^RUT - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	1.36%	1.10%	1.27%	1.80%
Weekly	3.05%	2.80%	3.10%	4.37%
Monthly	5.72%	6.49%	6.04%	9.20%
Quarterly	9.34%	11.33%	10.12%	16.38%
Annual	—	—	—	—
Option Time Horizon	—	—	—	—

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.44. Further, an Excess Kurtosis of 8.57 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.03%	70	0.72%	0.72%
-4.03% to -3.02%	111	1.14%	1.87%
-3.02% to -2.00%	333	3.43%	5.30%
-2.00% to -0.98%	1078	11.11%	16.40%
-0.98% to 0.04%	2988	30.79%	47.19%
0.04% to 1.05%	3599	37.08%	84.28%
1.05% to 2.07%	1058	10.90%	95.18%
2.07% to 3.09%	322	3.32%	98.50%
3.09% to 4.11%	77	0.79%	99.29%
Greater than 4.11%	69	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.32%	1.39%	77.77%	68.27%
±2σ	-2.68%	2.75%	95.19%	95.45%
±3σ	-4.03%	4.11%	98.57%	99.73%

Descriptive Statistics

Mean	0.037%
Standard Error	0.014%
Median	0.095%
Mode	0.107%
Standard Deviation	1.357%
Sample Variance	1.840%
Kurtosis	8.57
Skewness	-0.44
Range	23.663%
Minimum	-14.272%
Maximum	9.391%
Count	9705

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.882%	5285	54.46%	0.480%
Negative	-0.976%	4409	45.43%	-0.443%
Zero	0.000%	11	0.11%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.46%
20	1 Month	2.24%
60	1 Quarter	1.80%
250	1 Year	1.80%
750	3 Years	1.66%
1,250	5 Years	1.80%
2,500	10 Years	1.68%
5,000	20 Years	1.76%
12,500	50 Years	1.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.17. Further, an Excess Kurtosis of 19.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.90%	0	0.00%	0.00%
-1.90% to -1.08%	0	0.00%	0.00%
-1.08% to -0.26%	0	0.00%	0.00%
-0.26% to 0.56%	1700	17.51%	17.51%
0.56% to 1.39%	4389	45.22%	62.73%
1.39% to 2.21%	2146	22.11%	84.84%
2.21% to 3.03%	846	8.72%	93.56%
3.03% to 3.85%	343	3.53%	97.09%
3.85% to 4.67%	141	1.45%	98.55%
Greater than 4.67%	141	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.29%	2.48%	85.49%	68.27%
±2σ	-0.81%	3.58%	96.29%	95.45%
±3σ	-1.90%	4.67%	98.55%	99.73%

Descriptive Statistics

Mean	1.386%
Standard Error	0.011%
Median	1.113%
Mode	0.695%
Standard Deviation	1.096%
Sample Variance	1.202%
Kurtosis	19.45
Skewness	3.17
Range	14.204%
Minimum	0.122%
Maximum	14.326%
Count	9706

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.386%	9706	100.00%	1.386%
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 0.81. Further, an Excess Kurtosis of 9.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.82%	56	0.58%	0.58%
-3.82% to -2.87%	81	0.83%	1.41%
-2.87% to -1.92%	311	3.20%	4.62%
-1.92% to -0.96%	1104	11.37%	15.99%
-0.96% to -0.01%	3662	37.73%	53.72%
-0.01% to 0.94%	2891	29.79%	83.51%
0.94% to 1.89%	1041	10.73%	94.23%
1.89% to 2.84%	362	3.73%	97.96%
2.84% to 3.79%	125	1.29%	99.25%
Greater than 3.79%	73	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.28%	1.26%	77.65%	68.27%
±2σ	-2.55%	2.52%	94.92%	95.45%
±3σ	-3.82%	3.79%	98.67%	99.73%

Descriptive Statistics

Mean	-0.013%
Standard Error	0.013%
Median	-0.085%
Mode	0.000%
Standard Deviation	1.268%
Sample Variance	1.609%
Kurtosis	9.52
Skewness	0.81
Range	23.210%
Minimum	-8.884%
Maximum	14.326%
Count	9706

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.941%	4416	45.50%	0.428%
Negative	-0.811%	5275	54.35%	-0.441%
Zero	0.000%	15	0.15%	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 6.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.96%	15	0.75%	0.75%
-8.96% to -6.68%	24	1.19%	1.94%
-6.68% to -4.39%	81	4.03%	5.97%
-4.39% to -2.10%	205	10.20%	16.17%
-2.10% to 0.18%	614	30.55%	46.72%
0.18% to 2.47%	761	37.86%	84.58%
2.47% to 4.75%	221	11.00%	95.57%
4.75% to 7.04%	56	2.79%	98.36%
7.04% to 9.32%	21	1.04%	99.40%
Greater than 9.32%	12	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.87%	3.23%	78.11%	68.27%
±2σ	-5.92%	6.28%	94.98%	95.45%
±3σ	-8.96%	9.32%	98.66%	99.73%

Descriptive Statistics

Mean	0.181%
Standard Error	0.068%
Median	0.384%
Mode	0.370%
Standard Deviation	3.048%
Sample Variance	9.291%
Kurtosis	6.21
Skewness	-0.46
Range	41.109%
Minimum	-21.015%
Maximum	20.094%
Count	2010

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.087%	1119	55.67%	1.162%
Negative	-2.216%	890	44.28%	-0.981%
Zero	0.000%	1	0.05%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	4.91%
12	1 Quarter	3.99%
52	1 Year	4.26%
156	3 Years	4.01%
260	5 Years	4.37%
520	10 Years	4.08%
1,040	20 Years	4.30%
2,600	50 Years	3.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 16.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.60%	0	0.00%	0.00%
-4.60% to -2.50%	0	0.00%	0.00%
-2.50% to -0.40%	0	0.00%	0.00%
-0.40% to 1.69%	315	15.66%	15.66%
1.69% to 3.79%	971	48.28%	63.95%
3.79% to 5.89%	439	21.83%	85.78%
5.89% to 7.99%	165	8.20%	93.98%
7.99% to 10.09%	55	2.73%	96.72%
10.09% to 12.18%	26	1.29%	98.01%
Greater than 12.18%	40	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.99%	6.59%	86.28%	68.27%
±2σ	-1.80%	9.39%	96.12%	95.45%
±3σ	-4.60%	12.18%	98.01%	99.73%

Descriptive Statistics

Mean	3.792%
Standard Error	0.062%
Median	3.110%
Mode	1.567%
Standard Deviation	2.797%
Sample Variance	7.824%
Kurtosis	16.26
Skewness	3.09
Range	30.053%
Minimum	0.501%
Maximum	30.554%
Count	2011

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.792%	2011	100.00%	3.792%
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 1.35. Further, an Excess Kurtosis of 9.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.38%	9	0.45%	0.45%
-9.38% to -7.05%	16	0.80%	1.24%
-7.05% to -4.73%	56	2.78%	4.03%
-4.73% to -2.40%	225	11.19%	15.22%
-2.40% to -0.08%	801	39.83%	55.05%
-0.08% to 2.25%	592	29.44%	84.49%
2.25% to 4.57%	194	9.65%	94.13%
4.57% to 6.90%	75	3.73%	97.86%
6.90% to 9.22%	23	1.14%	99.01%
Greater than 9.22%	20	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.18%	3.02%	79.11%	68.27%
±2σ	-6.28%	6.12%	95.13%	95.45%
±3σ	-9.38%	9.22%	98.56%	99.73%

Descriptive Statistics

Mean	-0.079%
Standard Error	0.069%
Median	-0.391%
Mode	-1.295%
Standard Deviation	3.100%
Sample Variance	9.612%
Kurtosis	9.96
Skewness	1.35
Range	44.925%
Minimum	-16.734%
Maximum	28.191%
Count	2011

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.353%	881	43.81%	1.031%
Negative	-1.974%	1130	56.19%	-1.109%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.74. Further, an Excess Kurtosis of 2.65 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.40%	4	0.87%	0.87%
-16.40% to -12.11%	4	0.87%	1.73%
-12.11% to -7.82%	23	4.98%	6.71%
-7.82% to -3.54%	65	14.07%	20.78%
-3.54% to 0.75%	110	23.81%	44.59%
0.75% to 5.04%	163	35.28%	79.87%
5.04% to 9.33%	73	15.80%	95.67%
9.33% to 13.61%	15	3.25%	98.92%
13.61% to 17.90%	4	0.87%	99.78%
Greater than 17.90%	1	0.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.97%	6.47%	71.86%	68.27%
±2σ	-10.68%	12.18%	95.89%	95.45%
±3σ	-16.40%	17.90%	98.92%	99.73%

Descriptive Statistics

Mean	0.751%
Standard Error	0.266%
Median	1.551%
Mode	-0.429%
Standard Deviation	5.717%
Sample Variance	32.688%
Kurtosis	2.65
Skewness	-0.74
Range	49.052%
Minimum	-30.765%
Maximum	18.287%
Count	462

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.230%	284	61.47%	2.600%
Negative	-4.800%	178	38.53%	-1.849%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	8.16%
12	1 Year	8.16%
36	3 Years	8.59%
60	5 Years	9.20%
120	10 Years	9.10%
240	20 Years	9.20%
600	50 Years	8.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.12. Further, an Excess Kurtosis of 25.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.55%	0	0.00%	0.00%
-10.55% to -5.68%	0	0.00%	0.00%
-5.68% to -0.82%	0	0.00%	0.00%
-0.82% to 4.05%	45	9.72%	9.72%
4.05% to 8.91%	252	54.43%	64.15%
8.91% to 13.78%	112	24.19%	88.34%
13.78% to 18.64%	30	6.48%	94.82%
18.64% to 23.51%	11	2.38%	97.19%
23.51% to 28.38%	6	1.30%	98.49%
Greater than 28.38%	7	1.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.42%	15.40%	89.42%	68.27%
±2σ	-4.06%	21.89%	96.54%	95.45%
±3σ	-10.55%	28.38%	98.49%	99.73%

Descriptive Statistics

Mean	8.913%
Standard Error	0.302%
Median	7.402%
Mode	4.179%
Standard Deviation	6.488%
Sample Variance	42.089%
Kurtosis	25.86
Skewness	4.12
Range	61.854%
Minimum	1.829%
Maximum	63.683%
Count	463

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.913%	463	100.00%	8.913%
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 1.65. Further, an Excess Kurtosis of 8.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.53%	0	0.00%	0.00%
-18.53% to -14.00%	2	0.43%	0.43%
-14.00% to -9.46%	13	2.81%	3.24%
-9.46% to -4.93%	69	14.90%	18.14%
-4.93% to -0.40%	188	40.60%	58.75%
-0.40% to 4.13%	104	22.46%	81.21%
4.13% to 8.66%	56	12.10%	93.30%
8.66% to 13.20%	21	4.54%	97.84%
13.20% to 17.73%	5	1.08%	98.92%
Greater than 17.73%	5	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.44%	5.64%	75.38%	68.27%
±2σ	-12.49%	11.69%	96.11%	95.45%
±3σ	-18.53%	17.73%	98.92%	99.73%

Descriptive Statistics

Mean	-0.400%
Standard Error	0.281%
Median	-1.547%
Mode	-7.077%
Standard Deviation	6.043%
Sample Variance	36.520%
Kurtosis	8.03
Skewness	1.65
Range	59.773%
Minimum	-15.329%
Maximum	44.444%
Count	463

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.343%	176	38.01%	2.031%
Negative	-3.936%	286	61.77%	-2.431%
Zero	0.000%	1	0.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.25. Further, an Excess Kurtosis of 1.10 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.59%	1	0.65%	0.65%
-25.59% to -18.59%	3	1.95%	2.60%
-18.59% to -11.58%	7	4.55%	7.14%
-11.58% to -4.57%	18	11.69%	18.83%
-4.57% to 2.44%	44	28.57%	47.40%
2.44% to 9.45%	47	30.52%	77.92%
9.45% to 16.45%	26	16.88%	94.81%
16.45% to 23.46%	7	4.55%	99.35%
23.46% to 30.47%	0	0.00%	99.35%
Greater than 30.47%	1	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.91%	11.78%	69.48%	68.27%
±2σ	-16.25%	21.13%	94.81%	95.45%
±3σ	-25.59%	30.47%	98.70%	99.73%

Descriptive Statistics

Mean	2.438%
Standard Error	0.753%
Median	2.935%
Mode	-26.426%
Standard Deviation	9.344%
Sample Variance	87.308%
Kurtosis	1.10
Skewness	-0.25
Range	61.211%
Minimum	-26.426%
Maximum	34.785%
Count	154

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.141%	94	61.04%	4.969%
Negative	-6.496%	60	38.96%	-2.531%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	15.69%
12	3 Years	17.08%
20	5 Years	16.38%
40	10 Years	16.08%
80	20 Years	16.10%
200	50 Years	14.96%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.69. Further, an Excess Kurtosis of 9.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.96%	0	0.00%	0.00%
-16.96% to -8.46%	0	0.00%	0.00%
-8.46% to 0.03%	0	0.00%	0.00%
0.03% to 8.53%	24	15.48%	15.48%
8.53% to 17.02%	78	50.32%	65.81%
17.02% to 25.52%	32	20.65%	86.45%
25.52% to 34.02%	9	5.81%	92.26%
34.02% to 42.51%	6	3.87%	96.13%
42.51% to 51.01%	3	1.94%	98.06%
Greater than 51.01%	3	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.70%	28.35%	89.03%	68.27%
±2σ	-5.63%	39.68%	95.48%	95.45%
±3σ	-16.96%	51.01%	98.06%	99.73%

Descriptive Statistics

Mean	17.023%
Standard Error	0.910%
Median	14.262%
Mode	9.043%
Standard Deviation	11.328%
Sample Variance	128.323%
Kurtosis	9.45
Skewness	2.69
Range	70.907%
Minimum	4.924%
Maximum	75.831%
Count	155

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.023%	155	100.00%	17.023%
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 1.32. Further, an Excess Kurtosis of 3.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.61%	0	0.00%	0.00%
-31.61% to -24.02%	1	0.65%	0.65%
-24.02% to -16.43%	2	1.29%	1.94%
-16.43% to -8.84%	29	18.71%	20.65%
-8.84% to -1.25%	58	37.42%	58.06%
-1.25% to 6.34%	39	25.16%	83.23%
6.34% to 13.93%	16	10.32%	93.55%
13.93% to 21.52%	5	3.23%	96.77%
21.52% to 29.11%	1	0.65%	97.42%
Greater than 29.11%	4	2.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.37%	8.87%	74.84%	68.27%
±2σ	-21.49%	18.99%	94.84%	95.45%
±3σ	-31.61%	29.11%	97.42%	99.73%

Descriptive Statistics

Mean	-1.251%
Standard Error	0.813%
Median	-2.754%
Mode	-25.693%
Standard Deviation	10.120%
Sample Variance	102.413%
Kurtosis	3.34
Skewness	1.32
Range	67.279%
Minimum	-25.693%
Maximum	41.586%
Count	155

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.007%	61	39.35%	3.151%
Negative	-7.259%	94	60.65%	-4.402%
Zero	0.000%	0	0.00%	0.000%

^RUT Deep Analytical Report