HUBS - 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	3.13%	2.48%	2.73%	4.52%	4.61%	4.65%	248.58	272.60	237.38	285.47
Weekly	6.98%	6.23%	7.16%	10.55%	10.15%	10.24%	235.18	288.13	212.47	318.93
Monthly	12.80%	12.74%	13.00%	20.95%	21.14%	21.32%	210.72	321.58	170.57	397.27
Quarterly	22.09%	21.82%	23.28%	37.91%	36.61%	36.92%	180.51	375.40	125.18	541.35
Annual	—	—	—	—	73.22%	73.85%	125.18	541.35	60.19	1125.80
Option Time Horizon	—	—	—	—	27.64%	27.87%	197.46	343.18	149.78	452.42

Calculation Notes: Computed at 2026-03-23T16:43 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $260.32 | Strike (K): $270.00 (first OTM call ≥ spot) | Observed Mid-Price: $25.3500 (Bid $23.4000 / Ask $27.3000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 73.22% (CRR binomial tree, American, n=20 steps) | BS IV: 73.81% (European Black-Scholes) | Yahoo IV (Annual): 73.85% → 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 0.13. Further, an Excess Kurtosis of 4.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.26%	17	0.59%	0.59%
-9.26% to -6.91%	35	1.22%	1.81%
-6.91% to -4.57%	119	4.13%	5.94%
-4.57% to -2.22%	334	11.61%	17.55%
-2.22% to 0.12%	898	31.20%	48.75%
0.12% to 2.47%	1007	34.99%	83.74%
2.47% to 4.82%	324	11.26%	95.00%
4.82% to 7.16%	89	3.09%	98.09%
7.16% to 9.51%	28	0.97%	99.06%
Greater than 9.51%	27	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.00%	3.25%	77.00%	68.27%
±2σ	-6.13%	6.38%	94.65%	95.45%
±3σ	-9.26%	9.51%	98.47%	99.73%

Descriptive Statistics

Mean	0.124%
Standard Error	0.058%
Median	0.185%
Mode	0.000%
Standard Deviation	3.128%
Sample Variance	9.783%
Kurtosis	4.57
Skewness	0.13
Range	39.611%
Minimum	-19.855%
Maximum	19.756%
Count	2878

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.170%	1541	53.54%	1.162%
Negative	-2.251%	1327	46.11%	-1.038%
Zero	0.000%	10	0.35%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.15%
20	1 Month	6.36%
60	1 Quarter	6.21%
250	1 Year	4.59%
750	3 Years	3.79%
1,250	5 Years	4.52%
2,500	10 Years	4.25%
5,000	20 Years	4.26%
12,500	50 Years	4.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.58. Further, an Excess Kurtosis of 11.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.31%	0	0.00%	0.00%
-3.31% to -1.46%	0	0.00%	0.00%
-1.46% to 0.40%	0	0.00%	0.00%
0.40% to 2.26%	495	17.19%	17.19%
2.26% to 4.12%	1333	46.30%	63.49%
4.12% to 5.98%	598	20.77%	84.27%
5.98% to 7.84%	251	8.72%	92.98%
7.84% to 9.70%	103	3.58%	96.56%
9.70% to 11.55%	43	1.49%	98.05%
Greater than 11.55%	56	1.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.64%	6.60%	84.44%	68.27%
±2σ	-0.84%	9.07%	95.59%	95.45%
±3σ	-3.32%	11.55%	98.05%	99.73%

Descriptive Statistics

Mean	4.119%
Standard Error	0.046%
Median	3.456%
Mode	3.476%
Standard Deviation	2.478%
Sample Variance	6.142%
Kurtosis	11.61
Skewness	2.58
Range	28.407%
Minimum	1.014%
Maximum	29.421%
Count	2879

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.119%	2879	100.00%	4.119%
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 0.53. Further, an Excess Kurtosis of 4.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.15%	12	0.42%	0.42%
-8.15% to -6.11%	25	0.87%	1.29%
-6.11% to -4.07%	101	3.51%	4.79%
-4.07% to -2.02%	392	13.62%	18.41%
-2.02% to 0.02%	970	33.69%	52.10%
0.02% to 2.07%	875	30.39%	82.49%
2.07% to 4.11%	335	11.64%	94.13%
4.11% to 6.15%	104	3.61%	97.74%
6.15% to 8.20%	41	1.42%	99.17%
Greater than 8.20%	24	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.70%	2.75%	75.79%	68.27%
±2σ	-5.43%	5.47%	94.48%	95.45%
±3σ	-8.15%	8.20%	98.75%	99.73%

Descriptive Statistics

Mean	0.023%
Standard Error	0.051%
Median	-0.087%
Mode	0.000%
Standard Deviation	2.725%
Sample Variance	7.428%
Kurtosis	4.73
Skewness	0.53
Range	37.742%
Minimum	-13.906%
Maximum	23.836%
Count	2879

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.052%	1389	48.25%	0.990%
Negative	-1.878%	1482	51.48%	-0.967%
Zero	0.000%	8	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.08. Further, an Excess Kurtosis of 1.91 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.31%	5	0.84%	0.84%
-20.31% to -15.08%	9	1.51%	2.35%
-15.08% to -9.84%	27	4.52%	6.87%
-9.84% to -4.61%	69	11.56%	18.43%
-4.61% to 0.62%	191	31.99%	50.42%
0.62% to 5.86%	185	30.99%	81.41%
5.86% to 11.09%	77	12.90%	94.30%
11.09% to 16.32%	23	3.85%	98.16%
16.32% to 21.56%	8	1.34%	99.50%
Greater than 21.56%	3	0.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.35%	7.60%	73.53%	68.27%
±2σ	-13.33%	14.58%	94.81%	95.45%
±3σ	-20.31%	21.56%	98.66%	99.73%

Descriptive Statistics

Mean	0.624%
Standard Error	0.286%
Median	0.493%
Mode	-2.639%
Standard Deviation	6.978%
Sample Variance	48.695%
Kurtosis	1.91
Skewness	-0.08
Range	57.861%
Minimum	-28.922%
Maximum	28.939%
Count	597

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.286%	323	54.10%	2.860%
Negative	-4.871%	274	45.90%	-2.236%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.76%
12	1 Quarter	15.87%
52	1 Year	11.11%
156	3 Years	8.96%
260	5 Years	10.55%
520	10 Years	10.06%
1,040	20 Years	10.08%
2,600	50 Years	10.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.82. Further, an Excess Kurtosis of 4.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.98%	0	0.00%	0.00%
-7.98% to -3.31%	0	0.00%	0.00%
-3.31% to 1.36%	0	0.00%	0.00%
1.36% to 6.03%	125	20.90%	20.90%
6.03% to 10.71%	256	42.81%	63.71%
10.71% to 15.38%	117	19.57%	83.28%
15.38% to 20.05%	52	8.70%	91.97%
20.05% to 24.72%	20	3.34%	95.32%
24.72% to 29.39%	19	3.18%	98.49%
Greater than 29.39%	9	1.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.48%	16.93%	80.27%	68.27%
±2σ	-1.75%	23.16%	94.65%	95.45%
±3σ	-7.98%	29.39%	98.49%	99.73%

Descriptive Statistics

Mean	10.705%
Standard Error	0.255%
Median	8.998%
Mode	6.626%
Standard Deviation	6.229%
Sample Variance	38.802%
Kurtosis	4.48
Skewness	1.82
Range	44.450%
Minimum	2.846%
Maximum	47.296%
Count	598

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.705%	598	100.00%	10.705%
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 0.97. Further, an Excess Kurtosis of 3.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.56%	0	0.00%	0.00%
-21.56% to -16.19%	7	1.17%	1.17%
-16.19% to -10.82%	18	3.01%	4.18%
-10.82% to -5.45%	90	15.05%	19.23%
-5.45% to -0.07%	203	33.95%	53.18%
-0.07% to 5.30%	185	30.94%	84.11%
5.30% to 10.67%	54	9.03%	93.14%
10.67% to 16.05%	25	4.18%	97.32%
16.05% to 21.42%	8	1.34%	98.66%
Greater than 21.42%	8	1.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.24%	7.09%	75.75%	68.27%
±2σ	-14.40%	14.26%	95.15%	95.45%
±3σ	-21.56%	21.42%	98.66%	99.73%

Descriptive Statistics

Mean	-0.072%
Standard Error	0.293%
Median	-0.494%
Mode	-4.941%
Standard Deviation	7.164%
Sample Variance	51.328%
Kurtosis	3.38
Skewness	0.97
Range	60.191%
Minimum	-20.536%
Maximum	39.655%
Count	598

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.441%	279	46.66%	2.539%
Negative	-4.910%	318	53.18%	-2.611%
Zero	0.000%	1	0.17%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.07. Further, an Excess Kurtosis of 0.53 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.13%	0	0.00%	0.00%
-36.13% to -26.53%	2	1.46%	1.46%
-26.53% to -16.93%	8	5.84%	7.30%
-16.93% to -7.33%	14	10.22%	17.52%
-7.33% to 2.27%	46	33.58%	51.09%
2.27% to 11.87%	40	29.20%	80.29%
11.87% to 21.47%	17	12.41%	92.70%
21.47% to 31.07%	7	5.11%	97.81%
31.07% to 40.67%	3	2.19%	100.00%
Greater than 40.67%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.53%	15.07%	73.72%	68.27%
±2σ	-23.33%	27.87%	92.70%	95.45%
±3σ	-36.13%	40.67%	100.00%	99.73%

Descriptive Statistics

Mean	2.273%
Standard Error	1.094%
Median	2.107%
Mode	-30.227%
Standard Deviation	12.800%
Sample Variance	163.828%
Kurtosis	0.53
Skewness	0.07
Range	68.593%
Minimum	-30.227%
Maximum	38.366%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.594%	78	56.93%	6.032%
Negative	-8.726%	59	43.07%	-3.758%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	26.02%
12	1 Year	20.26%
36	3 Years	18.25%
60	5 Years	20.95%
120	10 Years	20.59%
240	20 Years	20.61%
600	50 Years	20.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.30. Further, an Excess Kurtosis of 9.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.46%	0	0.00%	0.00%
-14.46% to -4.90%	0	0.00%	0.00%
-4.90% to 4.65%	0	0.00%	0.00%
4.65% to 14.20%	28	20.29%	20.29%
14.20% to 23.75%	57	41.30%	61.59%
23.75% to 33.30%	26	18.84%	80.43%
33.30% to 42.86%	17	12.32%	92.75%
42.86% to 52.41%	6	4.35%	97.10%
52.41% to 61.96%	2	1.45%	98.55%
Greater than 61.96%	2	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.02%	36.49%	82.61%	68.27%
±2σ	-1.72%	49.22%	97.10%	95.45%
±3σ	-14.46%	61.96%	98.55%	99.73%

Descriptive Statistics

Mean	23.752%
Standard Error	1.084%
Median	19.651%
Mode	7.121%
Standard Deviation	12.736%
Sample Variance	162.203%
Kurtosis	9.52
Skewness	2.30
Range	93.936%
Minimum	7.121%
Maximum	101.057%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.752%	138	100.00%	23.752%
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 1.36 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.60%	0	0.00%	0.00%
-39.60% to -29.85%	0	0.00%	0.00%
-29.85% to -20.10%	8	5.80%	5.80%
-20.10% to -10.35%	19	13.77%	19.57%
-10.35% to -0.60%	48	34.78%	54.35%
-0.60% to 9.15%	40	28.99%	83.33%
9.15% to 18.90%	12	8.70%	92.03%
18.90% to 28.65%	5	3.62%	95.65%
28.65% to 38.40%	5	3.62%	99.28%
Greater than 38.40%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.60%	12.40%	76.81%	68.27%
±2σ	-26.60%	25.40%	94.20%	95.45%
±3σ	-39.60%	38.40%	99.28%	99.73%

Descriptive Statistics

Mean	-0.600%
Standard Error	1.107%
Median	-1.590%
Mode	-25.917%
Standard Deviation	13.001%
Sample Variance	169.030%
Kurtosis	1.36
Skewness	0.88
Range	68.417%
Minimum	-25.917%
Maximum	42.500%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.357%	60	43.48%	4.503%
Negative	-9.029%	78	56.52%	-5.103%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.22. 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 -59.43%	0	0.00%	0.00%
-59.43% to -42.87%	1	2.17%	2.17%
-42.87% to -26.30%	2	4.35%	6.52%
-26.30% to -9.73%	7	15.22%	21.74%
-9.73% to 6.83%	10	21.74%	43.48%
6.83% to 23.40%	16	34.78%	78.26%
23.40% to 39.96%	7	15.22%	93.48%
39.96% to 56.53%	3	6.52%	100.00%
56.53% to 73.09%	0	0.00%	100.00%
Greater than 73.09%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.26%	28.92%	65.22%	68.27%
±2σ	-37.34%	51.01%	95.65%	95.45%
±3σ	-59.43%	73.09%	100.00%	99.73%

Descriptive Statistics

Mean	6.831%
Standard Error	3.257%
Median	9.213%
Mode	-43.080%
Standard Deviation	22.087%
Sample Variance	487.822%
Kurtosis	-0.55
Skewness	-0.22
Range	87.262%
Minimum	-43.080%
Maximum	44.182%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.957%	26	56.52%	12.976%
Negative	-14.132%	20	43.48%	-6.144%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.16%
12	3 Years	35.65%
20	5 Years	37.91%
40	10 Years	36.58%
80	20 Years	36.58%
200	50 Years	36.58%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.80. Further, an Excess Kurtosis of 3.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.96%	0	0.00%	0.00%
-19.96% to -3.60%	0	0.00%	0.00%
-3.60% to 12.77%	0	0.00%	0.00%
12.77% to 29.13%	8	17.02%	17.02%
29.13% to 45.49%	24	51.06%	68.09%
45.49% to 61.85%	8	17.02%	85.11%
61.85% to 78.21%	3	6.38%	91.49%
78.21% to 94.58%	2	4.26%	95.74%
94.58% to 110.94%	0	0.00%	95.74%
Greater than 110.94%	2	4.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.67%	67.31%	78.72%	68.27%
±2σ	1.86%	89.12%	95.74%	95.45%
±3σ	-19.96%	110.94%	95.74%	99.73%

Descriptive Statistics

Mean	45.490%
Standard Error	3.182%
Median	42.298%
Mode	19.942%
Standard Deviation	21.816%
Sample Variance	475.938%
Kurtosis	3.95
Skewness	1.80
Range	101.878%
Minimum	19.942%
Maximum	121.820%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	45.490%	47	100.00%	45.490%
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 1.40. Further, an Excess Kurtosis of 2.47 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -71.53%	0	0.00%	0.00%
-71.53% to -54.07%	0	0.00%	0.00%
-54.07% to -36.61%	0	0.00%	0.00%
-36.61% to -19.15%	9	19.15%	19.15%
-19.15% to -1.70%	18	38.30%	57.45%
-1.70% to 15.76%	11	23.40%	80.85%
15.76% to 33.22%	6	12.77%	93.62%
33.22% to 50.67%	1	2.13%	95.74%
50.67% to 68.13%	1	2.13%	97.87%
Greater than 68.13%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.97%	21.58%	68.09%	68.27%
±2σ	-48.25%	44.85%	95.74%	95.45%
±3σ	-71.53%	68.13%	97.87%	99.73%

Descriptive Statistics

Mean	-1.697%
Standard Error	3.395%
Median	-8.971%
Mode	-30.923%
Standard Deviation	23.276%
Sample Variance	541.782%
Kurtosis	2.47
Skewness	1.40
Range	106.780%
Minimum	-30.923%
Maximum	75.857%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.104%	20	42.55%	8.129%
Negative	-17.105%	27	57.45%	-9.826%
Zero	0.000%	0	0.00%	0.000%

HUBS Deep Analytical Report