^NDX - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	1.63%	1.32%	1.47%	1.75%
Weekly	3.52%	3.29%	3.51%	4.27%
Monthly	6.74%	7.23%	6.93%	9.18%
Quarterly	11.37%	13.37%	11.23%	16.20%
Annual	—	—	—	—
Option Time Horizon	—	—	—	—

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.09. Further, an Excess Kurtosis of 8.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.83%	79	0.77%	0.77%
-4.83% to -3.60%	136	1.33%	2.11%
-3.60% to -2.38%	380	3.73%	5.84%
-2.38% to -1.16%	1055	10.35%	16.18%
-1.16% to 0.07%	3211	31.50%	47.68%
0.07% to 1.29%	3761	36.89%	84.57%
1.29% to 2.51%	1097	10.76%	95.33%
2.51% to 3.74%	303	2.97%	98.30%
3.74% to 4.96%	95	0.93%	99.23%
Greater than 4.96%	78	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.56%	1.70%	78.49%	68.27%
±2σ	-3.20%	3.33%	94.76%	95.45%
±3σ	-4.83%	4.96%	98.46%	99.73%

Descriptive Statistics

Mean	0.066%
Standard Error	0.016%
Median	0.123%
Mode	0.268%
Standard Deviation	1.631%
Sample Variance	2.659%
Kurtosis	8.06
Skewness	0.09
Range	33.849%
Minimum	-15.078%
Maximum	18.771%
Count	10195

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.072%	5594	54.87%	0.588%
Negative	-1.160%	4593	45.05%	-0.523%
Zero	0.000%	8	0.08%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.74%
20	1 Month	1.78%
60	1 Quarter	1.54%
250	1 Year	1.63%
750	3 Years	1.53%
1,250	5 Years	1.75%
2,500	10 Years	1.63%
5,000	20 Years	1.66%
12,500	50 Years	1.89%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.06. Further, an Excess Kurtosis of 18.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.18%	0	0.00%	0.00%
-2.18% to -1.18%	0	0.00%	0.00%
-1.18% to -0.19%	0	0.00%	0.00%
-0.19% to 0.80%	1541	15.11%	15.11%
0.80% to 1.80%	5020	49.23%	64.35%
1.80% to 2.79%	2144	21.03%	85.38%
2.79% to 3.78%	784	7.69%	93.07%
3.78% to 4.78%	357	3.50%	96.57%
4.78% to 5.77%	161	1.58%	98.15%
Greater than 5.77%	189	1.85%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.47%	3.12%	86.59%	68.27%
±2σ	-0.85%	4.45%	95.60%	95.45%
±3σ	-2.18%	5.77%	98.15%	99.73%

Descriptive Statistics

Mean	1.797%
Standard Error	0.013%
Median	1.429%
Mode	0.888%
Standard Deviation	1.325%
Sample Variance	1.755%
Kurtosis	18.30
Skewness	3.06
Range	21.019%
Minimum	0.214%
Maximum	21.233%
Count	10196

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.797%	10196	100.00%	1.797%
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 0.40. Further, an Excess Kurtosis of 9.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.42%	63	0.62%	0.62%
-4.42% to -3.32%	104	1.02%	1.64%
-3.32% to -2.22%	298	2.92%	4.56%
-2.22% to -1.12%	1109	10.88%	15.44%
-1.12% to -0.02%	3846	37.72%	53.16%
-0.02% to 1.08%	3102	30.42%	83.58%
1.08% to 2.18%	1085	10.64%	94.22%
2.18% to 3.28%	366	3.59%	97.81%
3.28% to 4.38%	128	1.26%	99.07%
Greater than 4.38%	95	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.49%	1.44%	78.65%	68.27%
±2σ	-2.96%	2.91%	94.73%	95.45%
±3σ	-4.42%	4.38%	98.45%	99.73%

Descriptive Statistics

Mean	-0.023%
Standard Error	0.015%
Median	-0.101%
Mode	-0.337%
Standard Deviation	1.467%
Sample Variance	2.152%
Kurtosis	9.56
Skewness	0.40
Range	35.199%
Minimum	-17.444%
Maximum	17.755%
Count	10196

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.064%	4676	45.86%	0.488%
Negative	-0.945%	5516	54.10%	-0.511%
Zero	0.000%	4	0.04%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.19. Further, an Excess Kurtosis of 3.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.23%	17	0.81%	0.81%
-10.23% to -7.59%	30	1.42%	2.23%
-7.59% to -4.96%	80	3.79%	6.02%
-4.96% to -2.32%	242	11.46%	17.48%
-2.32% to 0.32%	652	30.89%	48.37%
0.32% to 2.96%	721	34.15%	82.52%
2.96% to 5.59%	266	12.60%	95.12%
5.59% to 8.23%	69	3.27%	98.39%
8.23% to 10.87%	19	0.90%	99.29%
Greater than 10.87%	15	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.20%	3.83%	76.88%	68.27%
±2σ	-6.71%	7.35%	94.32%	95.45%
±3σ	-10.23%	10.87%	98.48%	99.73%

Descriptive Statistics

Mean	0.319%
Standard Error	0.077%
Median	0.450%
Mode	-1.027%
Standard Deviation	3.516%
Sample Variance	12.364%
Kurtosis	3.78
Skewness	-0.19
Range	42.306%
Minimum	-22.029%
Maximum	20.277%
Count	2111

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.502%	1205	57.08%	1.428%
Negative	-2.584%	906	42.92%	-1.109%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.67%
12	1 Quarter	3.22%
52	1 Year	3.90%
156	3 Years	3.72%
260	5 Years	4.27%
520	10 Years	3.96%
1,040	20 Years	3.97%
2,600	50 Years	4.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 9.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.12%	0	0.00%	0.00%
-5.12% to -2.65%	0	0.00%	0.00%
-2.65% to -0.18%	0	0.00%	0.00%
-0.18% to 2.29%	323	15.29%	15.29%
2.29% to 4.75%	1054	49.91%	65.20%
4.75% to 7.22%	428	20.27%	85.46%
7.22% to 9.69%	155	7.34%	92.80%
9.69% to 12.16%	65	3.08%	95.88%
12.16% to 14.62%	46	2.18%	98.06%
Greater than 14.62%	41	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.46%	8.04%	84.94%	68.27%
±2σ	-1.83%	11.33%	94.98%	95.45%
±3σ	-5.12%	14.62%	98.06%	99.73%

Descriptive Statistics

Mean	4.754%
Standard Error	0.072%
Median	3.846%
Mode	2.614%
Standard Deviation	3.290%
Sample Variance	10.824%
Kurtosis	9.43
Skewness	2.52
Range	29.620%
Minimum	0.699%
Maximum	30.319%
Count	2112

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.754%	2112	100.00%	4.754%
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 0.93. Further, an Excess Kurtosis of 5.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.67%	8	0.38%	0.38%
-10.67% to -8.04%	18	0.85%	1.23%
-8.04% to -5.41%	64	3.03%	4.26%
-5.41% to -2.78%	281	13.30%	17.57%
-2.78% to -0.15%	779	36.88%	54.45%
-0.15% to 2.48%	599	28.36%	82.81%
2.48% to 5.11%	233	11.03%	93.84%
5.11% to 7.74%	75	3.55%	97.40%
7.74% to 10.37%	33	1.56%	98.96%
Greater than 10.37%	22	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.66%	3.35%	77.04%	68.27%
±2σ	-7.16%	6.86%	94.79%	95.45%
±3σ	-10.67%	10.37%	98.58%	99.73%

Descriptive Statistics

Mean	-0.152%
Standard Error	0.076%
Median	-0.403%
Mode	-0.400%
Standard Deviation	3.506%
Sample Variance	12.290%
Kurtosis	5.53
Skewness	0.93
Range	45.111%
Minimum	-16.859%
Maximum	28.252%
Count	2112

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.707%	911	43.13%	1.168%
Negative	-2.321%	1201	56.87%	-1.320%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.37. Further, an Excess Kurtosis of 1.76 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.89%	4	0.82%	0.82%
-18.89% to -13.83%	5	1.03%	1.86%
-13.83% to -8.77%	22	4.54%	6.39%
-8.77% to -3.72%	58	11.96%	18.35%
-3.72% to 1.34%	138	28.45%	46.80%
1.34% to 6.39%	175	36.08%	82.89%
6.39% to 11.45%	56	11.55%	94.43%
11.45% to 16.50%	18	3.71%	98.14%
16.50% to 21.56%	8	1.65%	99.79%
Greater than 21.56%	1	0.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.40%	8.08%	73.81%	68.27%
±2σ	-12.14%	14.82%	94.02%	95.45%
±3σ	-18.88%	21.56%	98.97%	99.73%

Descriptive Statistics

Mean	1.338%
Standard Error	0.306%
Median	1.843%
Mode	-2.979%
Standard Deviation	6.741%
Sample Variance	45.446%
Kurtosis	1.76
Skewness	-0.37
Range	51.956%
Minimum	-26.975%
Maximum	24.981%
Count	485

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.363%	296	61.03%	3.273%
Negative	-4.965%	189	38.97%	-1.935%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	5.42%
12	1 Year	7.54%
36	3 Years	7.90%
60	5 Years	9.18%
120	10 Years	8.67%
240	20 Years	8.55%
600	50 Years	10.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.74. Further, an Excess Kurtosis of 12.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.90%	0	0.00%	0.00%
-10.90% to -5.47%	0	0.00%	0.00%
-5.47% to -0.05%	0	0.00%	0.00%
-0.05% to 5.37%	78	16.05%	16.05%
5.37% to 10.79%	241	49.59%	65.64%
10.79% to 16.21%	85	17.49%	83.13%
16.21% to 21.64%	49	10.08%	93.21%
21.64% to 27.06%	17	3.50%	96.71%
27.06% to 32.48%	2	0.41%	97.12%
Greater than 32.48%	14	2.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.56%	18.02%	86.63%	68.27%
±2σ	-3.67%	25.25%	95.88%	95.45%
±3σ	-10.90%	32.48%	97.12%	99.73%

Descriptive Statistics

Mean	10.791%
Standard Error	0.328%
Median	8.607%
Mode	6.754%
Standard Deviation	7.229%
Sample Variance	52.258%
Kurtosis	12.33
Skewness	2.74
Range	67.104%
Minimum	2.425%
Maximum	69.529%
Count	486

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.791%	486	100.00%	10.791%
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 1.14. Further, an Excess Kurtosis of 4.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.57%	0	0.00%	0.00%
-21.57% to -16.37%	1	0.21%	0.21%
-16.37% to -11.17%	20	4.12%	4.32%
-11.17% to -5.97%	64	13.17%	17.49%
-5.97% to -0.78%	186	38.27%	55.76%
-0.78% to 4.42%	127	26.13%	81.89%
4.42% to 9.62%	52	10.70%	92.59%
9.62% to 14.82%	23	4.73%	97.33%
14.82% to 20.02%	8	1.65%	98.97%
Greater than 20.02%	5	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.71%	6.16%	75.72%	68.27%
±2σ	-14.64%	13.09%	94.44%	95.45%
±3σ	-21.57%	20.02%	98.97%	99.73%

Descriptive Statistics

Mean	-0.775%
Standard Error	0.314%
Median	-1.599%
Mode	-7.826%
Standard Deviation	6.932%
Sample Variance	48.058%
Kurtosis	4.02
Skewness	1.14
Range	56.837%
Minimum	-19.898%
Maximum	36.939%
Count	486

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.532%	191	39.30%	2.174%
Negative	-4.859%	295	60.70%	-2.949%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.07. Further, an Excess Kurtosis of 2.31 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.12%	0	0.00%	0.00%
-30.12% to -21.59%	5	3.09%	3.09%
-21.59% to -13.07%	5	3.09%	6.17%
-13.07% to -4.54%	22	13.58%	19.75%
-4.54% to 3.99%	45	27.78%	47.53%
3.99% to 12.51%	52	32.10%	79.63%
12.51% to 21.04%	26	16.05%	95.68%
21.04% to 29.57%	4	2.47%	98.15%
29.57% to 38.09%	2	1.23%	99.38%
Greater than 38.09%	1	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.38%	15.36%	72.84%	68.27%
±2σ	-18.75%	26.72%	93.83%	95.45%
±3σ	-30.12%	38.09%	99.38%	99.73%

Descriptive Statistics

Mean	3.986%
Standard Error	0.893%
Median	4.502%
Mode	-28.455%
Standard Deviation	11.369%
Sample Variance	129.258%
Kurtosis	2.31
Skewness	0.07
Range	80.341%
Minimum	-28.455%
Maximum	51.886%
Count	162

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.516%	112	69.14%	6.579%
Negative	-8.401%	50	30.86%	-2.593%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	13.13%
12	3 Years	15.94%
20	5 Years	16.20%
40	10 Years	15.56%
80	20 Years	15.41%
200	50 Years	17.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 8.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.86%	0	0.00%	0.00%
-19.86% to -9.84%	0	0.00%	0.00%
-9.84% to 0.19%	0	0.00%	0.00%
0.19% to 10.21%	21	12.88%	12.88%
10.21% to 20.23%	88	53.99%	66.87%
20.23% to 30.26%	30	18.40%	85.28%
30.26% to 40.28%	12	7.36%	92.64%
40.28% to 50.31%	4	2.45%	95.09%
50.31% to 60.33%	3	1.84%	96.93%
Greater than 60.33%	5	3.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.87%	33.60%	87.73%	68.27%
±2σ	-6.50%	46.97%	94.48%	95.45%
±3σ	-19.86%	60.33%	96.93%	99.73%

Descriptive Statistics

Mean	20.235%
Standard Error	1.047%
Median	16.270%
Mode	22.320%
Standard Deviation	13.366%
Sample Variance	178.662%
Kurtosis	8.28
Skewness	2.52
Range	89.353%
Minimum	5.482%
Maximum	94.835%
Count	163

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.235%	163	100.00%	20.235%
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 1.11. Further, an Excess Kurtosis of 2.72 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.27%	0	0.00%	0.00%
-36.27% to -27.85%	1	0.61%	0.61%
-27.85% to -19.42%	3	1.84%	2.45%
-19.42% to -11.00%	28	17.18%	19.63%
-11.00% to -2.58%	66	40.49%	60.12%
-2.58% to 5.85%	37	22.70%	82.82%
5.85% to 14.27%	18	11.04%	93.87%
14.27% to 22.70%	3	1.84%	95.71%
22.70% to 31.12%	4	2.45%	98.16%
Greater than 31.12%	3	1.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.81%	8.66%	77.30%	68.27%
±2σ	-25.04%	19.89%	92.64%	95.45%
±3σ	-36.27%	31.12%	98.16%	99.73%

Descriptive Statistics

Mean	-2.575%
Standard Error	0.880%
Median	-4.249%
Mode	-34.161%
Standard Deviation	11.233%
Sample Variance	126.177%
Kurtosis	2.72
Skewness	1.11
Range	73.570%
Minimum	-34.161%
Maximum	39.409%
Count	163

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.016%	50	30.68%	3.072%
Negative	-8.146%	113	69.33%	-5.647%
Zero	0.000%	0	0.00%	0.000%

^NDX Deep Analytical Report