^VIX - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	7.13%	6.72%	5.90%	10.88%
Weekly	15.57%	18.12%	12.75%	25.45%
Monthly	21.85%	38.49%	20.44%	53.89%
Quarterly	29.74%	70.39%	26.14%	90.36%
Annual	—	—	—	—
Option Time Horizon	—	—	—	—

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.94. Further, an Excess Kurtosis of 16.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.15%	17	0.20%	0.20%
-21.15% to -15.80%	45	0.52%	0.72%
-15.80% to -10.45%	243	2.82%	3.54%
-10.45% to -5.11%	1190	13.82%	17.36%
-5.11% to 0.24%	3241	37.63%	54.99%
0.24% to 5.59%	2490	28.91%	83.90%
5.59% to 10.94%	893	10.37%	94.26%
10.94% to 16.29%	296	3.44%	97.70%
16.29% to 21.63%	93	1.08%	98.78%
Greater than 21.63%	105	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.89%	7.37%	78.40%	68.27%
±2σ	-14.02%	14.50%	95.77%	95.45%
±3σ	-21.15%	21.63%	98.58%	99.73%

Descriptive Statistics

Mean	0.242%
Standard Error	0.077%
Median	-0.426%
Mode	0.000%
Standard Deviation	7.130%
Sample Variance	50.837%
Kurtosis	16.25
Skewness	1.94
Range	151.352%
Minimum	-35.754%
Maximum	115.598%
Count	8613

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.522%	4004	46.49%	2.567%
Negative	-4.390%	4562	52.97%	-2.325%
Zero	0.000%	47	0.55%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	20.46%
20	1 Month	18.80%
60	1 Quarter	14.16%
250	1 Year	12.23%
750	3 Years	10.76%
1,250	5 Years	10.88%
2,500	10 Years	11.47%
5,000	20 Years	10.54%
12,500	50 Years	9.28%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.86. Further, an Excess Kurtosis of 87.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.35%	0	0.00%	0.00%
-11.35% to -6.30%	0	0.00%	0.00%
-6.30% to -1.26%	0	0.00%	0.00%
-1.26% to 3.78%	1003	11.64%	11.64%
3.78% to 8.82%	4515	52.41%	64.06%
8.82% to 13.86%	1960	22.75%	86.81%
13.86% to 18.90%	633	7.35%	94.16%
18.90% to 23.94%	280	3.25%	97.41%
23.94% to 28.99%	100	1.16%	98.57%
Greater than 28.99%	123	1.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.10%	15.54%	88.90%	68.27%
±2σ	-4.62%	22.26%	96.64%	95.45%
±3σ	-11.35%	28.99%	98.57%	99.73%

Descriptive Statistics

Mean	8.820%
Standard Error	0.072%
Median	7.194%
Mode	4.000%
Standard Deviation	6.722%
Sample Variance	45.185%
Kurtosis	87.67
Skewness	5.86
Range	179.874%
Minimum	1.144%
Maximum	181.018%
Count	8614

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.820%	8614	100.00%	8.820%
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 -0.29. Further, an Excess Kurtosis of 5.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.06%	68	0.79%	0.79%
-17.06% to -12.63%	133	1.54%	2.33%
-12.63% to -8.21%	312	3.62%	5.96%
-8.21% to -3.79%	998	11.59%	17.54%
-3.79% to 0.63%	2592	30.09%	47.63%
0.63% to 5.05%	2956	34.32%	81.95%
5.05% to 9.48%	1148	13.33%	95.28%
9.48% to 13.90%	298	3.46%	98.73%
13.90% to 18.32%	66	0.77%	99.50%
Greater than 18.32%	43	0.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.26%	6.53%	76.48%	68.27%
±2σ	-11.16%	12.42%	94.80%	95.45%
±3σ	-17.06%	18.32%	98.71%	99.73%

Descriptive Statistics

Mean	0.632%
Standard Error	0.064%
Median	0.901%
Mode	0.000%
Standard Deviation	5.896%
Sample Variance	34.764%
Kurtosis	5.49
Skewness	-0.29
Range	102.225%
Minimum	-50.589%
Maximum	51.636%
Count	8614

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.255%	4974	57.74%	2.457%
Negative	-4.381%	3588	41.65%	-1.825%
Zero	0.000%	52	0.60%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.45. Further, an Excess Kurtosis of 33.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.69%	1	0.06%	0.06%
-45.69% to -34.02%	2	0.11%	0.17%
-34.02% to -22.34%	46	2.58%	2.75%
-22.34% to -10.66%	236	13.22%	15.97%
-10.66% to 1.02%	710	39.78%	55.74%
1.02% to 12.70%	537	30.08%	85.83%
12.70% to 24.38%	168	9.41%	95.24%
24.38% to 36.05%	49	2.75%	97.98%
36.05% to 47.73%	17	0.95%	98.94%
Greater than 47.73%	19	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.55%	16.59%	80.45%	68.27%
±2σ	-30.12%	32.16%	96.69%	95.45%
±3σ	-45.69%	47.73%	98.88%	99.73%

Descriptive Statistics

Mean	1.019%
Standard Error	0.369%
Median	-0.649%
Mode	-24.014%
Standard Deviation	15.571%
Sample Variance	242.442%
Kurtosis	33.04
Skewness	3.45
Range	259.208%
Minimum	-46.305%
Maximum	212.903%
Count	1785

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.583%	856	47.95%	5.555%
Negative	-8.723%	928	51.99%	-4.535%
Zero	0.000%	1	0.06%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	41.66%
12	1 Quarter	30.37%
52	1 Year	28.95%
156	3 Years	25.68%
260	5 Years	25.45%
520	10 Years	26.88%
1,040	20 Years	24.77%
2,600	50 Years	21.90%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.73. Further, an Excess Kurtosis of 84.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.36%	0	0.00%	0.00%
-30.36% to -16.77%	0	0.00%	0.00%
-16.77% to -3.18%	0	0.00%	0.00%
-3.18% to 10.40%	139	7.78%	7.78%
10.40% to 23.99%	1016	56.89%	64.67%
23.99% to 37.58%	424	23.74%	88.41%
37.58% to 51.17%	122	6.83%	95.24%
51.17% to 64.76%	45	2.52%	97.76%
64.76% to 78.34%	18	1.01%	98.77%
Greater than 78.34%	22	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.88%	42.11%	91.10%	68.27%
±2σ	-12.24%	60.23%	96.98%	95.45%
±3σ	-30.36%	78.34%	98.77%	99.73%

Descriptive Statistics

Mean	23.993%
Standard Error	0.429%
Median	19.938%
Mode	13.300%
Standard Deviation	18.117%
Sample Variance	328.243%
Kurtosis	84.19
Skewness	6.73
Range	312.114%
Minimum	6.282%
Maximum	318.396%
Count	1786

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.993%	1786	100.00%	23.993%
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 -0.02. Further, an Excess Kurtosis of 2.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.13%	12	0.67%	0.67%
-37.13% to -27.57%	13	0.73%	1.40%
-27.57% to -18.01%	73	4.09%	5.49%
-18.01% to -8.45%	231	12.93%	18.42%
-8.45% to 1.12%	568	31.80%	50.22%
1.12% to 10.68%	558	31.24%	81.47%
10.68% to 20.24%	221	12.37%	93.84%
20.24% to 29.80%	68	3.81%	97.65%
29.80% to 39.37%	31	1.74%	99.38%
Greater than 39.37%	11	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.63%	13.87%	74.19%	68.27%
±2σ	-24.38%	26.62%	94.46%	95.45%
±3σ	-37.13%	39.37%	98.71%	99.73%

Descriptive Statistics

Mean	1.116%
Standard Error	0.302%
Median	1.038%
Mode	0.000%
Standard Deviation	12.750%
Sample Variance	162.558%
Kurtosis	2.35
Skewness	-0.02
Range	129.856%
Minimum	-67.084%
Maximum	62.772%
Count	1786

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.711%	967	54.14%	5.258%
Negative	-9.077%	815	45.63%	-4.142%
Zero	0.000%	4	0.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.49. Further, an Excess Kurtosis of 5.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.36%	0	0.00%	0.00%
-63.36% to -46.97%	0	0.00%	0.00%
-46.97% to -30.59%	14	3.41%	3.41%
-30.59% to -14.20%	70	17.07%	20.49%
-14.20% to 2.18%	155	37.80%	58.29%
2.18% to 18.57%	101	24.63%	82.93%
18.57% to 34.95%	39	9.51%	92.44%
34.95% to 51.34%	21	5.12%	97.56%
51.34% to 67.72%	5	1.22%	98.78%
Greater than 67.72%	5	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.66%	24.03%	75.85%	68.27%
±2σ	-41.51%	45.87%	96.34%	95.45%
±3σ	-63.36%	67.72%	98.78%	99.73%

Descriptive Statistics

Mean	2.182%
Standard Error	1.079%
Median	-0.814%
Mode	1.023%
Standard Deviation	21.846%
Sample Variance	477.261%
Kurtosis	5.22
Skewness	1.49
Range	180.468%
Minimum	-45.897%
Maximum	134.571%
Count	410

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.802%	194	47.32%	8.897%
Negative	-12.746%	216	52.68%	-6.715%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	47.38%
12	1 Year	55.48%
36	3 Years	54.22%
60	5 Years	53.89%
120	10 Years	56.56%
240	20 Years	51.70%
600	50 Years	44.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.56. Further, an Excess Kurtosis of 30.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.82%	0	0.00%	0.00%
-61.82% to -32.95%	0	0.00%	0.00%
-32.95% to -4.09%	0	0.00%	0.00%
-4.09% to 24.77%	37	9.00%	9.00%
24.77% to 53.64%	237	57.66%	66.67%
53.64% to 82.50%	91	22.14%	88.81%
82.50% to 111.37%	27	6.57%	95.38%
111.37% to 140.23%	10	2.43%	97.81%
140.23% to 169.10%	3	0.73%	98.54%
Greater than 169.10%	6	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.15%	92.12%	92.70%	68.27%
±2σ	-23.33%	130.61%	97.32%	95.45%
±3σ	-61.82%	169.10%	98.54%	99.73%

Descriptive Statistics

Mean	53.639%
Standard Error	1.898%
Median	43.957%
Mode	28.004%
Standard Deviation	38.486%
Sample Variance	1481.191%
Kurtosis	30.03
Skewness	4.56
Range	374.619%
Minimum	15.179%
Maximum	389.798%
Count	411

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	53.639%	411	100.00%	53.639%
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 0.44. Further, an Excess Kurtosis of 1.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.32%	0	0.00%	0.00%
-58.32% to -43.00%	4	0.97%	0.97%
-43.00% to -27.67%	25	6.08%	7.06%
-27.67% to -12.34%	57	13.87%	20.92%
-12.34% to 2.99%	129	31.39%	52.31%
2.99% to 18.32%	118	28.71%	81.02%
18.32% to 33.64%	52	12.65%	93.67%
33.64% to 48.97%	15	3.65%	97.32%
48.97% to 64.30%	6	1.46%	98.78%
Greater than 64.30%	5	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.45%	23.42%	72.99%	68.27%
±2σ	-37.89%	43.86%	94.65%	95.45%
±3σ	-58.32%	64.30%	98.78%	99.73%

Descriptive Statistics

Mean	2.987%
Standard Error	1.008%
Median	1.562%
Mode	-13.817%
Standard Deviation	20.437%
Sample Variance	417.670%
Kurtosis	1.24
Skewness	0.44
Range	142.307%
Minimum	-54.801%
Maximum	87.506%
Count	411

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.769%	226	54.99%	9.221%
Negative	-13.849%	185	45.01%	-6.234%
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 1.54. Further, an Excess Kurtosis of 4.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.29%	0	0.00%	0.00%
-85.29% to -62.98%	0	0.00%	0.00%
-62.98% to -40.68%	1	0.73%	0.73%
-40.68% to -18.37%	33	24.09%	24.82%
-18.37% to 3.93%	49	35.77%	60.58%
3.93% to 26.24%	25	18.25%	78.83%
26.24% to 48.54%	18	13.14%	91.97%
48.54% to 70.85%	8	5.84%	97.81%
70.85% to 93.15%	2	1.46%	99.27%
Greater than 93.15%	1	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.81%	33.67%	75.18%	68.27%
±2σ	-55.55%	63.41%	96.35%	95.45%
±3σ	-85.29%	93.15%	99.27%	99.73%

Descriptive Statistics

Mean	3.933%
Standard Error	2.541%
Median	-1.756%
Mode	0.000%
Standard Deviation	29.740%
Sample Variance	884.486%
Kurtosis	4.77
Skewness	1.54
Range	204.831%
Minimum	-43.759%
Maximum	161.072%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.142%	61	44.53%	12.976%
Negative	-16.741%	74	54.02%	-9.043%
Zero	0.000%	2	1.46%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	77.50%
12	3 Years	100.06%
20	5 Years	90.36%
40	10 Years	95.74%
80	20 Years	89.07%
200	50 Years	75.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.58. Further, an Excess Kurtosis of 15.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -114.59%	0	0.00%	0.00%
-114.59% to -61.80%	0	0.00%	0.00%
-61.80% to -9.01%	0	0.00%	0.00%
-9.01% to 43.79%	9	6.52%	6.52%
43.79% to 96.58%	87	63.04%	69.57%
96.58% to 149.38%	29	21.01%	90.58%
149.38% to 202.17%	7	5.07%	95.65%
202.17% to 254.96%	0	0.00%	95.65%
254.96% to 307.76%	1	0.72%	96.38%
Greater than 307.76%	5	3.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	26.19%	166.97%	92.75%	68.27%
±2σ	-44.20%	237.37%	95.65%	95.45%
±3σ	-114.59%	307.76%	96.38%	99.73%

Descriptive Statistics

Mean	96.581%
Standard Error	5.992%
Median	79.316%
Mode	29.235%
Standard Deviation	70.392%
Sample Variance	4955.104%
Kurtosis	15.82
Skewness	3.58
Range	509.554%
Minimum	29.235%
Maximum	538.789%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	96.581%	138	100.00%	96.581%
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 0.28. Further, an Excess Kurtosis of -0.01 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.54%	0	0.00%	0.00%
-74.54% to -54.94%	1	0.72%	0.72%
-54.94% to -35.33%	6	4.35%	5.07%
-35.33% to -15.72%	29	21.01%	26.09%
-15.72% to 3.88%	36	26.09%	52.17%
3.88% to 23.49%	32	23.19%	75.36%
23.49% to 43.10%	25	18.12%	93.48%
43.10% to 62.71%	7	5.07%	98.55%
62.71% to 82.31%	1	0.72%	99.28%
Greater than 82.31%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.26%	30.03%	66.67%	68.27%
±2σ	-48.40%	56.17%	96.38%	95.45%
±3σ	-74.54%	82.31%	99.28%	99.73%

Descriptive Statistics

Mean	3.885%
Standard Error	2.225%
Median	2.651%
Mode	-62.164%
Standard Deviation	26.143%
Sample Variance	683.464%
Kurtosis	-0.01
Skewness	0.28
Range	147.503%
Minimum	-62.164%
Maximum	85.339%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.342%	77	55.80%	12.466%
Negative	-19.413%	61	44.20%	-8.581%
Zero	0.000%	0	0.00%	0.000%

^VIX Deep Analytical Report