ARKK - 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	2.50%	2.00%	2.08%	3.89%	2.87%	3.15%	68.33	72.36	66.40	74.47
Weekly	5.44%	5.27%	5.48%	9.20%	6.31%	6.93%	66.02	74.90	61.98	79.78
Monthly	10.39%	10.98%	10.40%	19.16%	13.13%	14.43%	61.67	80.19	54.08	91.44
Quarterly	20.06%	21.59%	20.18%	34.85%	22.75%	24.99%	56.01	88.28	44.62	110.83
Annual	—	—	—	—	45.49%	49.98%	44.62	110.83	28.31	174.67
Option Time Horizon	—	—	—	—	17.17%	18.86%	59.23	83.49	49.88	99.13

Calculation Notes: Computed at 2026-03-23T16:44 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $70.32 | Strike (K): $72.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.2750 (Bid $3.9000 / Ask $4.6500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 45.49% (CRR binomial tree, American, n=20 steps) | BS IV: 45.88% (European Black-Scholes) | Yahoo IV (Annual): 49.98% → 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
2023-09-08	$0.3640
2021-12-29	$0.7830
2020-12-29	$2.0440
2019-12-27	$0.1910
2018-12-27	$1.1680
2017-12-27	$0.4880
2015-12-24	$0.4650

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.02. Further, an Excess Kurtosis of 3.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.41%	12	0.45%	0.45%
-7.41% to -5.54%	47	1.75%	2.19%
-5.54% to -3.66%	107	3.98%	6.18%
-3.66% to -1.79%	335	12.46%	18.64%
-1.79% to 0.08%	785	29.20%	47.84%
0.08% to 1.95%	915	34.04%	81.88%
1.95% to 3.83%	338	12.57%	94.46%
3.83% to 5.70%	108	4.02%	98.47%
5.70% to 7.57%	21	0.78%	99.26%
Greater than 7.57%	20	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.42%	2.58%	75.26%	68.27%
±2σ	-4.91%	5.07%	94.53%	95.45%
±3σ	-7.41%	7.57%	98.81%	99.73%

Descriptive Statistics

Mean	0.081%
Standard Error	0.048%
Median	0.175%
Mode	0.000%
Standard Deviation	2.496%
Sample Variance	6.229%
Kurtosis	3.26
Skewness	0.02
Range	32.209%
Minimum	-15.571%
Maximum	16.638%
Count	2688

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.763%	1442	53.65%	0.946%
Negative	-1.877%	1238	46.06%	-0.864%
Zero	0.000%	8	0.30%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.14%
20	1 Month	3.47%
60	1 Quarter	3.09%
250	1 Year	3.40%
750	3 Years	3.29%
1,250	5 Years	3.89%
2,500	10 Years	3.21%
5,000	20 Years	3.09%
12,500	50 Years	3.09%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.83. Further, an Excess Kurtosis of 6.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.23%	0	0.00%	0.00%
-3.23% to -1.73%	0	0.00%	0.00%
-1.73% to -0.23%	0	0.00%	0.00%
-0.23% to 1.27%	560	20.83%	20.83%
1.27% to 2.77%	1049	39.01%	59.84%
2.77% to 4.26%	606	22.54%	82.37%
4.26% to 5.76%	279	10.38%	92.75%
5.76% to 7.26%	113	4.20%	96.95%
7.26% to 8.76%	47	1.75%	98.70%
Greater than 8.76%	35	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.77%	4.76%	75.57%	68.27%
±2σ	-1.23%	6.76%	95.83%	95.45%
±3σ	-3.23%	8.76%	98.70%	99.73%

Descriptive Statistics

Mean	2.766%
Standard Error	0.039%
Median	2.322%
Mode	2.193%
Standard Deviation	1.997%
Sample Variance	3.986%
Kurtosis	6.26
Skewness	1.83
Range	18.269%
Minimum	0.005%
Maximum	18.274%
Count	2689

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.766%	2689	100.00%	2.766%
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 0.03. Further, an Excess Kurtosis of 3.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.15%	16	0.60%	0.60%
-6.15% to -4.59%	26	0.97%	1.56%
-4.59% to -3.03%	100	3.72%	5.28%
-3.03% to -1.47%	326	12.12%	17.40%
-1.47% to 0.09%	928	34.51%	51.92%
0.09% to 1.65%	805	29.94%	81.85%
1.65% to 3.21%	309	11.49%	93.34%
3.21% to 4.77%	114	4.24%	97.58%
4.77% to 6.33%	44	1.64%	99.22%
Greater than 6.33%	21	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.99%	2.17%	75.20%	68.27%
±2σ	-4.07%	4.25%	94.35%	95.45%
±3σ	-6.15%	6.33%	98.62%	99.73%

Descriptive Statistics

Mean	0.089%
Standard Error	0.040%
Median	0.022%
Mode	0.000%
Standard Deviation	2.080%
Sample Variance	4.325%
Kurtosis	3.10
Skewness	0.03
Range	24.509%
Minimum	-14.413%
Maximum	10.096%
Count	2689

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.566%	1352	50.28%	0.787%
Negative	-1.418%	1324	49.24%	-0.698%
Zero	0.000%	13	0.48%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.20. Further, an Excess Kurtosis of 2.25 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.94%	5	0.84%	0.84%
-15.94% to -11.86%	6	1.01%	1.85%
-11.86% to -7.78%	30	5.05%	6.90%
-7.78% to -3.70%	67	11.28%	18.18%
-3.70% to 0.38%	171	28.79%	46.97%
0.38% to 4.45%	204	34.34%	81.31%
4.45% to 8.53%	80	13.47%	94.78%
8.53% to 12.61%	24	4.04%	98.82%
12.61% to 16.69%	4	0.67%	99.49%
Greater than 16.69%	3	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.06%	5.81%	75.93%	68.27%
±2σ	-10.50%	11.25%	94.44%	95.45%
±3σ	-15.94%	16.69%	98.65%	99.73%

Descriptive Statistics

Mean	0.375%
Standard Error	0.223%
Median	0.603%
Mode	0.000%
Standard Deviation	5.439%
Sample Variance	29.583%
Kurtosis	2.25
Skewness	-0.20
Range	48.123%
Minimum	-24.194%
Maximum	23.929%
Count	594

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.849%	338	56.90%	2.190%
Negative	-4.261%	253	42.59%	-1.815%
Zero	0.000%	3	0.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.03%
12	1 Quarter	6.78%
52	1 Year	7.92%
156	3 Years	7.85%
260	5 Years	9.20%
520	10 Years	7.66%
1,040	20 Years	7.21%
2,600	50 Years	7.21%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.81. Further, an Excess Kurtosis of 4.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.42%	0	0.00%	0.00%
-8.42% to -4.47%	0	0.00%	0.00%
-4.47% to -0.52%	0	0.00%	0.00%
-0.52% to 3.43%	127	21.34%	21.34%
3.43% to 7.38%	224	37.65%	58.99%
7.38% to 11.33%	153	25.71%	84.71%
11.33% to 15.28%	44	7.39%	92.10%
15.28% to 19.23%	22	3.70%	95.80%
19.23% to 23.18%	13	2.18%	97.98%
Greater than 23.18%	12	2.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.11%	12.64%	79.33%	68.27%
±2σ	-3.16%	17.91%	94.96%	95.45%
±3σ	-8.42%	23.18%	97.98%	99.73%

Descriptive Statistics

Mean	7.377%
Standard Error	0.216%
Median	6.193%
Mode	5.282%
Standard Deviation	5.266%
Sample Variance	27.730%
Kurtosis	4.68
Skewness	1.81
Range	38.174%
Minimum	0.009%
Maximum	38.183%
Count	595

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.377%	595	100.00%	7.377%
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 1.22. Further, an Excess Kurtosis of 5.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.33%	2	0.34%	0.34%
-16.33% to -12.22%	1	0.17%	0.50%
-12.22% to -8.11%	21	3.53%	4.03%
-8.11% to -3.99%	85	14.29%	18.32%
-3.99% to 0.12%	237	39.83%	58.15%
0.12% to 4.23%	147	24.71%	82.86%
4.23% to 8.35%	59	9.92%	92.77%
8.35% to 12.46%	24	4.03%	96.81%
12.46% to 16.57%	13	2.18%	98.99%
Greater than 16.57%	6	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.37%	5.60%	78.32%	68.27%
±2σ	-10.85%	11.09%	95.13%	95.45%
±3σ	-16.33%	16.57%	98.66%	99.73%

Descriptive Statistics

Mean	0.119%
Standard Error	0.225%
Median	-0.567%
Mode	-4.378%
Standard Deviation	5.484%
Sample Variance	30.077%
Kurtosis	5.42
Skewness	1.22
Range	56.715%
Minimum	-18.946%
Maximum	37.769%
Count	595

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.608%	257	43.19%	1.990%
Negative	-3.313%	336	56.47%	-1.871%
Zero	0.000%	2	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.27. Further, an Excess Kurtosis of 0.41 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.67%	0	0.00%	0.00%
-29.67% to -21.88%	1	0.73%	0.73%
-21.88% to -14.08%	5	3.65%	4.38%
-14.08% to -6.29%	25	18.25%	22.63%
-6.29% to 1.51%	45	32.85%	55.47%
1.51% to 9.30%	29	21.17%	76.64%
9.30% to 17.10%	24	17.52%	94.16%
17.10% to 24.90%	4	2.92%	97.08%
24.90% to 32.69%	4	2.92%	100.00%
Greater than 32.69%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.88%	11.90%	66.42%	68.27%
±2σ	-19.28%	22.30%	94.16%	95.45%
±3σ	-29.67%	32.69%	100.00%	99.73%

Descriptive Statistics

Mean	1.509%
Standard Error	0.888%
Median	0.684%
Mode	-28.903%
Standard Deviation	10.394%
Sample Variance	108.030%
Kurtosis	0.41
Skewness	0.27
Range	60.345%
Minimum	-28.903%
Maximum	31.442%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.493%	76	55.47%	4.711%
Negative	-7.192%	61	44.53%	-3.202%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.62%
12	1 Year	16.54%
36	3 Years	16.96%
60	5 Years	19.16%
120	10 Years	16.69%
240	20 Years	15.71%
600	50 Years	15.71%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.60. Further, an Excess Kurtosis of 3.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.59%	0	0.00%	0.00%
-15.59% to -7.35%	0	0.00%	0.00%
-7.35% to 0.89%	1	0.72%	0.72%
0.89% to 9.12%	33	23.91%	24.64%
9.12% to 17.36%	46	33.33%	57.97%
17.36% to 25.60%	33	23.91%	81.88%
25.60% to 33.84%	15	10.87%	92.75%
33.84% to 42.08%	5	3.62%	96.38%
42.08% to 50.31%	2	1.45%	97.83%
Greater than 50.31%	3	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.38%	28.35%	76.09%	68.27%
±2σ	-4.61%	39.33%	96.38%	95.45%
±3σ	-15.59%	50.31%	97.83%	99.73%

Descriptive Statistics

Mean	17.363%
Standard Error	0.935%
Median	14.931%
Mode	0.196%
Standard Deviation	10.984%
Sample Variance	120.647%
Kurtosis	3.89
Skewness	1.60
Range	68.131%
Minimum	0.196%
Maximum	68.327%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.363%	138	100.00%	17.363%
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 0.56. Further, an Excess Kurtosis of 1.45 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.33%	0	0.00%	0.00%
-31.33% to -23.53%	1	0.72%	0.72%
-23.53% to -15.73%	6	4.35%	5.07%
-15.73% to -7.94%	23	16.67%	21.74%
-7.94% to -0.14%	41	29.71%	51.45%
-0.14% to 7.66%	39	28.26%	79.71%
7.66% to 15.45%	20	14.49%	94.20%
15.45% to 23.25%	5	3.62%	97.83%
23.25% to 31.05%	2	1.45%	99.28%
Greater than 31.05%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.54%	10.26%	68.84%	68.27%
±2σ	-20.93%	20.65%	94.93%	95.45%
±3σ	-31.33%	31.05%	99.28%	99.73%

Descriptive Statistics

Mean	-0.141%
Standard Error	0.885%
Median	-0.357%
Mode	-23.552%
Standard Deviation	10.396%
Sample Variance	108.070%
Kurtosis	1.45
Skewness	0.56
Range	65.213%
Minimum	-23.552%
Maximum	41.661%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.784%	67	48.55%	3.779%
Negative	-7.620%	71	51.45%	-3.920%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.36. Further, an Excess Kurtosis of 0.56 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.34%	0	0.00%	0.00%
-55.34% to -40.29%	0	0.00%	0.00%
-40.29% to -25.24%	3	6.52%	6.52%
-25.24% to -10.20%	5	10.87%	17.39%
-10.20% to 4.85%	19	41.30%	58.70%
4.85% to 19.89%	13	28.26%	86.96%
19.89% to 34.94%	1	2.17%	89.13%
34.94% to 49.98%	4	8.70%	97.83%
49.98% to 65.03%	1	2.17%	100.00%
Greater than 65.03%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.21%	24.91%	76.09%	68.27%
±2σ	-35.27%	44.97%	89.13%	95.45%
±3σ	-55.34%	65.03%	100.00%	99.73%

Descriptive Statistics

Mean	4.848%
Standard Error	2.958%
Median	3.079%
Mode	-37.518%
Standard Deviation	20.061%
Sample Variance	402.424%
Kurtosis	0.56
Skewness	0.36
Range	91.322%
Minimum	-37.518%
Maximum	53.804%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.006%	27	58.70%	9.982%
Negative	-12.431%	19	41.30%	-5.135%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.00%
12	3 Years	34.95%
20	5 Years	34.85%
40	10 Years	31.24%
80	20 Years	29.43%
200	50 Years	29.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 1.00. Further, an Excess Kurtosis of 0.46 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.15%	0	0.00%	0.00%
-30.15% to -13.96%	0	0.00%	0.00%
-13.96% to 2.23%	1	2.13%	2.13%
2.23% to 18.43%	9	19.15%	21.28%
18.43% to 34.62%	20	42.55%	63.83%
34.62% to 50.81%	8	17.02%	80.85%
50.81% to 67.00%	4	8.51%	89.36%
67.00% to 83.20%	3	6.38%	95.74%
83.20% to 99.39%	2	4.26%	100.00%
Greater than 99.39%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.03%	56.21%	70.21%	68.27%
±2σ	-8.56%	77.80%	95.74%	95.45%
±3σ	-30.15%	99.39%	100.00%	99.73%

Descriptive Statistics

Mean	34.620%
Standard Error	3.149%
Median	26.959%
Mode	0.196%
Standard Deviation	21.590%
Sample Variance	466.139%
Kurtosis	0.46
Skewness	1.00
Range	95.391%
Minimum	0.196%
Maximum	95.587%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.620%	47	100.00%	34.620%
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 1.22. Further, an Excess Kurtosis of 2.77 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.24%	0	0.00%	0.00%
-61.24% to -46.11%	0	0.00%	0.00%
-46.11% to -30.98%	2	4.26%	4.26%
-30.98% to -15.84%	6	12.77%	17.02%
-15.84% to -0.71%	17	36.17%	53.19%
-0.71% to 14.42%	14	29.79%	82.98%
14.42% to 29.55%	5	10.64%	93.62%
29.55% to 44.69%	1	2.13%	95.74%
44.69% to 59.82%	0	0.00%	95.74%
Greater than 59.82%	2	4.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.89%	19.47%	80.85%	68.27%
±2σ	-41.06%	39.64%	93.62%	95.45%
±3σ	-61.24%	59.82%	95.74%	99.73%

Descriptive Statistics

Mean	-0.711%
Standard Error	2.943%
Median	-1.152%
Mode	-33.084%
Standard Deviation	20.177%
Sample Variance	407.113%
Kurtosis	2.77
Skewness	1.22
Range	95.804%
Minimum	-33.084%
Maximum	62.720%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.923%	21	44.68%	6.668%
Negative	-13.339%	26	55.32%	-7.379%
Zero	0.000%	0	0.00%	0.000%

ARKK Deep Analytical Report