^DJI - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	1.09%	0.92%	1.02%	1.22%
Weekly	2.36%	2.24%	2.36%	2.88%
Monthly	4.18%	4.69%	4.26%	6.27%
Quarterly	6.42%	7.88%	6.39%	10.54%
Annual	—	—	—	—
Option Time Horizon	—	—	—	—

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.14. Further, an Excess Kurtosis of 12.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.25%	67	0.78%	0.78%
-3.25% to -2.43%	94	1.09%	1.87%
-2.43% to -1.61%	286	3.32%	5.19%
-1.61% to -0.78%	886	10.29%	15.47%
-0.78% to 0.04%	2866	33.27%	48.75%
0.04% to 0.86%	3069	35.63%	84.37%
0.86% to 1.68%	977	11.34%	95.72%
1.68% to 2.50%	241	2.80%	98.51%
2.50% to 3.32%	73	0.85%	99.36%
Greater than 3.32%	55	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.06%	1.13%	78.99%	68.27%
±2σ	-2.15%	2.23%	95.41%	95.45%
±3σ	-3.25%	3.32%	98.58%	99.73%

Descriptive Statistics

Mean	0.037%
Standard Error	0.012%
Median	0.055%
Mode	-0.003%
Standard Deviation	1.095%
Sample Variance	1.200%
Kurtosis	12.73
Skewness	-0.14
Range	24.292%
Minimum	-12.927%
Maximum	11.365%
Count	8614

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.718%	4598	53.38%	0.383%
Negative	-0.745%	4004	46.48%	-0.346%
Zero	0.000%	12	0.14%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.34%
20	1 Month	1.55%
60	1 Quarter	1.26%
250	1 Year	1.28%
750	3 Years	1.09%
1,250	5 Years	1.22%
2,500	10 Years	1.22%
5,000	20 Years	1.29%
12,500	50 Years	1.28%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.57. Further, an Excess Kurtosis of 22.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.50%	0	0.00%	0.00%
-1.50% to -0.81%	0	0.00%	0.00%
-0.81% to -0.12%	0	0.00%	0.00%
-0.12% to 0.57%	1219	14.15%	14.15%
0.57% to 1.26%	4292	49.82%	63.97%
1.26% to 1.95%	1905	22.11%	86.08%
1.95% to 2.63%	686	7.96%	94.05%
2.63% to 3.32%	271	3.15%	97.19%
3.32% to 4.01%	92	1.07%	98.26%
Greater than 4.01%	150	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.34%	2.17%	87.74%	68.27%
±2σ	-0.58%	3.09%	96.46%	95.45%
±3σ	-1.50%	4.01%	98.27%	99.73%

Descriptive Statistics

Mean	1.256%
Standard Error	0.010%
Median	1.028%
Mode	0.898%
Standard Deviation	0.918%
Sample Variance	0.842%
Kurtosis	22.95
Skewness	3.57
Range	12.757%
Minimum	0.167%
Maximum	12.924%
Count	8615

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.256%	8615	100.00%	1.256%
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 0.30. Further, an Excess Kurtosis of 8.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.09%	58	0.67%	0.67%
-3.09% to -2.33%	68	0.79%	1.46%
-2.33% to -1.56%	252	2.93%	4.39%
-1.56% to -0.79%	982	11.40%	15.79%
-0.79% to -0.02%	3132	36.36%	52.14%
-0.02% to 0.74%	2754	31.97%	84.11%
0.74% to 1.51%	886	10.28%	94.39%
1.51% to 2.28%	309	3.59%	97.98%
2.28% to 3.04%	95	1.10%	99.08%
Greater than 3.04%	79	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.05%	1.00%	78.44%	68.27%
±2σ	-2.07%	2.02%	95.11%	95.45%
±3σ	-3.09%	3.04%	98.41%	99.73%

Descriptive Statistics

Mean	-0.024%
Standard Error	0.011%
Median	-0.055%
Mode	0.050%
Standard Deviation	1.023%
Sample Variance	1.046%
Kurtosis	8.69
Skewness	0.30
Range	18.295%
Minimum	-9.855%
Maximum	8.440%
Count	8615

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.718%	4004	46.48%	0.334%
Negative	-0.670%	4599	53.38%	-0.358%
Zero	0.000%	12	0.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.06. Further, an Excess Kurtosis of 7.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.91%	17	0.95%	0.95%
-6.91% to -5.14%	17	0.95%	1.90%
-5.14% to -3.37%	62	3.47%	5.38%
-3.37% to -1.59%	199	11.15%	16.53%
-1.59% to 0.18%	565	31.65%	48.18%
0.18% to 1.95%	625	35.01%	83.19%
1.95% to 3.72%	221	12.38%	95.57%
3.72% to 5.49%	54	3.03%	98.60%
5.49% to 7.27%	12	0.67%	99.27%
Greater than 7.27%	13	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.19%	2.54%	77.14%	68.27%
±2σ	-4.55%	4.90%	95.41%	95.45%
±3σ	-6.91%	7.27%	98.32%	99.73%

Descriptive Statistics

Mean	0.177%
Standard Error	0.056%
Median	0.231%
Mode	-1.664%
Standard Deviation	2.363%
Sample Variance	5.583%
Kurtosis	7.15
Skewness	-0.06
Range	35.448%
Minimum	-15.356%
Maximum	20.092%
Count	1785

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.639%	994	55.69%	0.913%
Negative	-1.663%	790	44.26%	-0.736%
Zero	0.000%	1	0.06%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.91%
12	1 Quarter	2.85%
52	1 Year	3.01%
156	3 Years	2.57%
260	5 Years	2.88%
520	10 Years	2.93%
1,040	20 Years	3.08%
2,600	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 3.48. Further, an Excess Kurtosis of 21.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.58%	0	0.00%	0.00%
-3.58% to -1.90%	0	0.00%	0.00%
-1.90% to -0.22%	0	0.00%	0.00%
-0.22% to 1.46%	234	13.10%	13.10%
1.46% to 3.14%	911	51.01%	64.11%
3.14% to 4.82%	403	22.56%	86.67%
4.82% to 6.50%	132	7.39%	94.06%
6.50% to 8.18%	51	2.86%	96.92%
8.18% to 9.86%	17	0.95%	97.87%
Greater than 9.86%	38	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.90%	5.38%	88.69%	68.27%
±2σ	-1.34%	7.62%	96.14%	95.45%
±3σ	-3.58%	9.86%	97.87%	99.73%

Descriptive Statistics

Mean	3.137%
Standard Error	0.053%
Median	2.540%
Mode	1.712%
Standard Deviation	2.240%
Sample Variance	5.018%
Kurtosis	21.41
Skewness	3.48
Range	27.907%
Minimum	0.530%
Maximum	28.437%
Count	1786

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.137%	1786	100.00%	3.137%
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 1.00. Further, an Excess Kurtosis of 7.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.18%	8	0.45%	0.45%
-7.18% to -5.41%	15	0.84%	1.29%
-5.41% to -3.64%	50	2.80%	4.09%
-3.64% to -1.88%	235	13.16%	17.25%
-1.88% to -0.11%	637	35.67%	52.91%
-0.11% to 1.66%	552	30.91%	83.82%
1.66% to 3.42%	192	10.75%	94.57%
3.42% to 5.19%	60	3.36%	97.93%
5.19% to 6.96%	18	1.01%	98.94%
Greater than 6.96%	19	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.46%	2.25%	77.49%	68.27%
±2σ	-4.82%	4.60%	95.41%	95.45%
±3σ	-7.18%	6.96%	98.49%	99.73%

Descriptive Statistics

Mean	-0.109%
Standard Error	0.056%
Median	-0.211%
Mode	-0.104%
Standard Deviation	2.356%
Sample Variance	5.551%
Kurtosis	7.98
Skewness	1.00
Range	33.367%
Minimum	-12.244%
Maximum	21.123%
Count	1786

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.727%	788	44.12%	0.762%
Negative	-1.558%	998	55.88%	-0.871%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.46. Further, an Excess Kurtosis of 1.21 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.80%	4	0.98%	0.98%
-11.80% to -8.67%	6	1.46%	2.44%
-8.67% to -5.53%	15	3.66%	6.10%
-5.53% to -2.40%	54	13.17%	19.27%
-2.40% to 0.74%	109	26.59%	45.85%
0.74% to 3.87%	140	34.15%	80.00%
3.87% to 7.00%	57	13.90%	93.90%
7.00% to 10.14%	20	4.88%	98.78%
10.14% to 13.27%	4	0.98%	99.76%
Greater than 13.27%	1	0.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.44%	4.92%	70.73%	68.27%
±2σ	-7.62%	9.09%	95.37%	95.45%
±3σ	-11.80%	13.27%	98.78%	99.73%

Descriptive Statistics

Mean	0.736%
Standard Error	0.206%
Median	1.071%
Mode	-5.074%
Standard Deviation	4.179%
Sample Variance	17.461%
Kurtosis	1.21
Skewness	-0.46
Range	29.083%
Minimum	-15.132%
Maximum	13.951%
Count	410

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.155%	260	63.41%	2.001%
Negative	-3.456%	150	36.59%	-1.264%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	5.01%
12	1 Year	5.54%
36	3 Years	5.50%
60	5 Years	6.27%
120	10 Years	6.57%
240	20 Years	6.65%
600	50 Years	6.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.63. Further, an Excess Kurtosis of 21.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.07%	0	0.00%	0.00%
-7.07% to -3.56%	0	0.00%	0.00%
-3.56% to -0.04%	0	0.00%	0.00%
-0.04% to 3.47%	48	11.68%	11.68%
3.47% to 6.99%	229	55.72%	67.40%
6.99% to 10.50%	75	18.25%	85.64%
10.50% to 14.02%	31	7.54%	93.19%
14.02% to 17.53%	14	3.41%	96.59%
17.53% to 21.05%	8	1.95%	98.54%
Greater than 21.05%	6	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.30%	11.67%	88.56%	68.27%
±2σ	-2.39%	16.36%	96.11%	95.45%
±3σ	-7.07%	21.05%	98.54%	99.73%

Descriptive Statistics

Mean	6.987%
Standard Error	0.231%
Median	5.755%
Mode	3.057%
Standard Deviation	4.687%
Sample Variance	21.968%
Kurtosis	21.79
Skewness	3.63
Range	46.977%
Minimum	1.825%
Maximum	48.802%
Count	411

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.987%	411	100.00%	6.987%
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 0.85. Further, an Excess Kurtosis of 2.17 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.32%	0	0.00%	0.00%
-13.32% to -10.13%	2	0.49%	0.49%
-10.13% to -6.93%	16	3.89%	4.38%
-6.93% to -3.74%	62	15.09%	19.46%
-3.74% to -0.54%	152	36.98%	56.45%
-0.54% to 2.65%	102	24.82%	81.27%
2.65% to 5.84%	51	12.41%	93.67%
5.84% to 9.04%	15	3.65%	97.32%
9.04% to 12.23%	5	1.22%	98.54%
Greater than 12.23%	6	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.80%	3.72%	72.26%	68.27%
±2σ	-9.06%	7.97%	95.62%	95.45%
±3σ	-13.32%	12.23%	98.54%	99.73%

Descriptive Statistics

Mean	-0.544%
Standard Error	0.210%
Median	-1.052%
Mode	-3.793%
Standard Deviation	4.259%
Sample Variance	18.143%
Kurtosis	2.17
Skewness	0.85
Range	30.639%
Minimum	-12.809%
Maximum	17.830%
Count	411

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.639%	153	37.23%	1.355%
Negative	-3.024%	258	62.77%	-1.898%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.41. Further, an Excess Kurtosis of 0.60 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.09%	1	0.73%	0.73%
-17.09% to -12.28%	3	2.19%	2.92%
-12.28% to -7.47%	6	4.38%	7.30%
-7.47% to -2.65%	12	8.76%	16.06%
-2.65% to 2.16%	42	30.66%	46.72%
2.16% to 6.97%	45	32.85%	79.56%
6.97% to 11.78%	17	12.41%	91.97%
11.78% to 16.59%	10	7.30%	99.27%
16.59% to 21.41%	1	0.73%	100.00%
Greater than 21.41%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.26%	8.57%	73.72%	68.27%
±2σ	-10.68%	14.99%	93.43%	95.45%
±3σ	-17.09%	21.41%	99.27%	99.73%

Descriptive Statistics

Mean	2.157%
Standard Error	0.548%
Median	2.795%
Mode	-18.044%
Standard Deviation	6.416%
Sample Variance	41.165%
Kurtosis	0.60
Skewness	-0.41
Range	35.359%
Minimum	-18.044%
Maximum	17.315%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.805%	88	64.23%	3.729%
Negative	-4.395%	49	35.77%	-1.572%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	10.02%
12	3 Years	10.80%
20	5 Years	10.54%
40	10 Years	11.46%
80	20 Years	11.51%
200	50 Years	11.33%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.23. Further, an Excess Kurtosis of 15.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.30%	0	0.00%	0.00%
-11.30% to -5.39%	0	0.00%	0.00%
-5.39% to 0.52%	0	0.00%	0.00%
0.52% to 6.43%	19	13.77%	13.77%
6.43% to 12.34%	73	52.90%	66.67%
12.34% to 18.25%	28	20.29%	86.96%
18.25% to 24.16%	11	7.97%	94.93%
24.16% to 30.07%	3	2.17%	97.10%
30.07% to 35.98%	1	0.72%	97.83%
Greater than 35.98%	3	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.46%	20.22%	89.86%	68.27%
±2σ	-3.42%	28.10%	95.65%	95.45%
±3σ	-11.30%	35.98%	97.83%	99.73%

Descriptive Statistics

Mean	12.339%
Standard Error	0.671%
Median	10.837%
Mode	4.246%
Standard Deviation	7.880%
Sample Variance	62.093%
Kurtosis	15.20
Skewness	3.23
Range	58.097%
Minimum	4.246%
Maximum	62.343%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.339%	138	100.00%	12.339%
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 0.89. Further, an Excess Kurtosis of 1.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.85%	0	0.00%	0.00%
-20.85% to -16.06%	0	0.00%	0.00%
-16.06% to -11.27%	7	5.07%	5.07%
-11.27% to -6.48%	22	15.94%	21.01%
-6.48% to -1.69%	47	34.06%	55.07%
-1.69% to 3.10%	41	29.71%	84.78%
3.10% to 7.88%	10	7.25%	92.03%
7.88% to 12.68%	6	4.35%	96.38%
12.68% to 17.46%	4	2.90%	99.28%
Greater than 17.46%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.08%	4.69%	73.19%	68.27%
±2σ	-14.47%	11.08%	94.93%	95.45%
±3σ	-20.85%	17.46%	99.28%	99.73%

Descriptive Statistics

Mean	-1.694%
Standard Error	0.544%
Median	-2.486%
Mode	-14.759%
Standard Deviation	6.386%
Sample Variance	40.778%
Kurtosis	1.55
Skewness	0.89
Range	36.795%
Minimum	-14.759%
Maximum	22.036%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.734%	50	36.23%	1.715%
Negative	-5.345%	88	63.77%	-3.408%
Zero	0.000%	0	0.00%	0.000%

^DJI Deep Analytical Report