^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%	1.33%	1.47%	1.76%
Weekly	3.52%	3.29%	3.51%	4.30%
Monthly	6.75%	7.23%	6.94%	9.22%
Quarterly	11.36%	13.38%	11.22%	16.07%
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	0.78%	0.78%
-4.83% to -3.61%	136	1.34%	2.11%
-3.61% to -2.38%	379	3.73%	5.84%
-2.38% to -1.16%	1049	10.31%	16.15%
-1.16% to 0.07%	3205	31.50%	47.65%
0.07% to 1.29%	3758	36.94%	84.59%
1.29% to 2.51%	1092	10.73%	95.32%
2.51% to 3.74%	303	2.98%	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	-1.57%	1.70%	78.48%	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	0.124%
Mode	0.268%
Standard Deviation	1.632%
Sample Variance	2.662%
Kurtosis	8.06
Skewness	0.09
Range	33.849%
Minimum	-15.078%
Maximum	18.771%
Count	10174

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.073%	5585	54.90%	0.589%
Negative	-1.160%	4581	45.03%	-0.522%
Zero	0.000%	8	0.08%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.50%
20	1 Month	1.67%
60	1 Quarter	1.39%
250	1 Year	1.69%
750	3 Years	1.54%
1,250	5 Years	1.76%
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 18.27 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 -1.19%	0	0.00%	0.00%
-1.19% to -0.19%	0	0.00%	0.00%
-0.19% to 0.80%	1534	15.08%	15.08%
0.80% to 1.80%	5012	49.26%	64.33%
1.80% to 2.79%	2140	21.03%	85.37%
2.79% to 3.79%	782	7.69%	93.05%
3.79% to 4.78%	358	3.52%	96.57%
4.78% to 5.78%	160	1.57%	98.14%
Greater than 5.78%	189	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.47%	3.12%	86.60%	68.27%
±2σ	-0.86%	4.45%	95.60%	95.45%
±3σ	-2.18%	5.78%	98.15%	99.73%

Descriptive Statistics

Mean	1.797%
Standard Error	0.013%
Median	1.428%
Mode	0.888%
Standard Deviation	1.326%
Sample Variance	1.758%
Kurtosis	18.27
Skewness	3.06
Range	21.019%
Minimum	0.214%
Maximum	21.233%
Count	10175

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.797%	10175	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 9.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.43%	63	0.62%	0.62%
-4.43% to -3.33%	104	1.02%	1.64%
-3.33% to -2.23%	298	2.93%	4.57%
-2.23% to -1.12%	1104	10.85%	15.42%
-1.12% to -0.02%	3840	37.74%	53.16%
-0.02% to 1.08%	3097	30.44%	83.60%
1.08% to 2.18%	1080	10.61%	94.21%
2.18% to 3.28%	366	3.60%	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%	1.45%	78.65%	68.27%
±2σ	-2.96%	2.91%	94.73%	95.45%
±3σ	-4.43%	4.38%	98.45%	99.73%

Descriptive Statistics

Mean	-0.023%
Standard Error	0.015%
Median	-0.101%
Mode	-0.337%
Standard Deviation	1.468%
Sample Variance	2.155%
Kurtosis	9.55
Skewness	0.40
Range	35.199%
Minimum	-17.444%
Maximum	17.755%
Count	10175

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.064%	4666	45.86%	0.488%
Negative	-0.945%	5505	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 3.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.24%	17	0.81%	0.81%
-10.24% to -7.60%	30	1.42%	2.23%
-7.60% to -4.96%	80	3.80%	6.03%
-4.96% to -2.32%	242	11.49%	17.51%
-2.32% to 0.32%	648	30.75%	48.27%
0.32% to 2.96%	723	34.31%	82.58%
2.96% to 5.60%	264	12.53%	95.11%
5.60% to 8.24%	69	3.27%	98.39%
8.24% to 10.88%	19	0.90%	99.29%
Greater than 10.88%	15	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.20%	3.84%	76.93%	68.27%
±2σ	-6.72%	7.36%	94.30%	95.45%
±3σ	-10.24%	10.88%	98.48%	99.73%

Descriptive Statistics

Mean	0.321%
Standard Error	0.077%
Median	0.454%
Mode	-1.027%
Standard Deviation	3.519%
Sample Variance	12.384%
Kurtosis	3.77
Skewness	-0.19
Range	42.306%
Minimum	-22.029%
Maximum	20.277%
Count	2107

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.502%	1205	57.19%	1.431%
Negative	-2.592%	902	42.81%	-1.110%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.62%
12	1 Quarter	2.83%
52	1 Year	4.01%
156	3 Years	3.75%
260	5 Years	4.30%
520	10 Years	3.95%
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 2.51. Further, an Excess Kurtosis of 9.41 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	15.32%	15.32%
2.29% to 4.76%	1051	49.86%	65.18%
4.76% to 7.23%	428	20.30%	85.48%
7.23% to 9.70%	154	7.31%	92.79%
9.70% to 12.16%	65	3.08%	95.87%
12.16% to 14.63%	46	2.18%	98.06%
Greater than 14.63%	41	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.46%	8.05%	84.96%	68.27%
±2σ	-1.83%	11.34%	94.97%	95.45%
±3σ	-5.12%	14.64%	98.06%	99.73%

Descriptive Statistics

Mean	4.756%
Standard Error	0.072%
Median	3.847%
Mode	2.614%
Standard Deviation	3.293%
Sample Variance	10.842%
Kurtosis	9.41
Skewness	2.51
Range	29.620%
Minimum	0.699%
Maximum	30.319%
Count	2108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.756%	2108	100.00%	4.756%
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 5.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.68%	8	0.38%	0.38%
-10.68% to -8.05%	18	0.85%	1.23%
-8.05% to -5.42%	64	3.04%	4.27%
-5.42% to -2.79%	280	13.28%	17.55%
-2.79% to -0.15%	778	36.91%	54.46%
-0.15% to 2.48%	597	28.32%	82.78%
2.48% to 5.11%	233	11.05%	93.83%
5.11% to 7.74%	76	3.61%	97.44%
7.74% to 10.37%	32	1.52%	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%	76.99%	68.27%
±2σ	-7.17%	6.86%	94.78%	95.45%
±3σ	-10.68%	10.37%	98.58%	99.73%

Descriptive Statistics

Mean	-0.154%
Standard Error	0.076%
Median	-0.403%
Mode	-0.400%
Standard Deviation	3.508%
Sample Variance	12.309%
Kurtosis	5.52
Skewness	0.93
Range	45.111%
Minimum	-16.859%
Maximum	28.252%
Count	2108

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.709%	909	43.12%	1.168%
Negative	-2.324%	1199	56.88%	-1.322%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.38. 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	0.83%	0.83%
-18.89% to -13.83%	5	1.03%	1.86%
-13.83% to -8.77%	22	4.55%	6.40%
-8.77% to -3.71%	59	12.19%	18.60%
-3.71% to 1.35%	136	28.10%	46.69%
1.35% to 6.41%	175	36.16%	82.85%
6.41% to 11.46%	56	11.57%	94.42%
11.46% to 16.52%	18	3.72%	98.14%
16.52% to 21.58%	8	1.65%	99.79%
Greater than 21.58%	1	0.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.40%	8.09%	73.76%	68.27%
±2σ	-12.14%	14.84%	94.01%	95.45%
±3σ	-18.89%	21.58%	98.97%	99.73%

Descriptive Statistics

Mean	1.347%
Standard Error	0.307%
Median	1.846%
Mode	-2.979%
Standard Deviation	6.745%
Sample Variance	45.499%
Kurtosis	1.76
Skewness	-0.38
Range	51.956%
Minimum	-26.975%
Maximum	24.981%
Count	484

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.363%	296	61.16%	3.280%
Negative	-4.975%	188	38.84%	-1.932%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	5.05%
12	1 Year	7.96%
36	3 Years	8.08%
60	5 Years	9.22%
120	10 Years	8.68%
240	20 Years	8.55%
600	50 Years	10.05%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.73. Further, an Excess Kurtosis of 12.31 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 5.38%	78	16.08%	16.08%
5.38% to 10.80%	240	49.48%	65.57%
10.80% to 16.23%	85	17.53%	83.09%
16.23% to 21.65%	49	10.10%	93.20%
21.65% to 27.07%	17	3.51%	96.70%
27.07% to 32.50%	2	0.41%	97.11%
Greater than 32.50%	14	2.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.57%	18.03%	86.39%	68.27%
±2σ	-3.66%	25.27%	95.88%	95.45%
±3σ	-10.90%	32.50%	97.11%	99.73%

Descriptive Statistics

Mean	10.801%
Standard Error	0.328%
Median	8.613%
Mode	6.754%
Standard Deviation	7.233%
Sample Variance	52.318%
Kurtosis	12.31
Skewness	2.73
Range	67.104%
Minimum	2.425%
Maximum	69.529%
Count	485

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.801%	485	100.00%	10.801%
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 4.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.60%	0	0.00%	0.00%
-21.60% to -16.39%	1	0.21%	0.21%
-16.39% to -11.19%	20	4.12%	4.33%
-11.19% to -5.98%	64	13.20%	17.53%
-5.98% to -0.78%	186	38.35%	55.88%
-0.78% to 4.42%	126	25.98%	81.86%
4.42% to 9.63%	52	10.72%	92.58%
9.63% to 14.83%	23	4.74%	97.32%
14.83% to 20.04%	8	1.65%	98.97%
Greater than 20.04%	5	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.72%	6.16%	75.67%	68.27%
±2σ	-14.66%	13.10%	94.43%	95.45%
±3σ	-21.60%	20.04%	98.97%	99.73%

Descriptive Statistics

Mean	-0.780%
Standard Error	0.315%
Median	-1.609%
Mode	-7.826%
Standard Deviation	6.939%
Sample Variance	48.144%
Kurtosis	4.01
Skewness	1.14
Range	56.837%
Minimum	-19.898%
Maximum	36.939%
Count	485

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.552%	190	39.17%	2.175%
Negative	-4.859%	295	60.83%	-2.955%
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 2.33 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.06%	0	0.00%	0.00%
-30.06% to -21.55%	5	3.09%	3.09%
-21.55% to -13.03%	5	3.09%	6.17%
-13.03% to -4.51%	21	12.96%	19.14%
-4.51% to 4.00%	46	28.40%	47.53%
4.00% to 12.52%	53	32.72%	80.25%
12.52% to 21.04%	25	15.43%	95.68%
21.04% to 29.56%	4	2.47%	98.15%
29.56% to 38.07%	2	1.23%	99.38%
Greater than 38.07%	1	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.35%	15.36%	72.84%	68.27%
±2σ	-18.71%	26.72%	93.83%	95.45%
±3σ	-30.06%	38.07%	99.38%	99.73%

Descriptive Statistics

Mean	4.005%
Standard Error	0.892%
Median	4.502%
Mode	-28.455%
Standard Deviation	11.356%
Sample Variance	128.964%
Kurtosis	2.33
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	-8.339%	50	30.86%	-2.574%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	12.52%
12	3 Years	15.73%
20	5 Years	16.07%
40	10 Years	15.50%
80	20 Years	15.38%
200	50 Years	17.90%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.51. Further, an Excess Kurtosis of 8.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.93%	0	0.00%	0.00%
-19.93% to -9.89%	0	0.00%	0.00%
-9.89% to 0.14%	0	0.00%	0.00%
0.14% to 10.18%	21	12.88%	12.88%
10.18% to 20.22%	87	53.37%	66.26%
20.22% to 30.25%	31	19.02%	85.28%
30.25% to 40.29%	13	7.98%	93.25%
40.29% to 50.33%	3	1.84%	95.09%
50.33% to 60.37%	3	1.84%	96.93%
Greater than 60.37%	5	3.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.83%	33.60%	87.12%	68.27%
±2σ	-6.55%	46.98%	94.48%	95.45%
±3σ	-19.93%	60.37%	96.93%	99.73%

Descriptive Statistics

Mean	20.217%
Standard Error	1.048%
Median	16.270%
Mode	22.320%
Standard Deviation	13.383%
Sample Variance	179.107%
Kurtosis	8.24
Skewness	2.51
Range	89.353%
Minimum	5.482%
Maximum	94.835%
Count	163

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.217%	163	100.00%	20.217%
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 2.75 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.26%	0	0.00%	0.00%
-36.26% to -27.84%	1	0.61%	0.61%
-27.84% to -19.43%	3	1.84%	2.45%
-19.43% to -11.01%	28	17.18%	19.63%
-11.01% to -2.60%	64	39.26%	58.90%
-2.60% to 5.82%	39	23.93%	82.82%
5.82% to 14.24%	18	11.04%	93.87%
14.24% to 22.65%	3	1.84%	95.71%
22.65% to 31.07%	4	2.45%	98.16%
Greater than 31.07%	3	1.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.82%	8.63%	77.30%	68.27%
±2σ	-25.04%	19.85%	92.64%	95.45%
±3σ	-36.26%	31.07%	98.16%	99.73%

Descriptive Statistics

Mean	-2.595%
Standard Error	0.879%
Median	-4.249%
Mode	-34.161%
Standard Deviation	11.222%
Sample Variance	125.925%
Kurtosis	2.75
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	9.949%	50	30.68%	3.052%
Negative	-8.146%	113	69.33%	-5.647%
Zero	0.000%	0	0.00%	0.000%

^NDX Deep Analytical Report