^DJI - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	1.10%	0.92%	1.02%	1.21%
Weekly	2.36%	2.24%	2.36%	2.87%
Monthly	4.17%	4.69%	4.25%	6.29%
Quarterly	6.37%	7.91%	6.34%	10.20%
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 12.74 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%	93	1.08%	1.86%
-2.43% to -1.61%	284	3.30%	5.17%
-1.61% to -0.78%	881	10.25%	15.42%
-0.78% to 0.04%	2869	33.38%	48.80%
0.04% to 0.86%	3055	35.55%	84.35%
0.86% to 1.68%	978	11.38%	95.73%
1.68% to 2.50%	239	2.78%	98.51%
2.50% to 3.33%	73	0.85%	99.36%
Greater than 3.33%	55	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.06%	1.13%	79.04%	68.27%
±2σ	-2.15%	2.23%	95.42%	95.45%
±3σ	-3.25%	3.33%	98.58%	99.73%

Descriptive Statistics

Mean	0.038%
Standard Error	0.012%
Median	0.056%
Mode	-0.003%
Standard Deviation	1.096%
Sample Variance	1.200%
Kurtosis	12.74
Skewness	-0.14
Range	24.292%
Minimum	-12.927%
Maximum	11.365%
Count	8594

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.719%	4591	53.42%	0.384%
Negative	-0.745%	3991	46.44%	-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	1.08%
20	1 Month	1.22%
60	1 Quarter	1.08%
250	1 Year	1.28%
750	3 Years	1.09%
1,250	5 Years	1.21%
2,500	10 Years	1.21%
5,000	20 Years	1.28%
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 22.93 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	14.18%	14.18%
0.57% to 1.26%	4282	49.82%	64.00%
1.26% to 1.95%	1899	22.09%	86.10%
1.95% to 2.63%	683	7.95%	94.04%
2.63% to 3.32%	270	3.14%	97.18%
3.32% to 4.01%	92	1.07%	98.25%
Greater than 4.01%	150	1.75%	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%	96.45%	95.45%
±3σ	-1.50%	4.01%	98.27%	99.73%

Descriptive Statistics

Mean	1.256%
Standard Error	0.010%
Median	1.026%
Mode	0.898%
Standard Deviation	0.918%
Sample Variance	0.844%
Kurtosis	22.93
Skewness	3.57
Range	12.757%
Minimum	0.167%
Maximum	12.924%
Count	8595

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.256%	8595	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%	1.47%
-2.33% to -1.56%	251	2.92%	4.39%
-1.56% to -0.79%	980	11.40%	15.79%
-0.79% to -0.03%	3127	36.38%	52.17%
-0.03% to 0.74%	2746	31.95%	84.12%
0.74% to 1.51%	882	10.26%	94.38%
1.51% to 2.28%	309	3.60%	97.98%
2.28% to 3.04%	95	1.11%	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%	78.42%	68.27%
±2σ	-2.07%	2.02%	95.10%	95.45%
±3σ	-3.09%	3.04%	98.41%	99.73%

Descriptive Statistics

Mean	-0.025%
Standard Error	0.011%
Median	-0.056%
Mode	0.050%
Standard Deviation	1.023%
Sample Variance	1.047%
Kurtosis	8.69
Skewness	0.30
Range	18.295%
Minimum	-9.855%
Maximum	8.440%
Count	8595

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.718%	3991	46.43%	0.333%
Negative	-0.670%	4592	53.43%	-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 -0.07. Further, an Excess Kurtosis of 7.17 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 -5.13%	17	0.95%	1.91%
-5.13% to -3.36%	62	3.48%	5.39%
-3.36% to -1.59%	198	11.12%	16.51%
-1.59% to 0.18%	567	31.84%	48.34%
0.18% to 1.95%	620	34.81%	83.16%
1.95% to 3.73%	221	12.41%	95.56%
3.73% to 5.50%	54	3.03%	98.60%
5.50% 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	-2.18%	2.54%	77.20%	68.27%
±2σ	-4.54%	4.91%	95.40%	95.45%
±3σ	-6.91%	7.27%	98.32%	99.73%

Descriptive Statistics

Mean	0.182%
Standard Error	0.056%
Median	0.244%
Mode	-1.456%
Standard Deviation	2.363%
Sample Variance	5.583%
Kurtosis	7.17
Skewness	-0.07
Range	35.448%
Minimum	-15.356%
Maximum	20.092%
Count	1781

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.639%	994	55.81%	0.915%
Negative	-1.660%	786	44.13%	-0.733%
Zero	0.000%	1	0.06%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	2.31%
12	1 Quarter	2.07%
52	1 Year	2.93%
156	3 Years	2.55%
260	5 Years	2.87%
520	10 Years	2.91%
1,040	20 Years	3.07%
2,600	50 Years	3.07%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.59%	0	0.00%	0.00%
-3.59% to -1.91%	0	0.00%	0.00%
-1.91% to -0.23%	0	0.00%	0.00%
-0.23% to 1.45%	227	12.74%	12.74%
1.45% to 3.13%	917	51.46%	64.20%
3.13% to 4.82%	400	22.45%	86.64%
4.82% to 6.50%	132	7.41%	94.05%
6.50% to 8.18%	51	2.86%	96.91%
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	0.89%	5.38%	88.78%	68.27%
±2σ	-1.35%	7.62%	96.13%	95.45%
±3σ	-3.59%	9.86%	97.87%	99.73%

Descriptive Statistics

Mean	3.134%
Standard Error	0.053%
Median	2.534%
Mode	1.712%
Standard Deviation	2.242%
Sample Variance	5.027%
Kurtosis	21.38
Skewness	3.48
Range	27.907%
Minimum	0.530%
Maximum	28.437%
Count	1782

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.134%	1782	100.00%	3.134%
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 8.01 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 -3.65%	49	2.75%	4.04%
-3.65% to -1.88%	234	13.13%	17.17%
-1.88% to -0.11%	637	35.75%	52.92%
-0.11% to 1.65%	551	30.92%	83.84%
1.65% to 3.42%	191	10.72%	94.56%
3.42% to 5.19%	60	3.37%	97.92%
5.19% to 6.96%	18	1.01%	98.93%
Greater than 6.96%	19	1.07%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.47%	2.24%	77.50%	68.27%
±2σ	-4.83%	4.60%	95.40%	95.45%
±3σ	-7.18%	6.95%	98.48%	99.73%

Descriptive Statistics

Mean	-0.113%
Standard Error	0.056%
Median	-0.214%
Mode	-0.104%
Standard Deviation	2.356%
Sample Variance	5.552%
Kurtosis	8.01
Skewness	1.00
Range	33.367%
Minimum	-12.244%
Maximum	21.123%
Count	1782

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.725%	784	44.00%	0.759%
Negative	-1.558%	998	56.00%	-0.873%
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 1.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.74%	4	0.98%	0.98%
-11.74% to -8.62%	7	1.71%	2.69%
-8.62% to -5.49%	14	3.42%	6.11%
-5.49% to -2.37%	53	12.96%	19.07%
-2.37% to 0.76%	109	26.65%	45.72%
0.76% to 3.88%	141	34.47%	80.20%
3.88% to 7.01%	56	13.69%	93.89%
7.01% to 10.13%	20	4.89%	98.78%
10.13% to 13.26%	4	0.98%	99.76%
Greater than 13.26%	1	0.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.41%	4.92%	70.90%	68.27%
±2σ	-7.57%	9.09%	95.35%	95.45%
±3σ	-11.74%	13.26%	98.78%	99.73%

Descriptive Statistics

Mean	0.758%
Standard Error	0.206%
Median	1.103%
Mode	-5.074%
Standard Deviation	4.166%
Sample Variance	17.360%
Kurtosis	1.26
Skewness	-0.46
Range	29.083%
Minimum	-15.132%
Maximum	13.951%
Count	409

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.160%	260	63.57%	2.009%
Negative	-3.433%	149	36.43%	-1.251%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	3.63%
12	1 Year	5.55%
36	3 Years	5.47%
60	5 Years	6.29%
120	10 Years	6.57%
240	20 Years	6.63%
600	50 Years	6.63%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.09%	0	0.00%	0.00%
-7.09% to -3.57%	0	0.00%	0.00%
-3.57% to -0.05%	0	0.00%	0.00%
-0.05% to 3.47%	47	11.46%	11.46%
3.47% to 6.99%	230	56.10%	67.56%
6.99% to 10.50%	74	18.05%	85.61%
10.50% to 14.02%	31	7.56%	93.17%
14.02% to 17.54%	14	3.41%	96.59%
17.54% to 21.06%	8	1.95%	98.54%
Greater than 21.06%	6	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.29%	11.68%	88.54%	68.27%
±2σ	-2.40%	16.37%	96.10%	95.45%
±3σ	-7.09%	21.06%	98.54%	99.73%

Descriptive Statistics

Mean	6.985%
Standard Error	0.232%
Median	5.754%
Mode	3.057%
Standard Deviation	4.692%
Sample Variance	22.018%
Kurtosis	21.74
Skewness	3.63
Range	46.977%
Minimum	1.825%
Maximum	48.802%
Count	410

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.985%	410	100.00%	6.985%
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 0.86. Further, an Excess Kurtosis of 2.23 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.31%	0	0.00%	0.00%
-13.31% to -10.12%	2	0.49%	0.49%
-10.12% to -6.94%	16	3.90%	4.39%
-6.94% to -3.75%	62	15.12%	19.51%
-3.75% to -0.56%	153	37.32%	56.83%
-0.56% to 2.62%	101	24.63%	81.46%
2.62% to 5.81%	51	12.44%	93.90%
5.81% to 8.99%	14	3.41%	97.32%
8.99% to 12.18%	5	1.22%	98.54%
Greater than 12.18%	6	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.81%	3.68%	71.95%	68.27%
±2σ	-9.06%	7.93%	95.61%	95.45%
±3σ	-13.31%	12.18%	98.54%	99.73%

Descriptive Statistics

Mean	-0.565%
Standard Error	0.210%
Median	-1.104%
Mode	-3.793%
Standard Deviation	4.248%
Sample Variance	18.049%
Kurtosis	2.23
Skewness	0.86
Range	30.639%
Minimum	-12.809%
Maximum	17.830%
Count	410

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.617%	152	37.07%	1.341%
Negative	-3.029%	258	62.93%	-1.906%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.42. Further, an Excess Kurtosis of 0.69 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.89%	1	0.73%	0.73%
-16.89% to -12.12%	4	2.92%	3.65%
-12.12% to -7.34%	6	4.38%	8.03%
-7.34% to -2.56%	10	7.30%	15.33%
-2.56% to 2.22%	43	31.39%	46.72%
2.22% to 6.99%	45	32.85%	79.56%
6.99% to 11.77%	17	12.41%	91.97%
11.77% to 16.55%	10	7.30%	99.27%
16.55% to 21.33%	1	0.73%	100.00%
Greater than 21.33%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.15%	8.59%	74.45%	68.27%
±2σ	-10.52%	14.96%	93.43%	95.45%
±3σ	-16.89%	21.33%	99.27%	99.73%

Descriptive Statistics

Mean	2.217%
Standard Error	0.544%
Median	2.795%
Mode	-18.044%
Standard Deviation	6.370%
Sample Variance	40.577%
Kurtosis	0.69
Skewness	-0.42
Range	35.359%
Minimum	-18.044%
Maximum	17.315%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.757%	89	64.96%	3.740%
Negative	-4.345%	48	35.04%	-1.522%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	8.33%
12	3 Years	10.24%
20	5 Years	10.20%
40	10 Years	11.29%
80	20 Years	11.42%
200	50 Years	11.28%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.20. Further, an Excess Kurtosis of 14.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.46%	0	0.00%	0.00%
-11.46% to -5.52%	0	0.00%	0.00%
-5.52% to 0.41%	0	0.00%	0.00%
0.41% to 6.35%	19	13.77%	13.77%
6.35% to 12.28%	73	52.90%	66.67%
12.28% to 18.22%	28	20.29%	86.96%
18.22% to 24.15%	11	7.97%	94.93%
24.15% to 30.09%	3	2.17%	97.10%
30.09% to 36.02%	1	0.72%	97.83%
Greater than 36.02%	3	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.37%	20.20%	89.13%	68.27%
±2σ	-3.54%	28.11%	95.65%	95.45%
±3σ	-11.46%	36.02%	97.83%	99.73%

Descriptive Statistics

Mean	12.284%
Standard Error	0.674%
Median	10.766%
Mode	3.779%
Standard Deviation	7.913%
Sample Variance	62.617%
Kurtosis	14.99
Skewness	3.20
Range	58.564%
Minimum	3.779%
Maximum	62.343%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.284%	138	100.00%	12.284%
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 0.92. Further, an Excess Kurtosis of 1.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.78%	0	0.00%	0.00%
-20.78% to -16.03%	0	0.00%	0.00%
-16.03% to -11.27%	7	5.07%	5.07%
-11.27% to -6.51%	21	15.22%	20.29%
-6.51% to -1.76%	48	34.78%	55.07%
-1.76% to 3.00%	42	30.43%	85.51%
3.00% to 7.76%	9	6.52%	92.03%
7.76% to 12.51%	5	3.62%	95.65%
12.51% to 17.27%	5	3.62%	99.28%
Greater than 17.27%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.10%	4.58%	73.91%	68.27%
±2σ	-14.44%	10.93%	94.93%	95.45%
±3σ	-20.78%	17.27%	99.28%	99.73%

Descriptive Statistics

Mean	-1.757%
Standard Error	0.540%
Median	-2.486%
Mode	-14.759%
Standard Deviation	6.342%
Sample Variance	40.219%
Kurtosis	1.69
Skewness	0.92
Range	36.795%
Minimum	-14.759%
Maximum	22.036%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.687%	49	35.51%	1.664%
Negative	-5.305%	89	64.49%	-3.421%
Zero	0.000%	0	0.00%	0.000%

^DJI Deep Analytical Report