^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%	1.81%
Weekly	3.05%	2.80%	3.10%	4.40%
Monthly	5.72%	6.49%	6.05%	9.26%
Quarterly	9.33%	11.36%	10.11%	16.09%
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 8.59 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 -3.01%	113	1.17%	1.89%
-3.01% to -2.00%	328	3.39%	5.28%
-2.00% to -0.98%	1078	11.13%	16.41%
-0.98% to 0.04%	2983	30.80%	47.21%
0.04% to 1.05%	3590	37.07%	84.28%
1.05% to 2.07%	1055	10.89%	95.18%
2.07% to 3.09%	321	3.31%	98.49%
3.09% to 4.11%	77	0.80%	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%	77.81%	68.27%
±2σ	-2.67%	2.75%	95.15%	95.45%
±3σ	-4.03%	4.11%	98.56%	99.73%

Descriptive Statistics

Mean	0.038%
Standard Error	0.014%
Median	0.095%
Mode	0.107%
Standard Deviation	1.356%
Sample Variance	1.840%
Kurtosis	8.59
Skewness	-0.44
Range	23.663%
Minimum	-14.272%
Maximum	9.391%
Count	9684

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.882%	5275	54.47%	0.480%
Negative	-0.975%	4398	45.41%	-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	1.64%
20	1 Month	1.91%
60	1 Quarter	1.52%
250	1 Year	1.79%
750	3 Years	1.66%
1,250	5 Years	1.81%
2,500	10 Years	1.67%
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 3.18. Further, an Excess Kurtosis of 19.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.91%	0	0.00%	0.00%
-1.91% to -1.08%	0	0.00%	0.00%
-1.08% to -0.26%	0	0.00%	0.00%
-0.26% to 0.56%	1687	17.42%	17.42%
0.56% to 1.39%	4392	45.35%	62.77%
1.39% to 2.21%	2143	22.13%	84.89%
2.21% to 3.03%	840	8.67%	93.57%
3.03% to 3.85%	342	3.53%	97.10%
3.85% to 4.68%	140	1.45%	98.54%
Greater than 4.68%	141	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.29%	2.48%	85.52%	68.27%
±2σ	-0.81%	3.58%	96.29%	95.45%
±3σ	-1.91%	4.68%	98.54%	99.73%

Descriptive Statistics

Mean	1.385%
Standard Error	0.011%
Median	1.111%
Mode	0.695%
Standard Deviation	1.097%
Sample Variance	1.202%
Kurtosis	19.48
Skewness	3.18
Range	14.204%
Minimum	0.122%
Maximum	14.326%
Count	9685

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.385%	9685	100.00%	1.385%
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 9.53 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	0.84%	1.41%
-2.87% to -1.92%	310	3.20%	4.62%
-1.92% to -0.96%	1096	11.32%	15.93%
-0.96% to -0.01%	3660	37.79%	53.72%
-0.01% to 0.94%	2889	29.83%	83.55%
0.94% to 1.89%	1035	10.69%	94.24%
1.89% to 2.84%	360	3.72%	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%	77.74%	68.27%
±2σ	-2.55%	2.52%	94.93%	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	1.269%
Sample Variance	1.609%
Kurtosis	9.53
Skewness	0.81
Range	23.210%
Minimum	-8.884%
Maximum	14.326%
Count	9685

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.940%	4406	45.49%	0.428%
Negative	-0.811%	5264	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 6.22 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	1.20%	1.94%
-6.68% to -4.39%	81	4.04%	5.98%
-4.39% to -2.10%	204	10.17%	16.15%
-2.10% to 0.18%	611	30.46%	46.61%
0.18% to 2.47%	765	38.14%	84.75%
2.47% to 4.76%	217	10.82%	95.56%
4.76% to 7.04%	57	2.84%	98.40%
7.04% to 9.33%	20	1.00%	99.40%
Greater than 9.33%	12	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.86%	3.23%	78.12%	68.27%
±2σ	-5.91%	6.28%	94.97%	95.45%
±3σ	-8.96%	9.33%	98.65%	99.73%

Descriptive Statistics

Mean	0.184%
Standard Error	0.068%
Median	0.388%
Mode	0.370%
Standard Deviation	3.049%
Sample Variance	9.298%
Kurtosis	6.22
Skewness	-0.46
Range	41.109%
Minimum	-21.015%
Maximum	20.094%
Count	2006

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.086%	1119	55.78%	1.164%
Negative	-2.218%	886	44.17%	-0.980%
Zero	0.000%	1	0.05%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.66%
12	1 Quarter	3.27%
52	1 Year	4.22%
156	3 Years	4.02%
260	5 Years	4.40%
520	10 Years	4.07%
1,040	20 Years	4.29%
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 16.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.61%	0	0.00%	0.00%
-4.61% to -2.51%	0	0.00%	0.00%
-2.51% to -0.41%	0	0.00%	0.00%
-0.41% to 1.69%	315	15.70%	15.70%
1.69% to 3.79%	969	48.28%	63.98%
3.79% to 5.89%	438	21.82%	85.80%
5.89% to 7.99%	164	8.17%	93.97%
7.99% to 10.09%	55	2.74%	96.71%
10.09% to 12.19%	26	1.30%	98.01%
Greater than 12.19%	40	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.99%	6.59%	86.45%	68.27%
±2σ	-1.81%	9.39%	96.11%	95.45%
±3σ	-4.61%	12.19%	98.01%	99.73%

Descriptive Statistics

Mean	3.790%
Standard Error	0.062%
Median	3.105%
Mode	1.567%
Standard Deviation	2.799%
Sample Variance	7.832%
Kurtosis	16.27
Skewness	3.09
Range	30.053%
Minimum	0.501%
Maximum	30.554%
Count	2007

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.790%	2007	100.00%	3.790%
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 1.36. 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 -9.39%	9	0.45%	0.45%
-9.39% to -7.06%	16	0.80%	1.25%
-7.06% to -4.73%	56	2.79%	4.04%
-4.73% to -2.41%	224	11.16%	15.20%
-2.41% to -0.08%	799	39.81%	55.01%
-0.08% to 2.25%	592	29.50%	84.50%
2.25% to 4.57%	193	9.62%	94.12%
4.57% to 6.90%	75	3.74%	97.86%
6.90% to 9.22%	23	1.15%	99.00%
Greater than 9.22%	20	1.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.18%	3.02%	79.07%	68.27%
±2σ	-6.29%	6.12%	95.12%	95.45%
±3σ	-9.39%	9.22%	98.56%	99.73%

Descriptive Statistics

Mean	-0.081%
Standard Error	0.069%
Median	-0.398%
Mode	-1.295%
Standard Deviation	3.102%
Sample Variance	9.625%
Kurtosis	9.96
Skewness	1.36
Range	44.925%
Minimum	-16.734%
Maximum	28.191%
Count	2007

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.357%	877	43.70%	1.030%
Negative	-1.974%	1130	56.30%	-1.111%
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 -0.75. Further, an Excess Kurtosis of 2.67 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.39%	4	0.87%	0.87%
-16.39% to -12.10%	4	0.87%	1.74%
-12.10% to -7.81%	23	4.99%	6.72%
-7.81% to -3.52%	65	14.10%	20.82%
-3.52% to 0.77%	108	23.43%	44.25%
0.77% to 5.05%	164	35.57%	79.83%
5.05% to 9.34%	73	15.84%	95.66%
9.34% to 13.63%	15	3.25%	98.92%
13.63% to 17.92%	4	0.87%	99.78%
Greater than 17.92%	1	0.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.95%	6.48%	71.80%	68.27%
±2σ	-10.67%	12.20%	95.88%	95.45%
±3σ	-16.39%	17.92%	98.92%	99.73%

Descriptive Statistics

Mean	0.766%
Standard Error	0.266%
Median	1.573%
Mode	-0.429%
Standard Deviation	5.718%
Sample Variance	32.692%
Kurtosis	2.67
Skewness	-0.75
Range	49.052%
Minimum	-30.765%
Maximum	18.287%
Count	461

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.234%	284	61.60%	2.608%
Negative	-4.799%	177	38.40%	-1.843%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	6.91%
12	1 Year	8.17%
36	3 Years	8.68%
60	5 Years	9.26%
120	10 Years	9.09%
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 25.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.57%	0	0.00%	0.00%
-10.57% to -5.70%	0	0.00%	0.00%
-5.70% to -0.83%	0	0.00%	0.00%
-0.83% to 4.04%	45	9.74%	9.74%
4.04% to 8.91%	252	54.55%	64.29%
8.91% to 13.78%	111	24.03%	88.31%
13.78% to 18.65%	30	6.49%	94.81%
18.65% to 23.52%	11	2.38%	97.19%
23.52% to 28.39%	6	1.30%	98.48%
Greater than 28.39%	7	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.42%	15.40%	89.39%	68.27%
±2σ	-4.08%	21.90%	96.54%	95.45%
±3σ	-10.57%	28.39%	98.48%	99.73%

Descriptive Statistics

Mean	8.911%
Standard Error	0.302%
Median	7.394%
Mode	4.179%
Standard Deviation	6.494%
Sample Variance	42.178%
Kurtosis	25.81
Skewness	4.12
Range	61.854%
Minimum	1.829%
Maximum	63.683%
Count	462

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.911%	462	100.00%	8.911%
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 1.66. Further, an Excess Kurtosis of 8.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.55%	0	0.00%	0.00%
-18.55% to -14.02%	2	0.43%	0.43%
-14.02% to -9.48%	13	2.81%	3.25%
-9.48% to -4.95%	69	14.94%	18.18%
-4.95% to -0.41%	188	40.69%	58.87%
-0.41% to 4.12%	104	22.51%	81.39%
4.12% to 8.66%	55	11.90%	93.29%
8.66% to 13.19%	21	4.55%	97.84%
13.19% 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	-6.46%	5.63%	75.32%	68.27%
±2σ	-12.51%	11.68%	96.10%	95.45%
±3σ	-18.55%	17.73%	98.92%	99.73%

Descriptive Statistics

Mean	-0.413%
Standard Error	0.281%
Median	-1.576%
Mode	-7.077%
Standard Deviation	6.046%
Sample Variance	36.559%
Kurtosis	8.04
Skewness	1.66
Range	59.773%
Minimum	-15.329%
Maximum	44.444%
Count	462

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.349%	175	37.88%	2.026%
Negative	-3.940%	286	61.91%	-2.439%
Zero	0.000%	1	0.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.26. Further, an Excess Kurtosis of 1.13 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.51%	1	0.65%	0.65%
-25.51% to -18.51%	3	1.95%	2.60%
-18.51% to -11.51%	7	4.55%	7.14%
-11.51% to -4.52%	19	12.34%	19.48%
-4.52% to 2.48%	43	27.92%	47.40%
2.48% to 9.47%	48	31.17%	78.57%
9.47% to 16.47%	25	16.23%	94.81%
16.47% to 23.47%	7	4.55%	99.35%
23.47% to 30.46%	0	0.00%	99.35%
Greater than 30.46%	1	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.85%	11.81%	69.48%	68.27%
±2σ	-16.18%	21.13%	94.81%	95.45%
±3σ	-25.51%	30.46%	98.70%	99.73%

Descriptive Statistics

Mean	2.478%
Standard Error	0.752%
Median	2.935%
Mode	-26.426%
Standard Deviation	9.328%
Sample Variance	87.017%
Kurtosis	1.13
Skewness	-0.26
Range	61.211%
Minimum	-26.426%
Maximum	34.785%
Count	154

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.075%	95	61.69%	4.981%
Negative	-6.534%	59	38.31%	-2.503%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	14.29%
12	3 Years	16.61%
20	5 Years	16.09%
40	10 Years	15.94%
80	20 Years	16.03%
200	50 Years	14.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.68. Further, an Excess Kurtosis of 9.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.09%	0	0.00%	0.00%
-17.09% to -8.58%	0	0.00%	0.00%
-8.58% to -0.06%	0	0.00%	0.00%
-0.06% to 8.46%	25	16.13%	16.13%
8.46% to 16.98%	77	49.68%	65.81%
16.98% to 25.50%	32	20.65%	86.45%
25.50% to 34.02%	9	5.81%	92.26%
34.02% to 42.54%	6	3.87%	96.13%
42.54% to 51.06%	3	1.94%	98.06%
Greater than 51.06%	3	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.62%	28.34%	88.39%	68.27%
±2σ	-5.74%	39.70%	95.48%	95.45%
±3σ	-17.09%	51.06%	98.06%	99.73%

Descriptive Statistics

Mean	16.982%
Standard Error	0.912%
Median	14.262%
Mode	9.043%
Standard Deviation	11.359%
Sample Variance	129.024%
Kurtosis	9.36
Skewness	2.68
Range	70.907%
Minimum	4.924%
Maximum	75.831%
Count	155

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.982%	155	100.00%	16.982%
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 1.34. Further, an Excess Kurtosis of 3.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.62%	0	0.00%	0.00%
-31.62% to -24.04%	1	0.65%	0.65%
-24.04% to -16.46%	2	1.29%	1.94%
-16.46% to -8.87%	29	18.71%	20.65%
-8.87% to -1.29%	57	36.77%	57.42%
-1.29% to 6.29%	40	25.81%	83.23%
6.29% to 13.88%	16	10.32%	93.55%
13.88% to 21.46%	5	3.23%	96.77%
21.46% to 29.04%	1	0.65%	97.42%
Greater than 29.04%	4	2.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.40%	8.82%	74.19%	68.27%
±2σ	-21.51%	18.93%	94.84%	95.45%
±3σ	-31.62%	29.04%	97.42%	99.73%

Descriptive Statistics

Mean	-1.291%
Standard Error	0.812%
Median	-2.754%
Mode	-25.693%
Standard Deviation	10.111%
Sample Variance	102.235%
Kurtosis	3.38
Skewness	1.34
Range	67.279%
Minimum	-25.693%
Maximum	41.586%
Count	155

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.073%	60	38.71%	3.125%
Negative	-7.206%	95	61.29%	-4.417%
Zero	0.000%	0	0.00%	0.000%

^RUT Deep Analytical Report