HOOD - 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	4.67%	3.66%	3.92%	6.00%	4.01%	4.11%	73.12	79.23	70.24	82.47
Weekly	10.13%	11.25%	9.61%	14.50%	8.83%	9.05%	69.68	83.14	63.79	90.81
Monthly	21.62%	21.40%	19.82%	33.34%	18.39%	18.84%	63.33	91.47	52.69	109.93
Quarterly	46.94%	60.08%	45.44%	66.41%	31.84%	32.64%	55.35	104.65	40.26	143.89
Annual	—	—	—	—	63.69%	65.27%	40.26	143.89	21.29	272.04
Option Time Horizon	—	—	—	—	24.50%	25.11%	59.57	97.24	46.63	124.23

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $76.11 | Strike (K): $80.00 (first OTM call ≥ spot) | Observed Mid-Price: $6.0750 (Bid $5.9500 / Ask $6.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 63.69% (CRR binomial tree, American, n=20 steps) | BS IV: 64.45% (European Black-Scholes) | Yahoo IV (Annual): 65.27% → 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 1.33. Further, an Excess Kurtosis of 15.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.85%	5	0.44%	0.44%
-13.85% to -10.34%	8	0.70%	1.14%
-10.34% to -6.84%	45	3.93%	5.07%
-6.84% to -3.33%	135	11.79%	16.86%
-3.33% to 0.17%	396	34.59%	51.44%
0.17% to 3.68%	370	32.31%	83.76%
3.68% to 7.18%	139	12.14%	95.90%
7.18% to 10.69%	26	2.27%	98.17%
10.69% to 14.19%	13	1.14%	99.30%
Greater than 14.19%	8	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.50%	4.85%	80.09%	68.27%
±2σ	-9.17%	9.52%	95.90%	95.45%
±3σ	-13.85%	14.19%	98.86%	99.73%

Descriptive Statistics

Mean	0.174%
Standard Error	0.138%
Median	0.021%
Mode	0.000%
Standard Deviation	4.673%
Sample Variance	21.834%
Kurtosis	15.44
Skewness	1.33
Range	77.995%
Minimum	-27.589%
Maximum	50.406%
Count	1145

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.351%	574	50.13%	1.680%
Negative	-3.084%	559	48.82%	-1.506%
Zero	0.000%	12	1.05%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.29%
20	1 Month	7.18%
60	1 Quarter	5.65%
250	1 Year	6.46%
750	3 Years	5.41%
1,250	5 Years	6.00%
2,500	10 Years	6.00%
5,000	20 Years	6.00%
12,500	50 Years	6.00%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.47. Further, an Excess Kurtosis of 40.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.22%	0	0.00%	0.00%
-5.22% to -2.47%	0	0.00%	0.00%
-2.47% to 0.27%	0	0.00%	0.00%
0.27% to 3.02%	153	13.35%	13.35%
3.02% to 5.77%	560	48.87%	62.22%
5.77% to 8.52%	284	24.78%	87.00%
8.52% to 11.26%	100	8.73%	95.72%
11.26% to 14.01%	18	1.57%	97.29%
14.01% to 16.76%	12	1.05%	98.34%
Greater than 16.76%	19	1.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.10%	9.43%	87.52%	68.27%
±2σ	-1.56%	13.09%	96.95%	95.45%
±3σ	-5.22%	16.76%	98.34%	99.73%

Descriptive Statistics

Mean	5.768%
Standard Error	0.108%
Median	4.884%
Mode	1.985%
Standard Deviation	3.663%
Sample Variance	13.421%
Kurtosis	40.44
Skewness	4.47
Range	54.979%
Minimum	1.271%
Maximum	56.250%
Count	1146

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.768%	1146	100.00%	5.768%
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 Fairly Symmetrical with a Skewness factor of 0.01. Further, an Excess Kurtosis of 5.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.74%	9	0.79%	0.79%
-11.74% to -8.80%	6	0.52%	1.31%
-8.80% to -5.87%	28	2.44%	3.75%
-5.87% to -2.93%	155	13.53%	17.28%
-2.93% to 0.01%	398	34.73%	52.01%
0.01% to 2.94%	360	31.41%	83.42%
2.94% to 5.88%	122	10.65%	94.07%
5.88% to 8.82%	42	3.66%	97.73%
8.82% to 11.75%	17	1.48%	99.21%
Greater than 11.75%	9	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.91%	3.92%	77.49%	68.27%
±2σ	-7.83%	7.84%	95.03%	95.45%
±3σ	-11.74%	11.75%	98.43%	99.73%

Descriptive Statistics

Mean	0.006%
Standard Error	0.116%
Median	-0.158%
Mode	0.000%
Standard Deviation	3.916%
Sample Variance	15.337%
Kurtosis	5.47
Skewness	0.01
Range	46.051%
Minimum	-22.645%
Maximum	23.406%
Count	1146

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.890%	550	47.99%	1.387%
Negative	-2.691%	588	51.31%	-1.381%
Zero	0.000%	8	0.70%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.65. Further, an Excess Kurtosis of 2.60 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.60%	0	0.00%	0.00%
-29.60% to -22.00%	3	1.26%	1.26%
-22.00% to -14.40%	13	5.46%	6.72%
-14.40% to -6.81%	28	11.76%	18.49%
-6.81% to 0.79%	79	33.19%	51.68%
0.79% to 8.39%	72	30.25%	81.93%
8.39% to 15.99%	27	11.34%	93.28%
15.99% to 23.59%	12	5.04%	98.32%
23.59% to 31.18%	2	0.84%	99.16%
Greater than 31.18%	2	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.34%	10.92%	73.95%	68.27%
±2σ	-19.47%	21.05%	93.28%	95.45%
±3σ	-29.60%	31.18%	99.16%	99.73%

Descriptive Statistics

Mean	0.792%
Standard Error	0.657%
Median	0.215%
Mode	0.000%
Standard Deviation	10.130%
Sample Variance	102.616%
Kurtosis	2.60
Skewness	0.65
Range	74.837%
Minimum	-24.014%
Maximum	50.823%
Count	238

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.116%	120	50.42%	4.092%
Negative	-6.890%	114	47.90%	-3.300%
Zero	0.000%	4	1.68%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	16.89%
12	1 Quarter	12.49%
52	1 Year	15.47%
156	3 Years	13.13%
260	5 Years	14.50%
520	10 Years	14.50%
1,040	20 Years	14.50%
2,600	50 Years	14.50%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.91. Further, an Excess Kurtosis of 42.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.05%	0	0.00%	0.00%
-18.05% to -9.62%	0	0.00%	0.00%
-9.62% to -1.18%	0	0.00%	0.00%
-1.18% to 7.25%	27	11.30%	11.30%
7.25% to 15.69%	121	50.63%	61.92%
15.69% to 24.12%	55	23.01%	84.94%
24.12% to 32.56%	22	9.21%	94.14%
32.56% to 40.99%	9	3.77%	97.91%
40.99% to 49.43%	3	1.26%	99.16%
Greater than 49.43%	2	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.44%	26.93%	89.96%	68.27%
±2σ	-6.81%	38.18%	96.65%	95.45%
±3σ	-18.05%	49.43%	99.16%	99.73%

Descriptive Statistics

Mean	15.687%
Standard Error	0.727%
Median	12.950%
Mode	15.785%
Standard Deviation	11.247%
Sample Variance	126.489%
Kurtosis	42.82
Skewness	4.91
Range	124.365%
Minimum	4.382%
Maximum	128.747%
Count	239

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.687%	239	100.00%	15.687%
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 0.37. Further, an Excess Kurtosis of 1.12 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.76%	1	0.42%	0.42%
-28.76% to -21.55%	1	0.42%	0.84%
-21.55% to -14.35%	13	5.44%	6.28%
-14.35% to -7.14%	32	13.39%	19.67%
-7.14% to 0.07%	80	33.47%	53.14%
0.07% to 7.28%	73	30.54%	83.68%
7.28% to 14.49%	18	7.53%	91.21%
14.49% to 21.70%	13	5.44%	96.65%
21.70% to 28.91%	6	2.51%	99.16%
Greater than 28.91%	2	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.54%	9.69%	75.31%	68.27%
±2σ	-19.15%	19.30%	92.89%	95.45%
±3σ	-28.76%	28.91%	98.74%	99.73%

Descriptive Statistics

Mean	0.073%
Standard Error	0.622%
Median	-0.637%
Mode	-33.291%
Standard Deviation	9.612%
Sample Variance	92.384%
Kurtosis	1.12
Skewness	0.37
Range	63.894%
Minimum	-33.291%
Maximum	30.603%
Count	239

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.592%	113	47.28%	3.589%
Negative	-6.670%	126	52.72%	-3.516%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.72. Further, an Excess Kurtosis of -0.16 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.37%	0	0.00%	0.00%
-61.37% to -45.15%	0	0.00%	0.00%
-45.15% to -28.93%	1	1.82%	1.82%
-28.93% to -12.71%	13	23.64%	25.45%
-12.71% to 3.51%	19	34.55%	60.00%
3.51% to 19.72%	10	18.18%	78.18%
19.72% to 35.94%	6	10.91%	89.09%
35.94% to 52.16%	5	9.09%	98.18%
52.16% to 68.38%	1	1.82%	100.00%
Greater than 68.38%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.12%	25.13%	69.09%	68.27%
±2σ	-39.74%	46.75%	96.36%	95.45%
±3σ	-61.37%	68.38%	100.00%	99.73%

Descriptive Statistics

Mean	3.506%
Standard Error	2.916%
Median	-0.746%
Mode	-31.534%
Standard Deviation	21.624%
Sample Variance	467.583%
Kurtosis	-0.16
Skewness	0.72
Range	91.347%
Minimum	-31.534%
Maximum	59.813%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.904%	27	49.09%	10.262%
Negative	-13.270%	28	50.91%	-6.756%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.86%
12	1 Year	33.36%
36	3 Years	30.87%
60	5 Years	33.34%
120	10 Years	33.34%
240	20 Years	33.34%
600	50 Years	33.34%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.31. Further, an Excess Kurtosis of 8.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.07%	0	0.00%	0.00%
-25.07% to -9.03%	0	0.00%	0.00%
-9.03% to 7.02%	0	0.00%	0.00%
7.02% to 23.07%	14	25.00%	25.00%
23.07% to 39.11%	20	35.71%	60.71%
39.11% to 55.16%	14	25.00%	85.71%
55.16% to 71.21%	4	7.14%	92.86%
71.21% to 87.25%	2	3.57%	96.43%
87.25% to 103.30%	1	1.79%	98.21%
Greater than 103.30%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.72%	60.51%	87.50%	68.27%
±2σ	-3.68%	81.91%	96.43%	95.45%
±3σ	-25.07%	103.30%	98.21%	99.73%

Descriptive Statistics

Mean	39.114%
Standard Error	2.859%
Median	31.896%
Mode	14.623%
Standard Deviation	21.396%
Sample Variance	457.772%
Kurtosis	8.37
Skewness	2.31
Range	126.170%
Minimum	14.623%
Maximum	140.793%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.114%	56	100.00%	39.114%
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 0.13. Further, an Excess Kurtosis of -0.54 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.62%	0	0.00%	0.00%
-58.62% to -43.75%	0	0.00%	0.00%
-43.75% to -28.88%	5	8.93%	8.93%
-28.88% to -14.02%	10	17.86%	26.79%
-14.02% to 0.85%	13	23.21%	50.00%
0.85% to 15.71%	12	21.43%	71.43%
15.71% to 30.58%	12	21.43%	92.86%
30.58% to 45.45%	3	5.36%	98.21%
45.45% to 60.31%	1	1.79%	100.00%
Greater than 60.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.97%	20.67%	62.50%	68.27%
±2σ	-38.79%	40.49%	98.21%	95.45%
±3σ	-58.62%	60.31%	100.00%	99.73%

Descriptive Statistics

Mean	0.848%
Standard Error	2.649%
Median	0.701%
Mode	-36.867%
Standard Deviation	19.821%
Sample Variance	392.871%
Kurtosis	-0.54
Skewness	0.13
Range	85.234%
Minimum	-36.867%
Maximum	48.367%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.026%	28	50.00%	8.513%
Negative	-15.329%	28	50.00%	-7.664%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.96. Further, an Excess Kurtosis of 0.78 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -128.01%	0	0.00%	0.00%
-128.01% to -92.80%	0	0.00%	0.00%
-92.80% to -57.60%	1	5.26%	5.26%
-57.60% to -22.40%	4	21.05%	26.32%
-22.40% to 12.81%	5	26.32%	52.63%
12.81% to 48.01%	6	31.58%	84.21%
48.01% to 83.22%	1	5.26%	89.47%
83.22% to 118.42%	1	5.26%	94.74%
118.42% to 153.62%	1	5.26%	100.00%
Greater than 153.62%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.13%	59.75%	84.21%	68.27%
±2σ	-81.07%	106.68%	89.47%	95.45%
±3σ	-128.01%	153.62%	100.00%	99.73%

Descriptive Statistics

Mean	12.808%
Standard Error	10.768%
Median	-0.512%
Mode	-59.537%
Standard Deviation	46.938%
Sample Variance	2203.212%
Kurtosis	0.78
Skewness	0.96
Range	180.695%
Minimum	-59.537%
Maximum	121.158%
Count	19

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.865%	9	47.37%	24.094%
Negative	-21.443%	10	52.63%	-11.286%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	64.81%
12	3 Years	69.17%
20	5 Years	66.41%
40	10 Years	66.41%
80	20 Years	66.41%
200	50 Years	66.41%

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 5.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -93.34%	0	0.00%	0.00%
-93.34% to -48.28%	0	0.00%	0.00%
-48.28% to -3.23%	0	0.00%	0.00%
-3.23% to 41.83%	3	15.00%	15.00%
41.83% to 86.89%	10	50.00%	65.00%
86.89% to 131.95%	3	15.00%	80.00%
131.95% to 177.00%	3	15.00%	95.00%
177.00% to 222.06%	0	0.00%	95.00%
222.06% to 267.12%	0	0.00%	95.00%
Greater than 267.12%	1	5.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	26.81%	146.97%	80.00%	68.27%
±2σ	-33.26%	207.04%	95.00%	95.45%
±3σ	-93.34%	267.12%	95.00%	99.73%

Descriptive Statistics

Mean	86.889%
Standard Error	13.433%
Median	66.738%
Mode	21.053%
Standard Deviation	60.076%
Sample Variance	3609.116%
Kurtosis	5.28
Skewness	2.02
Range	262.951%
Minimum	21.053%
Maximum	284.004%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	86.889%	20	100.00%	86.889%
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 1.67. 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 -132.10%	0	0.00%	0.00%
-132.10% to -98.02%	0	0.00%	0.00%
-98.02% to -63.94%	0	0.00%	0.00%
-63.94% to -29.87%	5	25.00%	25.00%
-29.87% to 4.21%	6	30.00%	55.00%
4.21% to 38.28%	5	25.00%	80.00%
38.28% to 72.36%	3	15.00%	95.00%
72.36% to 106.44%	0	0.00%	95.00%
106.44% to 140.51%	0	0.00%	95.00%
Greater than 140.51%	1	5.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-41.23%	49.64%	85.00%	68.27%
±2σ	-86.66%	95.08%	95.00%	95.45%
±3σ	-132.10%	140.51%	95.00%	99.73%

Descriptive Statistics

Mean	4.209%
Standard Error	10.160%
Median	0.799%
Mode	-54.379%
Standard Deviation	45.435%
Sample Variance	2064.371%
Kurtosis	4.48
Skewness	1.67
Range	203.142%
Minimum	-54.379%
Maximum	148.763%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.899%	10	50.00%	17.950%
Negative	-27.481%	10	50.00%	-13.741%
Zero	0.000%	0	0.00%	0.000%

HOOD Deep Analytical Report