	22.980%
Sample Variance	528.072%
Kurtosis	0.65
Skewness	1.14
Range	95.868%
Minimum	19.818%
Maximum	115.686%
Count	51

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	47.443%	51	100.00%	47.443%
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 1.69. Further, an Excess Kurtosis of 3.90 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -80.69%	0	0.00%	0.00%
-80.69% to -60.14%	0	0.00%	0.00%
-60.14% to -39.60%	0	0.00%	0.00%
-39.60% to -19.05%	11	21.57%	21.57%
-19.05% to 1.49%	20	39.22%	60.78%
1.49% to 22.04%	13	25.49%	86.27%
22.04% to 42.59%	4	7.84%	94.12%
42.59% to 63.13%	1	1.96%	96.08%
63.13% to 83.68%	1	1.96%	98.04%
Greater than 83.68%	1	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.90%	28.89%	78.43%	68.27%
±2σ	-53.29%	56.28%	96.08%	95.45%
±3σ	-80.69%	83.68%	98.04%	99.73%

Descriptive Statistics

Mean	1.494%
Standard Error	3.836%
Median	-5.867%
Mode	-33.704%
Standard Deviation	27.394%
Sample Variance	750.429%
Kurtosis	3.90
Skewness	1.69
Range	141.895%
Minimum	-33.704%
Maximum	108.191%
Count	51

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.074%	22	43.14%	10.816%
Negative	-16.395%	29	56.86%	-9.323%
Zero	0.000%	0	0.00%	0.000%

RNG Deep Analytical Report