ROKU - 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%	3.24%	3.76%	5.52%	4.03%	4.08%	92.91	100.71	89.24	104.85
Weekly	11.62%	11.80%	10.68%	13.22%	8.87%	8.99%	88.52	105.70	81.00	115.51
Monthly	23.62%	22.66%	20.78%	28.25%	18.47%	18.71%	80.42	116.35	66.86	139.95
Quarterly	37.53%	38.10%	35.31%	50.03%	31.99%	32.41%	70.25	133.19	51.02	183.41
Annual	—	—	—	—	63.98%	64.82%	51.02	183.41	26.91	347.75
Option Time Horizon	—	—	—	—	24.15%	24.47%	75.98	123.15	59.68	156.79

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $96.73 | Strike (K): $100.00 (first OTM call ≥ spot) | Observed Mid-Price: $8.2000 (Bid $7.7000 / Ask $8.7000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 63.98% (CRR binomial tree, American, n=20 steps) | BS IV: 64.52% (European Black-Scholes) | Yahoo IV (Annual): 64.82% → 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 1.27. Further, an Excess Kurtosis of 14.57 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%	13	0.61%	0.61%
-13.81% to -10.31%	16	0.75%	1.36%
-10.31% to -6.82%	59	2.77%	4.13%
-6.82% to -3.32%	256	12.02%	16.15%
-3.32% to 0.17%	766	35.96%	52.11%
0.17% to 3.67%	684	32.11%	84.23%
3.67% to 7.16%	232	10.89%	95.12%
7.16% to 10.66%	62	2.91%	98.03%
10.66% to 14.15%	27	1.27%	99.30%
Greater than 14.15%	15	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.49%	4.83%	79.58%	68.27%
±2σ	-9.15%	9.49%	95.68%	95.45%
±3σ	-13.81%	14.15%	98.69%	99.73%

Descriptive Statistics

Mean	0.172%
Standard Error	0.101%
Median	0.013%
Mode	0.000%
Standard Deviation	4.661%
Sample Variance	21.726%
Kurtosis	14.57
Skewness	1.27
Range	78.746%
Minimum	-23.810%
Maximum	54.936%
Count	2130

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.285%	1068	50.14%	1.647%
Negative	-2.969%	1058	49.67%	-1.475%
Zero	0.000%	4	0.19%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.97%
20	1 Month	4.78%
60	1 Quarter	4.66%
250	1 Year	4.64%
750	3 Years	4.79%
1,250	5 Years	5.52%
2,500	10 Years	5.87%
5,000	20 Years	5.87%
12,500	50 Years	5.87%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.47. Further, an Excess Kurtosis of 26.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.08%	0	0.00%	0.00%
-4.08% to -1.65%	0	0.00%	0.00%
-1.65% to 0.78%	0	0.00%	0.00%
0.78% to 3.21%	365	17.13%	17.13%
3.21% to 5.64%	956	44.86%	61.99%
5.64% to 8.07%	489	22.95%	84.94%
8.07% to 10.50%	192	9.01%	93.95%
10.50% to 12.93%	68	3.19%	97.14%
12.93% to 15.36%	28	1.31%	98.45%
Greater than 15.36%	33	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.40%	8.88%	84.51%	68.27%
±2σ	-0.84%	12.12%	96.20%	95.45%
±3σ	-4.08%	15.36%	98.45%	99.73%

Descriptive Statistics

Mean	5.639%
Standard Error	0.070%
Median	4.874%
Mode	4.388%
Standard Deviation	3.240%
Sample Variance	10.501%
Kurtosis	26.29
Skewness	3.47
Range	48.159%
Minimum	1.047%
Maximum	49.206%
Count	2131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.639%	2131	100.00%	5.639%
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 -0.32. Further, an Excess Kurtosis of 5.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.25%	17	0.80%	0.80%
-11.25% to -8.43%	21	0.99%	1.78%
-8.43% to -5.61%	68	3.19%	4.97%
-5.61% to -2.78%	281	13.19%	18.16%
-2.78% to 0.04%	671	31.49%	49.65%
0.04% to 2.86%	670	31.44%	81.09%
2.86% to 5.69%	282	13.23%	94.32%
5.69% to 8.51%	94	4.41%	98.73%
8.51% to 11.33%	20	0.94%	99.67%
Greater than 11.33%	7	0.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.72%	3.80%	74.89%	68.27%
±2σ	-7.49%	7.57%	95.12%	95.45%
±3σ	-11.25%	11.33%	98.87%	99.73%

Descriptive Statistics

Mean	0.040%
Standard Error	0.082%
Median	0.070%
Mode	0.000%
Standard Deviation	3.764%
Sample Variance	14.171%
Kurtosis	5.43
Skewness	-0.32
Range	59.261%
Minimum	-32.766%
Maximum	26.495%
Count	2131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.751%	1079	50.63%	1.393%
Negative	-2.756%	1046	49.09%	-1.353%
Zero	0.000%	6	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.81. Further, an Excess Kurtosis of 26.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.95%	0	0.00%	0.00%
-33.95% to -25.23%	5	1.13%	1.13%
-25.23% to -16.52%	7	1.58%	2.71%
-16.52% to -7.80%	70	15.84%	18.55%
-7.80% to 0.91%	150	33.94%	52.49%
0.91% to 9.63%	142	32.13%	84.62%
9.63% to 18.34%	50	11.31%	95.93%
18.34% to 27.06%	10	2.26%	98.19%
27.06% to 35.77%	4	0.90%	99.10%
Greater than 35.77%	4	0.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.71%	12.53%	78.96%	68.27%
±2σ	-22.33%	24.15%	96.61%	95.45%
±3σ	-33.95%	35.77%	99.10%	99.73%

Descriptive Statistics

Mean	0.914%
Standard Error	0.553%
Median	0.330%
Mode	2.004%
Standard Deviation	11.620%
Sample Variance	135.017%
Kurtosis	26.10
Skewness	2.81
Range	154.518%
Minimum	-33.680%
Maximum	120.838%
Count	442

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.325%	229	51.81%	4.313%
Negative	-7.088%	212	47.96%	-3.400%
Zero	0.000%	1	0.23%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.16%
12	1 Quarter	11.00%
52	1 Year	10.75%
156	3 Years	11.40%
260	5 Years	13.22%
520	10 Years	14.27%
1,040	20 Years	14.27%
2,600	50 Years	14.27%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.18. Further, an Excess Kurtosis of 48.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.77%	0	0.00%	0.00%
-19.77% to -10.92%	0	0.00%	0.00%
-10.92% to -2.06%	0	0.00%	0.00%
-2.06% to 6.79%	43	9.71%	9.71%
6.79% to 15.64%	245	55.30%	65.01%
15.64% to 24.50%	102	23.02%	88.04%
24.50% to 33.35%	30	6.77%	94.81%
33.35% to 42.21%	9	2.03%	96.84%
42.21% to 51.06%	8	1.81%	98.65%
Greater than 51.06%	6	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.84%	27.45%	90.52%	68.27%
±2σ	-7.96%	39.25%	96.39%	95.45%
±3σ	-19.77%	51.06%	98.65%	99.73%

Descriptive Statistics

Mean	15.645%
Standard Error	0.561%
Median	12.520%
Mode	7.756%
Standard Deviation	11.805%
Sample Variance	139.347%
Kurtosis	48.82
Skewness	5.18
Range	151.783%
Minimum	4.076%
Maximum	155.859%
Count	443

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.645%	443	100.00%	15.645%
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 0.32. Further, an Excess Kurtosis of 4.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.64%	3	0.68%	0.68%
-31.64% to -23.63%	4	0.90%	1.58%
-23.63% to -15.63%	13	2.93%	4.51%
-15.63% to -7.62%	61	13.77%	18.28%
-7.62% to 0.39%	153	34.54%	52.82%
0.39% to 8.39%	129	29.12%	81.94%
8.39% to 16.40%	58	13.09%	95.03%
16.40% to 24.41%	14	3.16%	98.19%
24.41% to 32.42%	4	0.90%	99.10%
Greater than 32.42%	4	0.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.29%	11.06%	75.17%	68.27%
±2σ	-20.96%	21.74%	95.49%	95.45%
±3σ	-31.64%	32.42%	98.42%	99.73%

Descriptive Statistics

Mean	0.388%
Standard Error	0.507%
Median	-0.233%
Mode	-14.688%
Standard Deviation	10.676%
Sample Variance	113.971%
Kurtosis	4.47
Skewness	0.32
Range	113.254%
Minimum	-54.952%
Maximum	58.302%
Count	443

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.312%	214	48.31%	4.015%
Negative	-7.018%	229	51.69%	-3.628%
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 1.55. Further, an Excess Kurtosis of 4.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.24%	0	0.00%	0.00%
-67.24% to -49.53%	0	0.00%	0.00%
-49.53% to -31.82%	1	0.98%	0.98%
-31.82% to -14.10%	23	22.55%	23.53%
-14.10% to 3.61%	33	32.35%	55.88%
3.61% to 21.32%	30	29.41%	85.29%
21.32% to 39.04%	5	4.90%	90.20%
39.04% to 56.75%	8	7.84%	98.04%
56.75% to 74.46%	0	0.00%	98.04%
Greater than 74.46%	2	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.01%	27.23%	72.55%	68.27%
±2σ	-43.62%	50.84%	98.04%	95.45%
±3σ	-67.24%	74.46%	98.04%	99.73%

Descriptive Statistics

Mean	3.610%
Standard Error	2.338%
Median	1.703%
Mode	-32.770%
Standard Deviation	23.617%
Sample Variance	557.751%
Kurtosis	4.49
Skewness	1.55
Range	148.177%
Minimum	-32.770%
Maximum	115.407%
Count	102

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.100%	57	55.88%	10.115%
Negative	-14.744%	45	44.12%	-6.505%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	17.73%
12	1 Year	20.31%
36	3 Years	25.31%
60	5 Years	28.25%
120	10 Years	32.72%
240	20 Years	32.72%
600	50 Years	32.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.75. Further, an Excess Kurtosis of 13.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.64%	0	0.00%	0.00%
-28.64% to -11.64%	0	0.00%	0.00%
-11.64% to 5.36%	0	0.00%	0.00%
5.36% to 22.36%	15	14.56%	14.56%
22.36% to 39.35%	45	43.69%	58.25%
39.35% to 56.35%	25	24.27%	82.52%
56.35% to 73.35%	12	11.65%	94.17%
73.35% to 90.35%	4	3.88%	98.06%
90.35% to 107.35%	1	0.97%	99.03%
Greater than 107.35%	1	0.97%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.69%	62.02%	82.52%	68.27%
±2σ	-5.97%	84.68%	96.12%	95.45%
±3σ	-28.64%	107.35%	99.03%	99.73%

Descriptive Statistics

Mean	39.354%
Standard Error	2.233%
Median	33.912%
Mode	9.247%
Standard Deviation	22.664%
Sample Variance	513.680%
Kurtosis	13.48
Skewness	2.75
Range	169.833%
Minimum	9.247%
Maximum	179.080%
Count	103

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	39.354%	103	100.00%	39.354%
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 0.10. Further, an Excess Kurtosis of -0.07 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.69%	0	0.00%	0.00%
-61.69% to -46.10%	1	0.97%	0.97%
-46.10% to -30.52%	7	6.80%	7.77%
-30.52% to -14.93%	10	9.71%	17.48%
-14.93% to 0.66%	41	39.81%	57.28%
0.66% to 16.24%	22	21.36%	78.64%
16.24% to 31.83%	12	11.65%	90.29%
31.83% to 47.41%	9	8.74%	99.03%
47.41% to 63.00%	1	0.97%	100.00%
Greater than 63.00%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.13%	21.44%	69.90%	68.27%
±2σ	-40.91%	42.22%	96.12%	95.45%
±3σ	-61.69%	63.00%	100.00%	99.73%

Descriptive Statistics

Mean	0.655%
Standard Error	2.048%
Median	-2.350%
Mode	-53.440%
Standard Deviation	20.782%
Sample Variance	431.911%
Kurtosis	-0.07
Skewness	0.10
Range	101.691%
Minimum	-53.440%
Maximum	48.251%
Count	103

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.086%	45	43.69%	8.338%
Negative	-13.645%	58	56.31%	-7.684%
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 0.58. Further, an Excess Kurtosis of -0.18 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -101.88%	0	0.00%	0.00%
-101.88% to -73.73%	0	0.00%	0.00%
-73.73% to -45.58%	1	2.94%	2.94%
-45.58% to -17.44%	9	26.47%	29.41%
-17.44% to 10.71%	9	26.47%	55.88%
10.71% to 38.85%	7	20.59%	76.47%
38.85% to 67.00%	5	14.71%	91.18%
67.00% to 95.15%	2	5.88%	97.06%
95.15% to 123.29%	1	2.94%	100.00%
Greater than 123.29%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.82%	48.24%	70.59%	68.27%
±2σ	-64.35%	85.77%	94.12%	95.45%
±3σ	-101.88%	123.29%	100.00%	99.73%

Descriptive Statistics

Mean	10.709%
Standard Error	6.436%
Median	2.558%
Mode	-46.195%
Standard Deviation	37.528%
Sample Variance	1408.327%
Kurtosis	-0.18
Skewness	0.58
Range	145.508%
Minimum	-46.195%
Maximum	99.313%
Count	34

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.935%	20	58.82%	20.550%
Negative	-23.900%	14	41.18%	-9.841%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	36.43%
12	3 Years	49.35%
20	5 Years	50.03%
40	10 Years	60.93%
80	20 Years	60.93%
200	50 Years	60.93%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.57. Further, an Excess Kurtosis of 3.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.32%	0	0.00%	0.00%
-34.32% to -5.75%	0	0.00%	0.00%
-5.75% to 22.82%	0	0.00%	0.00%
22.82% to 51.40%	8	22.86%	22.86%
51.40% to 79.97%	12	34.29%	57.14%
79.97% to 108.54%	9	25.71%	82.86%
108.54% to 137.12%	4	11.43%	94.29%
137.12% to 165.69%	1	2.86%	97.14%
165.69% to 194.26%	0	0.00%	97.14%
Greater than 194.26%	1	2.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	41.87%	118.07%	74.29%	68.27%
±2σ	3.78%	156.16%	94.29%	95.45%
±3σ	-34.32%	194.26%	97.14%	99.73%

Descriptive Statistics

Mean	79.970%
Standard Error	6.440%
Median	77.897%
Mode	28.478%
Standard Deviation	38.097%
Sample Variance	1451.355%
Kurtosis	3.97
Skewness	1.57
Range	188.315%
Minimum	28.478%
Maximum	216.793%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	79.970%	35	100.00%	79.970%
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 0.80. Further, an Excess Kurtosis of 0.05 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -105.12%	0	0.00%	0.00%
-105.12% to -78.64%	0	0.00%	0.00%
-78.64% to -52.16%	0	0.00%	0.00%
-52.16% to -25.67%	8	22.86%	22.86%
-25.67% to 0.81%	12	34.29%	57.14%
0.81% to 27.30%	9	25.71%	82.86%
27.30% to 53.78%	2	5.71%	88.57%
53.78% to 80.27%	2	5.71%	94.29%
80.27% to 106.75%	2	5.71%	100.00%
Greater than 106.75%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.50%	36.12%	71.43%	68.27%
±2σ	-69.81%	71.44%	94.29%	95.45%
±3σ	-105.12%	106.75%	100.00%	99.73%

Descriptive Statistics

Mean	0.813%
Standard Error	5.969%
Median	-2.120%
Mode	-49.680%
Standard Deviation	35.312%
Sample Variance	1246.907%
Kurtosis	0.05
Skewness	0.80
Range	136.503%
Minimum	-49.680%
Maximum	86.823%
Count	35

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.859%	16	45.71%	14.564%
Negative	-25.331%	19	54.29%	-13.751%
Zero	0.000%	0	0.00%	0.000%

ROKU Deep Analytical Report