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	4.66%	3.64%	3.90%	6.00%	4.10%	4.16%	69.53	75.47	66.73	78.63
Weekly	10.08%	11.16%	9.58%	14.48%	9.03%	9.15%	66.18	79.29	60.47	86.78
Monthly	21.46%	21.33%	19.65%	33.13%	18.80%	19.05%	60.02	87.42	49.74	105.51
Quarterly	47.11%	59.97%	45.62%	66.47%	32.57%	33.00%	52.31	100.32	37.77	138.94
Annual	—	—	—	—	65.13%	65.99%	37.77	138.94	19.69	266.50
Option Time Horizon	—	—	—	—	24.58%	24.91%	56.65	92.63	44.30	118.44

Calculation Notes: Computed at 2026-03-23T16:34 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $72.44 | Strike (K): $75.00 (first OTM call ≥ spot) | Observed Mid-Price: $6.2250 (Bid $6.0500 / Ask $6.4000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 65.13% (CRR binomial tree, American, n=20 steps) | BS IV: 65.71% (European Black-Scholes) | Yahoo IV (Annual): 65.99% → 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 15.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.81%	5	0.43%	0.43%
-13.81% to -10.31%	8	0.69%	1.11%
-10.31% to -6.82%	45	3.86%	4.97%
-6.82% to -3.33%	141	12.09%	17.07%
-3.33% to 0.17%	401	34.39%	51.46%
0.17% to 3.66%	376	32.25%	83.70%
3.66% to 7.16%	142	12.18%	95.88%
7.16% to 10.65%	27	2.32%	98.20%
10.65% to 14.14%	13	1.11%	99.31%
Greater than 14.14%	8	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.49%	4.83%	79.93%	68.27%
±2σ	-9.15%	9.48%	95.97%	95.45%
±3σ	-13.81%	14.14%	98.89%	99.73%

Descriptive Statistics

Mean	0.168%
Standard Error	0.136%
Median	0.015%
Mode	0.000%
Standard Deviation	4.658%
Sample Variance	21.692%
Kurtosis	15.37
Skewness	1.33
Range	77.995%
Minimum	-27.589%
Maximum	50.406%
Count	1166

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.350%	584	50.09%	1.678%
Negative	-3.088%	570	48.88%	-1.510%
Zero	0.000%	12	1.03%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.17%
20	1 Month	5.57%
60	1 Quarter	5.58%
250	1 Year	6.10%
750	3 Years	5.42%
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 4.49. Further, an Excess Kurtosis of 40.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.17%	0	0.00%	0.00%
-5.17% to -2.44%	0	0.00%	0.00%
-2.44% to 0.29%	0	0.00%	0.00%
0.29% to 3.02%	154	13.20%	13.20%
3.02% to 5.75%	573	49.10%	62.30%
5.75% to 8.48%	284	24.34%	86.63%
8.48% to 11.21%	106	9.08%	95.72%
11.21% to 13.94%	19	1.63%	97.34%
13.94% to 16.67%	12	1.03%	98.37%
Greater than 16.67%	19	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.11%	9.39%	87.75%	68.27%
±2σ	-1.53%	13.03%	97.00%	95.45%
±3σ	-5.17%	16.67%	98.37%	99.73%

Descriptive Statistics

Mean	5.752%
Standard Error	0.107%
Median	4.883%
Mode	1.985%
Standard Deviation	3.639%
Sample Variance	13.242%
Kurtosis	40.89
Skewness	4.49
Range	54.979%
Minimum	1.271%
Maximum	56.250%
Count	1167

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.752%	1167	100.00%	5.752%
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 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 -11.71%	9	0.77%	0.77%
-11.71% to -8.78%	6	0.51%	1.29%
-8.78% to -5.85%	29	2.49%	3.77%
-5.85% to -2.93%	160	13.71%	17.48%
-2.93% to -0.00%	396	33.93%	51.41%
-0.00% to 2.92%	372	31.88%	83.29%
2.92% to 5.85%	127	10.88%	94.17%
5.85% to 8.78%	42	3.60%	97.77%
8.78% to 11.70%	17	1.46%	99.23%
Greater than 11.70%	9	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.90%	3.90%	77.29%	68.27%
±2σ	-7.80%	7.80%	95.12%	95.45%
±3σ	-11.71%	11.70%	98.46%	99.73%

Descriptive Statistics

Mean	-0.002%
Standard Error	0.114%
Median	-0.171%
Mode	0.000%
Standard Deviation	3.901%
Sample Variance	15.215%
Kurtosis	5.47
Skewness	0.01
Range	46.051%
Minimum	-22.645%
Maximum	23.406%
Count	1167

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.881%	559	47.90%	1.380%
Negative	-2.688%	600	51.41%	-1.382%
Zero	0.000%	8	0.69%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.66. Further, an Excess Kurtosis of 2.63 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.48%	0	0.00%	0.00%
-29.48% to -21.92%	3	1.24%	1.24%
-21.92% to -14.36%	13	5.37%	6.61%
-14.36% to -6.80%	28	11.57%	18.18%
-6.80% to 0.76%	82	33.88%	52.07%
0.76% to 8.32%	71	29.34%	81.40%
8.32% to 15.88%	29	11.98%	93.39%
15.88% to 23.45%	12	4.96%	98.35%
23.45% to 31.01%	2	0.83%	99.17%
Greater than 31.01%	2	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.32%	10.84%	74.38%	68.27%
±2σ	-19.40%	20.93%	93.39%	95.45%
±3σ	-29.49%	31.01%	99.17%	99.73%

Descriptive Statistics

Mean	0.761%
Standard Error	0.648%
Median	0.123%
Mode	0.000%
Standard Deviation	10.082%
Sample Variance	101.646%
Kurtosis	2.63
Skewness	0.66
Range	74.837%
Minimum	-24.014%
Maximum	50.823%
Count	242

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.134%	121	50.00%	4.067%
Negative	-6.838%	117	48.35%	-3.306%
Zero	0.000%	4	1.65%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	12.93%
12	1 Quarter	13.28%
52	1 Year	14.62%
156	3 Years	13.20%
260	5 Years	14.48%
520	10 Years	14.48%
1,040	20 Years	14.48%
2,600	50 Years	14.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.95. Further, an Excess Kurtosis of 43.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.81%	0	0.00%	0.00%
-17.81% to -9.44%	0	0.00%	0.00%
-9.44% to -1.07%	0	0.00%	0.00%
-1.07% to 7.29%	28	11.52%	11.52%
7.29% to 15.66%	123	50.62%	62.14%
15.66% to 24.03%	56	23.05%	85.19%
24.03% to 32.40%	22	9.05%	94.24%
32.40% to 40.76%	8	3.29%	97.53%
40.76% to 49.13%	4	1.65%	99.18%
Greater than 49.13%	2	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.50%	26.82%	89.71%	68.27%
±2σ	-6.65%	37.97%	96.71%	95.45%
±3σ	-17.81%	49.13%	99.18%	99.73%

Descriptive Statistics

Mean	15.661%
Standard Error	0.716%
Median	12.950%
Mode	15.785%
Standard Deviation	11.156%
Sample Variance	124.459%
Kurtosis	43.57
Skewness	4.95
Range	124.365%
Minimum	4.382%
Maximum	128.747%
Count	243

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.661%	243	100.00%	15.661%
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 0.36. 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 -28.66%	1	0.41%	0.41%
-28.66% to -21.48%	1	0.41%	0.82%
-21.48% to -14.29%	13	5.35%	6.17%
-14.29% to -7.11%	34	13.99%	20.16%
-7.11% to 0.07%	79	32.51%	52.67%
0.07% to 7.26%	76	31.28%	83.95%
7.26% to 14.44%	18	7.41%	91.36%
14.44% to 21.62%	13	5.35%	96.71%
21.62% to 28.81%	6	2.47%	99.18%
Greater than 28.81%	2	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.51%	9.65%	74.90%	68.27%
±2σ	-19.08%	19.23%	93.00%	95.45%
±3σ	-28.66%	28.81%	98.77%	99.73%

Descriptive Statistics

Mean	0.072%
Standard Error	0.614%
Median	-0.474%
Mode	-33.291%
Standard Deviation	9.578%
Sample Variance	91.734%
Kurtosis	1.12
Skewness	0.36
Range	63.894%
Minimum	-33.291%
Maximum	30.603%
Count	243

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.520%	116	47.74%	3.590%
Negative	-6.731%	127	52.26%	-3.518%
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 0.74. Further, an Excess Kurtosis of -0.10 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.02%	0	0.00%	0.00%
-61.02% to -44.93%	0	0.00%	0.00%
-44.93% to -28.83%	1	1.79%	1.79%
-28.83% to -12.74%	13	23.21%	25.00%
-12.74% to 3.36%	20	35.71%	60.71%
3.36% to 19.45%	10	17.86%	78.57%
19.45% to 35.55%	6	10.71%	89.29%
35.55% to 51.64%	4	7.14%	96.43%
51.64% to 67.74%	2	3.57%	100.00%
Greater than 67.74%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.10%	24.82%	69.64%	68.27%
±2σ	-39.56%	46.28%	96.43%	95.45%
±3σ	-61.02%	67.74%	100.00%	99.73%

Descriptive Statistics

Mean	3.356%
Standard Error	2.868%
Median	-1.467%
Mode	-31.534%
Standard Deviation	21.460%
Sample Variance	460.525%
Kurtosis	-0.10
Skewness	0.74
Range	91.347%
Minimum	-31.534%
Maximum	59.813%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.904%	27	48.21%	10.079%
Negative	-12.982%	29	51.79%	-6.723%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	24.76%
12	1 Year	32.17%
36	3 Years	30.99%
60	5 Years	33.13%
120	10 Years	33.13%
240	20 Years	33.13%
600	50 Years	33.13%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.32. Further, an Excess Kurtosis of 8.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.15%	0	0.00%	0.00%
-25.15% to -9.15%	0	0.00%	0.00%
-9.15% to 6.84%	0	0.00%	0.00%
6.84% to 22.84%	15	26.32%	26.32%
22.84% to 38.84%	20	35.09%	61.40%
38.84% to 54.84%	13	22.81%	84.21%
54.84% to 70.84%	5	8.77%	92.98%
70.84% to 86.84%	2	3.51%	96.49%
86.84% to 102.84%	1	1.75%	98.25%
Greater than 102.84%	1	1.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	17.51%	60.18%	87.72%	68.27%
±2σ	-3.82%	81.51%	96.49%	95.45%
±3σ	-25.15%	102.84%	98.25%	99.73%

Descriptive Statistics

Mean	38.843%
Standard Error	2.826%
Median	31.226%
Mode	14.623%
Standard Deviation	21.332%
Sample Variance	455.073%
Kurtosis	8.42
Skewness	2.32
Range	126.170%
Minimum	14.623%
Maximum	140.793%
Count	57

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.843%	57	100.00%	38.843%
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 -0.50 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.09%	0	0.00%	0.00%
-58.09% to -43.35%	0	0.00%	0.00%
-43.35% to -28.61%	5	8.77%	8.77%
-28.61% to -13.87%	10	17.54%	26.32%
-13.87% to 0.87%	13	22.81%	49.12%
0.87% to 15.61%	13	22.81%	71.93%
15.61% to 30.35%	12	21.05%	92.98%
30.35% to 45.09%	3	5.26%	98.25%
45.09% to 59.83%	1	1.75%	100.00%
Greater than 59.83%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.78%	20.52%	61.40%	68.27%
±2σ	-38.44%	40.17%	98.25%	95.45%
±3σ	-58.09%	59.83%	100.00%	99.73%

Descriptive Statistics

Mean	0.869%
Standard Error	2.603%
Median	1.604%
Mode	-36.867%
Standard Deviation	19.653%
Sample Variance	386.255%
Kurtosis	-0.50
Skewness	0.13
Range	85.234%
Minimum	-36.867%
Maximum	48.367%
Count	57

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.509%	29	50.88%	8.399%
Negative	-15.329%	28	49.12%	-7.530%
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 0.95. Further, an Excess Kurtosis of 0.75 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -128.72%	0	0.00%	0.00%
-128.72% to -93.39%	0	0.00%	0.00%
-93.39% to -58.06%	1	5.26%	5.26%
-58.06% to -22.72%	4	21.05%	26.32%
-22.72% to 12.61%	5	26.32%	52.63%
12.61% to 47.94%	6	31.58%	84.21%
47.94% to 83.27%	1	5.26%	89.47%
83.27% to 118.61%	1	5.26%	94.74%
118.61% to 153.94%	1	5.26%	100.00%
Greater than 153.94%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.50%	59.72%	84.21%	68.27%
±2σ	-81.61%	106.83%	89.47%	95.45%
±3σ	-128.72%	153.94%	100.00%	99.73%

Descriptive Statistics

Mean	12.608%
Standard Error	10.808%
Median	-0.512%
Mode	-59.537%
Standard Deviation	47.110%
Sample Variance	2219.321%
Kurtosis	0.75
Skewness	0.95
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	-21.823%	10	52.63%	-11.486%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	65.12%
12	3 Years	69.28%
20	5 Years	66.47%
40	10 Years	66.47%
80	20 Years	66.47%
200	50 Years	66.47%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -92.91%	0	0.00%	0.00%
-92.91% to -47.93%	0	0.00%	0.00%
-47.93% to -2.95%	0	0.00%	0.00%
-2.95% to 42.03%	4	20.00%	20.00%
42.03% to 87.01%	9	45.00%	65.00%
87.01% to 131.99%	3	15.00%	80.00%
131.99% to 176.97%	3	15.00%	95.00%
176.97% to 221.94%	0	0.00%	95.00%
221.94% to 266.92%	0	0.00%	95.00%
Greater than 266.92%	1	5.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	27.04%	146.98%	80.00%	68.27%
±2σ	-32.94%	206.95%	95.00%	95.45%
±3σ	-92.91%	266.92%	95.00%	99.73%

Descriptive Statistics

Mean	87.008%
Standard Error	13.410%
Median	66.737%
Mode	21.053%
Standard Deviation	59.972%
Sample Variance	3596.686%
Kurtosis	5.31
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	87.008%	20	100.00%	87.008%
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 1.63. Further, an Excess Kurtosis of 4.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -132.34%	0	0.00%	0.00%
-132.34% to -98.12%	0	0.00%	0.00%
-98.12% to -63.90%	0	0.00%	0.00%
-63.90% to -29.68%	5	25.00%	25.00%
-29.68% to 4.54%	6	30.00%	55.00%
4.54% to 38.76%	6	30.00%	85.00%
38.76% to 72.98%	2	10.00%	95.00%
72.98% to 107.19%	0	0.00%	95.00%
107.19% to 141.41%	0	0.00%	95.00%
Greater than 141.41%	1	5.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-41.09%	50.16%	85.00%	68.27%
±2σ	-86.71%	95.79%	95.00%	95.45%
±3σ	-132.34%	141.41%	95.00%	99.73%

Descriptive Statistics

Mean	4.539%
Standard Error	10.202%
Median	0.799%
Mode	-54.379%
Standard Deviation	45.625%
Sample Variance	2081.647%
Kurtosis	4.30
Skewness	1.63
Range	203.142%
Minimum	-54.379%
Maximum	148.763%
Count	20

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.558%	10	50.00%	18.279%
Negative	-27.481%	10	50.00%	-13.741%
Zero	0.000%	0	0.00%	0.000%

HOOD Deep Analytical Report