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%	3.93%	2.80%	3.15%	69.52	73.52	67.60	75.60
Weekly	5.45%	5.28%	5.50%	9.33%	6.15%	6.94%	67.22	76.03	63.21	80.85
Monthly	10.43%	11.01%	10.44%	19.38%	12.81%	14.44%	62.89	81.26	55.33	92.37
Quarterly	20.04%	21.60%	20.17%	34.83%	22.19%	25.01%	57.26	89.25	45.87	111.43
Annual	—	—	—	—	44.38%	50.02%	45.87	111.43	29.43	173.68
Option Time Horizon	—	—	—	—	14.51%	16.35%	61.84	82.65	53.49	95.56

Calculation Notes: Computed at 2026-02-22T14:25 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $71.49 | Strike (K): $73.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.6250 (Bid $3.2000 / Ask $4.0500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 44.38% (CRR binomial tree, American, n=20 steps) | BS IV: 44.79% (European Black-Scholes) | Yahoo IV (Annual): 50.02% → 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 3.28 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%	46	1.72%	2.17%
-5.54% to -3.67%	108	4.05%	6.22%
-3.67% to -1.79%	327	12.26%	18.49%
-1.79% to 0.08%	782	29.32%	47.81%
0.08% to 1.96%	910	34.12%	81.93%
1.96% to 3.83%	333	12.49%	94.41%
3.83% to 5.70%	108	4.05%	98.46%
5.70% to 7.58%	21	0.79%	99.25%
Greater than 7.58%	20	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.42%	2.58%	75.33%	68.27%
±2σ	-4.91%	5.08%	94.49%	95.45%
±3σ	-7.41%	7.58%	98.80%	99.73%

Descriptive Statistics

Mean	0.082%
Standard Error	0.048%
Median	0.176%
Mode	0.000%
Standard Deviation	2.498%
Sample Variance	6.240%
Kurtosis	3.28
Skewness	0.02
Range	32.209%
Minimum	-15.571%
Maximum	16.638%
Count	2667

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.761%	1432	53.69%	0.946%
Negative	-1.876%	1227	46.01%	-0.863%
Zero	0.000%	8	0.30%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.27%
20	1 Month	3.64%
60	1 Quarter	2.89%
250	1 Year	3.56%
750	3 Years	3.31%
1,250	5 Years	3.93%
2,500	10 Years	3.20%
5,000	20 Years	3.08%
12,500	50 Years	3.08%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.24%	0	0.00%	0.00%
-3.24% to -1.74%	0	0.00%	0.00%
-1.74% to -0.24%	0	0.00%	0.00%
-0.24% to 1.26%	558	20.91%	20.91%
1.26% to 2.76%	1038	38.91%	59.82%
2.76% to 4.26%	602	22.56%	82.38%
4.26% to 5.77%	275	10.31%	92.69%
5.77% to 7.27%	113	4.24%	96.93%
7.27% to 8.77%	47	1.76%	98.69%
Greater than 8.77%	35	1.31%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.76%	4.77%	75.52%	68.27%
±2σ	-1.24%	6.77%	95.80%	95.45%
±3σ	-3.24%	8.77%	98.69%	99.73%

Descriptive Statistics

Mean	2.764%
Standard Error	0.039%
Median	2.313%
Mode	2.193%
Standard Deviation	2.002%
Sample Variance	4.010%
Kurtosis	6.23
Skewness	1.83
Range	18.269%
Minimum	0.005%
Maximum	18.274%
Count	2668

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.764%	2668	100.00%	2.764%
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 3.12 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%	1.57%
-4.59% to -3.03%	99	3.71%	5.28%
-3.03% to -1.47%	322	12.07%	17.35%
-1.47% to 0.09%	929	34.82%	52.17%
0.09% to 1.66%	791	29.65%	81.82%
1.66% to 3.22%	307	11.51%	93.33%
3.22% to 4.78%	114	4.27%	97.60%
4.78% to 6.34%	43	1.61%	99.21%
Greater than 6.34%	21	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.99%	2.17%	75.26%	68.27%
±2σ	-4.07%	4.26%	94.34%	95.45%
±3σ	-6.15%	6.34%	98.61%	99.73%

Descriptive Statistics

Mean	0.094%
Standard Error	0.040%
Median	0.022%
Mode	0.000%
Standard Deviation	2.081%
Sample Variance	4.329%
Kurtosis	3.12
Skewness	0.03
Range	24.509%
Minimum	-14.413%
Maximum	10.096%
Count	2668

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.567%	1344	50.38%	0.789%
Negative	-1.416%	1311	49.14%	-0.696%
Zero	0.000%	13	0.49%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.21. 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 -15.97%	5	0.85%	0.85%
-15.97% to -11.88%	6	1.02%	1.86%
-11.88% to -7.79%	30	5.08%	6.95%
-7.79% to -3.71%	66	11.19%	18.14%
-3.71% to 0.38%	168	28.47%	46.61%
0.38% to 4.47%	205	34.75%	81.36%
4.47% to 8.55%	79	13.39%	94.75%
8.55% to 12.64%	24	4.07%	98.81%
12.64% to 16.73%	4	0.68%	99.49%
Greater than 16.73%	3	0.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.07%	5.83%	76.27%	68.27%
±2σ	-10.52%	11.28%	94.75%	95.45%
±3σ	-15.97%	16.73%	98.64%	99.73%

Descriptive Statistics

Mean	0.380%
Standard Error	0.224%
Median	0.655%
Mode	0.000%
Standard Deviation	5.450%
Sample Variance	29.698%
Kurtosis	2.25
Skewness	-0.21
Range	48.123%
Minimum	-24.194%
Maximum	23.929%
Count	590

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.847%	337	57.12%	2.197%
Negative	-4.289%	250	42.37%	-1.817%
Zero	0.000%	3	0.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.80%
12	1 Quarter	6.31%
52	1 Year	8.27%
156	3 Years	7.91%
260	5 Years	9.33%
520	10 Years	7.64%
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 1.80. Further, an Excess Kurtosis of 4.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.47%	0	0.00%	0.00%
-8.47% to -4.51%	0	0.00%	0.00%
-4.51% to -0.55%	0	0.00%	0.00%
-0.55% to 3.42%	126	21.32%	21.32%
3.42% to 7.38%	223	37.73%	59.05%
7.38% to 11.34%	152	25.72%	84.77%
11.34% to 15.30%	44	7.45%	92.22%
15.30% to 19.27%	21	3.55%	95.77%
19.27% to 23.23%	13	2.20%	97.97%
Greater than 23.23%	12	2.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.09%	12.66%	79.36%	68.27%
±2σ	-3.19%	17.94%	94.92%	95.45%
±3σ	-8.47%	23.23%	97.97%	99.73%

Descriptive Statistics

Mean	7.378%
Standard Error	0.217%
Median	6.182%
Mode	5.282%
Standard Deviation	5.283%
Sample Variance	27.914%
Kurtosis	4.63
Skewness	1.80
Range	38.174%
Minimum	0.009%
Maximum	38.183%
Count	591

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.378%	591	100.00%	7.378%
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 1.23. Further, an Excess Kurtosis of 5.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.36%	2	0.34%	0.34%
-16.36% to -12.24%	1	0.17%	0.51%
-12.24% to -8.12%	21	3.55%	4.06%
-8.12% to -4.00%	84	14.21%	18.27%
-4.00% to 0.12%	236	39.93%	58.21%
0.12% to 4.25%	145	24.53%	82.74%
4.25% to 8.37%	59	9.98%	92.72%
8.37% to 12.49%	24	4.06%	96.79%
12.49% to 16.61%	13	2.20%	98.98%
Greater than 16.61%	6	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.37%	5.62%	78.34%	68.27%
±2σ	-10.87%	11.11%	95.09%	95.45%
±3σ	-16.36%	16.61%	98.65%	99.73%

Descriptive Statistics

Mean	0.124%
Standard Error	0.226%
Median	-0.567%
Mode	-4.378%
Standard Deviation	5.495%
Sample Variance	30.190%
Kurtosis	5.40
Skewness	1.23
Range	56.715%
Minimum	-18.946%
Maximum	37.769%
Count	591

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.623%	255	43.15%	1.995%
Negative	-3.311%	334	56.51%	-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 0.26. Further, an Excess Kurtosis of 0.38 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.75%	0	0.00%	0.00%
-29.75% to -21.93%	1	0.74%	0.74%
-21.93% to -14.11%	5	3.68%	4.41%
-14.11% to -6.29%	25	18.38%	22.79%
-6.29% to 1.53%	44	32.35%	55.15%
1.53% to 9.36%	29	21.32%	76.47%
9.36% to 17.18%	24	17.65%	94.12%
17.18% to 25.00%	4	2.94%	97.06%
25.00% to 32.82%	4	2.94%	100.00%
Greater than 32.82%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.90%	11.96%	66.18%	68.27%
±2σ	-19.32%	22.39%	94.12%	95.45%
±3σ	-29.75%	32.82%	100.00%	99.73%

Descriptive Statistics

Mean	1.533%
Standard Error	0.894%
Median	0.694%
Mode	-28.903%
Standard Deviation	10.429%
Sample Variance	108.772%
Kurtosis	0.38
Skewness	0.26
Range	60.345%
Minimum	-28.903%
Maximum	31.442%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.493%	76	55.88%	4.746%
Negative	-7.282%	60	44.12%	-3.213%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.21%
12	1 Year	17.37%
36	3 Years	17.11%
60	5 Years	19.38%
120	10 Years	16.74%
240	20 Years	15.75%
600	50 Years	15.75%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.59. Further, an Excess Kurtosis of 3.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.62%	0	0.00%	0.00%
-15.62% to -7.36%	0	0.00%	0.00%
-7.36% to 0.90%	1	0.73%	0.73%
0.90% to 9.15%	33	24.09%	24.82%
9.15% to 17.41%	45	32.85%	57.66%
17.41% to 25.67%	33	24.09%	81.75%
25.67% to 33.93%	15	10.95%	92.70%
33.93% to 42.18%	5	3.65%	96.35%
42.18% to 50.44%	2	1.46%	97.81%
Greater than 50.44%	3	2.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.40%	28.42%	75.91%	68.27%
±2σ	-4.61%	39.43%	96.35%	95.45%
±3σ	-15.62%	50.44%	97.81%	99.73%

Descriptive Statistics

Mean	17.412%
Standard Error	0.941%
Median	15.149%
Mode	0.196%
Standard Deviation	11.010%
Sample Variance	121.212%
Kurtosis	3.84
Skewness	1.59
Range	68.131%
Minimum	0.196%
Maximum	68.327%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.412%	137	100.00%	17.412%
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 1.41 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.45%	0	0.00%	0.00%
-31.45% to -23.62%	0	0.00%	0.00%
-23.62% to -15.79%	6	4.38%	4.38%
-15.79% to -7.96%	24	17.52%	21.90%
-7.96% to -0.14%	41	29.93%	51.82%
-0.14% to 7.69%	38	27.74%	79.56%
7.69% to 15.52%	20	14.60%	94.16%
15.52% to 23.35%	5	3.65%	97.81%
23.35% to 31.18%	2	1.46%	99.27%
Greater than 31.18%	1	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.57%	10.30%	69.34%	68.27%
±2σ	-21.01%	20.74%	95.62%	95.45%
±3σ	-31.45%	31.18%	99.27%	99.73%

Descriptive Statistics

Mean	-0.135%
Standard Error	0.892%
Median	-0.465%
Mode	-23.552%
Standard Deviation	10.437%
Sample Variance	108.940%
Kurtosis	1.41
Skewness	0.56
Range	65.213%
Minimum	-23.552%
Maximum	41.661%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.918%	66	48.17%	3.814%
Negative	-7.620%	71	51.83%	-3.949%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.35. Further, an Excess Kurtosis of 0.57 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.24%	0	0.00%	0.00%
-55.24% to -40.21%	0	0.00%	0.00%
-40.21% to -25.18%	3	6.52%	6.52%
-25.18% to -10.15%	5	10.87%	17.39%
-10.15% to 4.88%	19	41.30%	58.70%
4.88% to 19.91%	13	28.26%	86.96%
19.91% to 34.95%	1	2.17%	89.13%
34.95% to 49.98%	4	8.70%	97.83%
49.98% to 65.01%	1	2.17%	100.00%
Greater than 65.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.16%	24.93%	73.91%	68.27%
±2σ	-35.20%	44.97%	89.13%	95.45%
±3σ	-55.24%	65.01%	100.00%	99.73%

Descriptive Statistics

Mean	4.884%
Standard Error	2.955%
Median	3.080%
Mode	-37.518%
Standard Deviation	20.041%
Sample Variance	401.652%
Kurtosis	0.57
Skewness	0.35
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	-12.342%	19	41.30%	-5.098%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	30.89%
12	3 Years	34.92%
20	5 Years	34.83%
40	10 Years	31.23%
80	20 Years	29.42%
200	50 Years	29.42%

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 -30.19%	0	0.00%	0.00%
-30.19% to -13.99%	0	0.00%	0.00%
-13.99% to 2.21%	1	2.13%	2.13%
2.21% to 18.41%	9	19.15%	21.28%
18.41% to 34.61%	20	42.55%	63.83%
34.61% to 50.81%	8	17.02%	80.85%
50.81% to 67.01%	4	8.51%	89.36%
67.01% to 83.21%	3	6.38%	95.74%
83.21% to 99.41%	2	4.26%	100.00%
Greater than 99.41%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.01%	56.21%	70.21%	68.27%
±2σ	-8.59%	77.81%	95.74%	95.45%
±3σ	-30.19%	99.41%	100.00%	99.73%

Descriptive Statistics

Mean	34.609%
Standard Error	3.151%
Median	26.959%
Mode	0.196%
Standard Deviation	21.601%
Sample Variance	466.590%
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	34.609%	47	100.00%	34.609%
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 1.23. Further, an Excess Kurtosis of 2.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.25%	0	0.00%	0.00%
-61.25% to -46.12%	0	0.00%	0.00%
-46.12% to -31.00%	2	4.26%	4.26%
-31.00% to -15.88%	6	12.77%	17.02%
-15.88% to -0.75%	17	36.17%	53.19%
-0.75% to 14.37%	14	29.79%	82.98%
14.37% to 29.50%	5	10.64%	93.62%
29.50% to 44.62%	1	2.13%	95.74%
44.62% to 59.75%	0	0.00%	95.74%
Greater than 59.75%	2	4.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.92%	19.41%	78.72%	68.27%
±2σ	-41.08%	39.58%	93.62%	95.45%
±3σ	-61.25%	59.75%	95.74%	99.73%

Descriptive Statistics

Mean	-0.751%
Standard Error	2.942%
Median	-1.152%
Mode	-33.084%
Standard Deviation	20.166%
Sample Variance	406.675%
Kurtosis	2.79
Skewness	1.23
Range	95.804%
Minimum	-33.084%
Maximum	62.720%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.834%	21	44.68%	6.628%
Negative	-13.339%	26	55.32%	-7.379%
Zero	0.000%	0	0.00%	0.000%

ARKK Deep Analytical Report