^VIX - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	7.12%	6.68%	5.87%	10.79%
Weekly	15.58%	18.08%	12.76%	25.23%
Monthly	21.84%	38.52%	20.46%	53.73%
Quarterly	29.53%	70.51%	26.05%	87.30%
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 1.95. Further, an Excess Kurtosis of 16.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.12%	17	0.20%	0.20%
-21.12% to -15.78%	46	0.54%	0.73%
-15.78% to -10.44%	241	2.80%	3.54%
-10.44% to -5.10%	1187	13.81%	17.35%
-5.10% to 0.24%	3233	37.62%	54.97%
0.24% to 5.58%	2489	28.97%	83.94%
5.58% to 10.92%	891	10.37%	94.31%
10.92% to 16.26%	290	3.37%	97.68%
16.26% to 21.60%	94	1.09%	98.78%
Greater than 21.60%	105	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.88%	7.36%	78.45%	68.27%
±2σ	-14.00%	14.48%	95.76%	95.45%
±3σ	-21.12%	21.60%	98.58%	99.73%

Descriptive Statistics

Mean	0.239%
Standard Error	0.077%
Median	-0.426%
Mode	0.000%
Standard Deviation	7.121%
Sample Variance	50.713%
Kurtosis	16.37
Skewness	1.95
Range	151.352%
Minimum	-35.754%
Maximum	115.598%
Count	8593

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.508%	3995	46.49%	2.561%
Negative	-4.385%	4551	52.96%	-2.322%
Zero	0.000%	47	0.55%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	10.73%
20	1 Month	14.33%
60	1 Quarter	11.19%
250	1 Year	11.85%
750	3 Years	10.63%
1,250	5 Years	10.79%
2,500	10 Years	11.40%
5,000	20 Years	10.48%
12,500	50 Years	9.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.92. Further, an Excess Kurtosis of 89.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.26%	0	0.00%	0.00%
-11.26% to -6.25%	0	0.00%	0.00%
-6.25% to -1.24%	0	0.00%	0.00%
-1.24% to 3.78%	1002	11.66%	11.66%
3.78% to 8.79%	4492	52.27%	63.93%
8.79% to 13.80%	1965	22.86%	86.79%
13.80% to 18.82%	634	7.38%	94.17%
18.82% to 23.83%	279	3.25%	97.42%
23.83% to 28.84%	101	1.18%	98.59%
Greater than 28.84%	121	1.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.11%	15.47%	88.85%	68.27%
±2σ	-4.58%	22.16%	96.68%	95.45%
±3σ	-11.26%	28.84%	98.59%	99.73%

Descriptive Statistics

Mean	8.790%
Standard Error	0.072%
Median	7.184%
Mode	4.000%
Standard Deviation	6.684%
Sample Variance	44.678%
Kurtosis	89.72
Skewness	5.92
Range	179.874%
Minimum	1.144%
Maximum	181.018%
Count	8594

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.790%	8594	100.00%	8.790%
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 -16.98%	67	0.78%	0.78%
-16.98% to -12.58%	136	1.58%	2.36%
-12.58% to -8.18%	314	3.65%	6.02%
-8.18% to -3.78%	990	11.52%	17.54%
-3.78% to 0.62%	2582	30.04%	47.58%
0.62% to 5.03%	2945	34.27%	81.85%
5.03% to 9.43%	1153	13.42%	95.26%
9.43% to 13.83%	300	3.49%	98.75%
13.83% to 18.23%	64	0.74%	99.50%
Greater than 18.23%	43	0.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.25%	6.50%	76.43%	68.27%
±2σ	-11.12%	12.37%	94.82%	95.45%
±3σ	-16.98%	18.23%	98.72%	99.73%

Descriptive Statistics

Mean	0.625%
Standard Error	0.063%
Median	0.899%
Mode	0.000%
Standard Deviation	5.870%
Sample Variance	34.452%
Kurtosis	5.43
Skewness	-0.32
Range	102.225%
Minimum	-50.589%
Maximum	51.636%
Count	8594

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.237%	4963	57.75%	2.447%
Negative	-4.373%	3579	41.65%	-1.821%
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 33.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.73%	1	0.06%	0.06%
-45.73% to -34.05%	2	0.11%	0.17%
-34.05% to -22.36%	46	2.58%	2.75%
-22.36% to -10.68%	235	13.19%	15.95%
-10.68% to 1.01%	710	39.87%	55.81%
1.01% to 12.69%	534	29.98%	85.79%
12.69% to 24.38%	168	9.43%	95.23%
24.38% to 36.06%	49	2.75%	97.98%
36.06% to 47.75%	17	0.95%	98.93%
Greater than 47.75%	19	1.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.57%	16.59%	80.52%	68.27%
±2σ	-30.15%	32.17%	96.69%	95.45%
±3σ	-45.73%	47.75%	98.88%	99.73%

Descriptive Statistics

Mean	1.008%
Standard Error	0.369%
Median	-0.671%
Mode	-24.014%
Standard Deviation	15.580%
Sample Variance	242.725%
Kurtosis	33.05
Skewness	3.45
Range	259.208%
Minimum	-46.305%
Maximum	212.903%
Count	1781

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.599%	852	47.84%	5.549%
Negative	-8.715%	928	52.11%	-4.541%
Zero	0.000%	1	0.06%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	30.73%
12	1 Quarter	21.89%
52	1 Year	28.21%
156	3 Years	25.46%
260	5 Years	25.23%
520	10 Years	26.71%
1,040	20 Years	24.65%
2,600	50 Years	21.85%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.78. Further, an Excess Kurtosis of 85.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.31%	0	0.00%	0.00%
-30.31% to -16.75%	0	0.00%	0.00%
-16.75% to -3.19%	0	0.00%	0.00%
-3.19% to 10.38%	137	7.69%	7.69%
10.38% to 23.94%	1016	57.01%	64.70%
23.94% to 37.50%	421	23.63%	88.33%
37.50% to 51.06%	121	6.79%	95.12%
51.06% to 64.62%	48	2.69%	97.81%
64.62% to 78.18%	17	0.95%	98.77%
Greater than 78.18%	22	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.86%	42.02%	91.19%	68.27%
±2σ	-12.23%	60.10%	96.97%	95.45%
±3σ	-30.31%	78.18%	98.77%	99.73%

Descriptive Statistics

Mean	23.936%
Standard Error	0.428%
Median	19.886%
Mode	13.300%
Standard Deviation	18.081%
Sample Variance	326.911%
Kurtosis	85.15
Skewness	6.78
Range	312.114%
Minimum	6.282%
Maximum	318.396%
Count	1782

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.936%	1782	100.00%	23.936%
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 2.34 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.17%	12	0.67%	0.67%
-37.17% to -27.59%	13	0.73%	1.40%
-27.59% to -18.02%	73	4.10%	5.50%
-18.02% to -8.45%	231	12.96%	18.46%
-8.45% to 1.12%	565	31.71%	50.17%
1.12% to 10.70%	558	31.31%	81.48%
10.70% to 20.27%	220	12.35%	93.83%
20.27% to 29.84%	68	3.82%	97.64%
29.84% to 39.41%	31	1.74%	99.38%
Greater than 39.41%	11	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.64%	13.89%	74.13%	68.27%
±2σ	-24.40%	26.65%	94.44%	95.45%
±3σ	-37.17%	39.41%	98.71%	99.73%

Descriptive Statistics

Mean	1.123%
Standard Error	0.302%
Median	1.042%
Mode	0.000%
Standard Deviation	12.763%
Sample Variance	162.899%
Kurtosis	2.34
Skewness	-0.02
Range	129.856%
Minimum	-67.084%
Maximum	62.772%
Count	1782

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.720%	966	54.21%	5.269%
Negative	-9.099%	812	45.57%	-4.146%
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 1.50. Further, an Excess Kurtosis of 5.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.39%	0	0.00%	0.00%
-63.39% to -47.01%	0	0.00%	0.00%
-47.01% to -30.63%	13	3.18%	3.18%
-30.63% to -14.25%	70	17.11%	20.29%
-14.25% to 2.12%	156	38.14%	58.44%
2.12% to 18.50%	100	24.45%	82.89%
18.50% to 34.88%	38	9.29%	92.18%
34.88% to 51.26%	22	5.38%	97.56%
51.26% to 67.64%	5	1.22%	98.78%
Greater than 67.64%	5	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.71%	23.96%	76.04%	68.27%
±2σ	-41.55%	45.80%	96.33%	95.45%
±3σ	-63.39%	67.63%	98.78%	99.73%

Descriptive Statistics

Mean	2.124%
Standard Error	1.080%
Median	-0.857%
Mode	1.023%
Standard Deviation	21.837%
Sample Variance	476.866%
Kurtosis	5.26
Skewness	1.50
Range	180.468%
Minimum	-45.897%
Maximum	134.571%
Count	409

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.766%	193	47.19%	8.855%
Negative	-12.746%	216	52.81%	-6.731%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	35.65%
12	1 Year	55.56%
36	3 Years	54.20%
60	5 Years	53.73%
120	10 Years	56.35%
240	20 Years	51.54%
600	50 Years	44.74%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -61.97%	0	0.00%	0.00%
-61.97% to -33.08%	0	0.00%	0.00%
-33.08% to -4.19%	0	0.00%	0.00%
-4.19% to 24.70%	36	8.78%	8.78%
24.70% to 53.59%	237	57.80%	66.59%
53.59% to 82.48%	91	22.20%	88.78%
82.48% to 111.37%	27	6.59%	95.37%
111.37% to 140.26%	10	2.44%	97.80%
140.26% to 169.15%	3	0.73%	98.54%
Greater than 169.15%	6	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	15.07%	92.11%	92.68%	68.27%
±2σ	-23.45%	130.63%	97.32%	95.45%
±3σ	-61.97%	169.15%	98.54%	99.73%

Descriptive Statistics

Mean	53.589%
Standard Error	1.902%
Median	43.941%
Mode	28.004%
Standard Deviation	38.520%
Sample Variance	1483.790%
Kurtosis	30.02
Skewness	4.56
Range	374.619%
Minimum	15.179%
Maximum	389.798%
Count	410

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	53.589%	410	100.00%	53.589%
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 1.23 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.39%	0	0.00%	0.00%
-58.39% to -43.04%	4	0.98%	0.98%
-43.04% to -27.70%	25	6.10%	7.07%
-27.70% to -12.35%	57	13.90%	20.98%
-12.35% to 3.00%	128	31.22%	52.20%
3.00% to 18.34%	118	28.78%	80.98%
18.34% to 33.69%	52	12.68%	93.66%
33.69% to 49.03%	15	3.66%	97.32%
49.03% to 64.38%	6	1.46%	98.78%
Greater than 64.38%	5	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.46%	23.46%	72.93%	68.27%
±2σ	-37.93%	43.92%	94.63%	95.45%
±3σ	-58.39%	64.38%	98.78%	99.73%

Descriptive Statistics

Mean	2.996%
Standard Error	1.010%
Median	1.588%
Mode	-13.817%
Standard Deviation	20.461%
Sample Variance	418.634%
Kurtosis	1.23
Skewness	0.44
Range	142.307%
Minimum	-54.801%
Maximum	87.506%
Count	410

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.841%	225	54.88%	9.242%
Negative	-13.842%	185	45.12%	-6.246%
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 1.57. Further, an Excess Kurtosis of 5.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.87%	0	0.00%	0.00%
-84.87% to -62.73%	0	0.00%	0.00%
-62.73% to -40.58%	1	0.73%	0.73%
-40.58% to -18.43%	33	24.09%	24.82%
-18.43% to 3.72%	48	35.04%	59.85%
3.72% to 25.86%	27	19.71%	79.56%
25.86% to 48.01%	17	12.41%	91.97%
48.01% to 70.16%	8	5.84%	97.81%
70.16% to 92.31%	2	1.46%	99.27%
Greater than 92.31%	1	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.81%	33.25%	75.91%	68.27%
±2σ	-55.34%	62.78%	95.62%	95.45%
±3σ	-84.87%	92.31%	99.27%	99.73%

Descriptive Statistics

Mean	3.716%
Standard Error	2.523%
Median	-1.756%
Mode	0.000%
Standard Deviation	29.530%
Sample Variance	872.019%
Kurtosis	5.01
Skewness	1.57
Range	204.831%
Minimum	-43.759%
Maximum	161.072%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.655%	61	44.53%	12.759%
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	62.21%
12	3 Years	94.97%
20	5 Years	87.30%
40	10 Years	94.21%
80	20 Years	88.31%
200	50 Years	75.35%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -115.49%	0	0.00%	0.00%
-115.49% to -62.61%	0	0.00%	0.00%
-62.61% to -9.73%	0	0.00%	0.00%
-9.73% to 43.15%	8	5.80%	5.80%
43.15% to 96.03%	89	64.49%	70.29%
96.03% to 148.91%	28	20.29%	90.58%
148.91% to 201.79%	7	5.07%	95.65%
201.79% to 254.67%	0	0.00%	95.65%
254.67% to 307.55%	1	0.72%	96.38%
Greater than 307.55%	5	3.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	25.53%	166.54%	92.75%	68.27%
±2σ	-44.98%	237.04%	95.65%	95.45%
±3σ	-115.49%	307.55%	96.38%	99.73%

Descriptive Statistics

Mean	96.031%
Standard Error	6.002%
Median	78.970%
Mode	29.235%
Standard Deviation	70.506%
Sample Variance	4971.055%
Kurtosis	15.81
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	96.031%	138	100.00%	96.031%
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 0.27. 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 -74.13%	0	0.00%	0.00%
-74.13% to -54.59%	1	0.72%	0.72%
-54.59% to -35.05%	6	4.35%	5.07%
-35.05% to -15.51%	29	21.01%	26.09%
-15.51% to 4.03%	36	26.09%	52.17%
4.03% to 23.57%	32	23.19%	75.36%
23.57% to 43.11%	25	18.12%	93.48%
43.11% to 62.65%	7	5.07%	98.55%
62.65% to 82.19%	1	0.72%	99.28%
Greater than 82.19%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.03%	30.08%	67.39%	68.27%
±2σ	-48.08%	56.13%	96.38%	95.45%
±3σ	-74.13%	82.19%	99.28%	99.73%

Descriptive Statistics

Mean	4.028%
Standard Error	2.218%
Median	2.651%
Mode	-62.164%
Standard Deviation	26.053%
Sample Variance	678.751%
Kurtosis	0.01
Skewness	0.27
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	-19.090%	61	44.20%	-8.438%
Zero	0.000%	0	0.00%	0.000%

^VIX Deep Analytical Report