^GSPC - Detail Report

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)
Daily	1.04%	0.88%	0.98%	1.30%
Weekly	2.38%	2.17%	2.41%	3.16%
Monthly	4.30%	4.54%	4.38%	6.84%
Quarterly	6.87%	7.63%	6.88%	12.02%
Annual	—	—	—	—
Option Time Horizon	—	—	—	—

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.57. Further, an Excess Kurtosis of 19.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.08%	110	0.68%	0.68%
-3.08% to -2.30%	181	1.12%	1.81%
-2.30% to -1.52%	538	3.34%	5.15%
-1.52% to -0.74%	1716	10.66%	15.80%
-0.74% to 0.03%	5374	33.37%	49.18%
0.03% to 0.81%	5662	35.16%	84.34%
0.81% to 1.59%	1786	11.09%	95.43%
1.59% to 2.37%	487	3.02%	98.45%
2.37% to 3.15%	138	0.86%	99.31%
Greater than 3.15%	111	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.00%	1.07%	78.85%	68.27%
±2σ	-2.04%	2.11%	95.29%	95.45%
±3σ	-3.08%	3.15%	98.63%	99.73%

Descriptive Statistics

Mean	0.034%
Standard Error	0.008%
Median	0.047%
Mode	0.000%
Standard Deviation	1.039%
Sample Variance	1.079%
Kurtosis	19.56
Skewness	-0.57
Range	32.047%
Minimum	-20.467%
Maximum	11.580%
Count	16103

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.689%	8527	52.95%	0.365%
Negative	-0.709%	7525	46.73%	-0.331%
Zero	0.000%	51	0.32%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.09%
20	1 Month	1.19%
60	1 Quarter	0.99%
250	1 Year	1.32%
750	3 Years	1.14%
1,250	5 Years	1.30%
2,500	10 Years	1.24%
5,000	20 Years	1.33%
12,500	50 Years	1.32%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.97. Further, an Excess Kurtosis of 53.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.24%	0	0.00%	0.00%
-1.24% to -0.58%	0	0.00%	0.00%
-0.58% to 0.08%	0	0.00%	0.00%
0.08% to 0.74%	3408	21.16%	21.16%
0.74% to 1.40%	5778	35.88%	57.04%
1.40% to 2.06%	4508	27.99%	85.03%
2.06% to 2.73%	1489	9.25%	94.28%
2.73% to 3.39%	519	3.22%	97.50%
3.39% to 4.05%	207	1.29%	98.79%
Greater than 4.05%	195	1.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.52%	2.29%	80.54%	68.27%
±2σ	-0.36%	3.17%	96.75%	95.45%
±3σ	-1.24%	4.05%	98.79%	99.73%

Descriptive Statistics

Mean	1.403%
Standard Error	0.007%
Median	1.276%
Mode	0.609%
Standard Deviation	0.882%
Sample Variance	0.778%
Kurtosis	53.30
Skewness	3.97
Range	25.593%
Minimum	0.146%
Maximum	25.739%
Count	16104

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.403%	16104	100.00%	1.403%
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 1.44. Further, an Excess Kurtosis of 37.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.97%	100	0.62%	0.62%
-2.97% to -2.23%	142	0.88%	1.50%
-2.23% to -1.50%	484	3.01%	4.51%
-1.50% to -0.76%	1825	11.33%	15.84%
-0.76% to -0.02%	5771	35.84%	51.68%
-0.02% to 0.72%	5201	32.30%	83.97%
0.72% to 1.46%	1716	10.66%	94.63%
1.46% to 2.19%	570	3.54%	98.17%
2.19% to 2.93%	179	1.11%	99.28%
Greater than 2.93%	116	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.00%	0.96%	78.90%	68.27%
±2σ	-1.99%	1.95%	95.42%	95.45%
±3σ	-2.97%	2.93%	98.66%	99.73%

Descriptive Statistics

Mean	-0.019%
Standard Error	0.008%
Median	-0.043%
Mode	0.000%
Standard Deviation	0.984%
Sample Variance	0.968%
Kurtosis	37.14
Skewness	1.44
Range	35.472%
Minimum	-9.738%
Maximum	25.734%
Count	16104

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.687%	7540	46.82%	0.322%
Negative	-0.644%	8507	52.83%	-0.340%
Zero	0.000%	57	0.35%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.52. 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 -6.97%	21	0.63%	0.63%
-6.97% to -5.18%	36	1.08%	1.71%
-5.18% to -3.40%	139	4.16%	5.86%
-3.40% to -1.62%	406	12.14%	18.01%
-1.62% to 0.17%	996	29.79%	47.80%
0.17% to 1.95%	1183	35.39%	83.19%
1.95% to 3.73%	413	12.35%	95.54%
3.73% to 5.52%	95	2.84%	98.38%
5.52% to 7.30%	36	1.08%	99.46%
Greater than 7.30%	18	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.21%	2.54%	77.65%	68.27%
±2σ	-4.59%	4.92%	95.15%	95.45%
±3σ	-6.97%	7.30%	98.83%	99.73%

Descriptive Statistics

Mean	0.166%
Standard Error	0.041%
Median	0.272%
Mode	1.262%
Standard Deviation	2.378%
Sample Variance	5.655%
Kurtosis	9.52
Skewness	-0.52
Range	44.725%
Minimum	-27.328%
Maximum	17.397%
Count	3343

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.648%	1873	56.03%	0.923%
Negative	-1.727%	1465	43.82%	-0.757%
Zero	0.000%	5	0.15%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	2.46%
12	1 Quarter	1.90%
52	1 Year	3.09%
156	3 Years	2.74%
260	5 Years	3.16%
520	10 Years	3.00%
1,040	20 Years	3.21%
2,600	50 Years	3.18%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.07. Further, an Excess Kurtosis of 38.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.19%	0	0.00%	0.00%
-3.19% to -1.57%	0	0.00%	0.00%
-1.57% to 0.06%	0	0.00%	0.00%
0.06% to 1.68%	494	14.77%	14.77%
1.68% to 3.31%	1613	48.24%	63.01%
3.31% to 4.93%	754	22.55%	85.56%
4.93% to 6.56%	291	8.70%	94.26%
6.56% to 8.18%	101	3.02%	97.28%
8.18% to 9.81%	40	1.20%	98.47%
Greater than 9.81%	51	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.14%	5.47%	86.51%	68.27%
±2σ	-1.03%	7.64%	96.62%	95.45%
±3σ	-3.19%	9.81%	98.47%	99.73%

Descriptive Statistics

Mean	3.306%
Standard Error	0.037%
Median	2.776%
Mode	1.747%
Standard Deviation	2.167%
Sample Variance	4.696%
Kurtosis	38.12
Skewness	4.07
Range	39.326%
Minimum	0.571%
Maximum	39.897%
Count	3344

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.306%	3344	100.00%	3.306%
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 1.73. Further, an Excess Kurtosis of 22.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.32%	14	0.42%	0.42%
-7.32% to -5.51%	25	0.75%	1.17%
-5.51% to -3.71%	92	2.75%	3.92%
-3.71% to -1.90%	425	12.71%	16.63%
-1.90% to -0.10%	1261	37.71%	54.34%
-0.10% to 1.71%	951	28.44%	82.78%
1.71% to 3.52%	382	11.42%	94.20%
3.52% to 5.32%	130	3.89%	98.09%
5.32% to 7.13%	41	1.23%	99.31%
Greater than 7.13%	23	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.50%	2.31%	78.32%	68.27%
±2σ	-4.91%	4.72%	95.39%	95.45%
±3σ	-7.32%	7.13%	98.89%	99.73%

Descriptive Statistics

Mean	-0.095%
Standard Error	0.042%
Median	-0.268%
Mode	0.000%
Standard Deviation	2.407%
Sample Variance	5.793%
Kurtosis	22.19
Skewness	1.73
Range	49.752%
Minimum	-12.147%
Maximum	37.605%
Count	3344

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.804%	1458	43.60%	0.787%
Negative	-1.568%	1881	56.25%	-0.882%
Zero	0.000%	5	0.15%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.43. Further, an Excess Kurtosis of 1.62 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.20%	4	0.52%	0.52%
-12.20% to -8.97%	13	1.69%	2.21%
-8.97% to -5.75%	41	5.33%	7.54%
-5.75% to -2.53%	84	10.92%	18.47%
-2.53% to 0.69%	213	27.70%	46.16%
0.69% to 3.92%	257	33.42%	79.58%
3.92% to 7.14%	116	15.08%	94.67%
7.14% to 10.36%	30	3.90%	98.57%
10.36% to 13.59%	10	1.30%	99.87%
Greater than 13.59%	1	0.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.60%	4.99%	73.34%	68.27%
±2σ	-7.90%	9.29%	94.15%	95.45%
±3σ	-12.20%	13.58%	99.35%	99.73%

Descriptive Statistics

Mean	0.694%
Standard Error	0.155%
Median	0.987%
Mode	1.132%
Standard Deviation	4.297%
Sample Variance	18.466%
Kurtosis	1.62
Skewness	-0.43
Range	38.068%
Minimum	-21.763%
Maximum	16.305%
Count	769

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.357%	463	60.21%	2.021%
Negative	-3.346%	305	39.66%	-1.327%
Zero	0.000%	1	0.13%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	3.19%
12	1 Year	5.93%
36	3 Years	5.86%
60	5 Years	6.84%
120	10 Years	6.68%
240	20 Years	6.88%
600	50 Years	6.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.65. Further, an Excess Kurtosis of 23.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.45%	0	0.00%	0.00%
-6.45% to -3.05%	0	0.00%	0.00%
-3.05% to 0.36%	0	0.00%	0.00%
0.36% to 3.76%	108	14.03%	14.03%
3.76% to 7.16%	387	50.26%	64.29%
7.16% to 10.56%	172	22.34%	86.62%
10.56% to 13.97%	53	6.88%	93.51%
13.97% to 17.37%	27	3.51%	97.01%
17.37% to 20.77%	13	1.69%	98.70%
Greater than 20.77%	10	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.62%	11.70%	88.44%	68.27%
±2σ	-1.91%	16.24%	95.97%	95.45%
±3σ	-6.45%	20.77%	98.70%	99.73%

Descriptive Statistics

Mean	7.162%
Standard Error	0.164%
Median	5.996%
Mode	4.261%
Standard Deviation	4.537%
Sample Variance	20.587%
Kurtosis	23.32
Skewness	3.65
Range	49.963%
Minimum	2.000%
Maximum	51.963%
Count	770

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.162%	770	100.00%	7.162%
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 0.91. Further, an Excess Kurtosis of 3.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.61%	2	0.26%	0.26%
-13.61% to -10.32%	3	0.39%	0.65%
-10.32% to -7.04%	25	3.25%	3.90%
-7.04% to -3.76%	126	16.36%	20.26%
-3.76% to -0.48%	273	35.45%	55.71%
-0.48% to 2.81%	204	26.49%	82.21%
2.81% to 6.09%	79	10.26%	92.47%
6.09% to 9.37%	37	4.81%	97.27%
9.37% to 12.65%	15	1.95%	99.22%
Greater than 12.65%	6	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.85%	3.90%	75.06%	68.27%
±2σ	-9.23%	8.28%	94.29%	95.45%
±3σ	-13.61%	12.65%	98.96%	99.73%

Descriptive Statistics

Mean	-0.477%
Standard Error	0.158%
Median	-0.933%
Mode	-4.088%
Standard Deviation	4.377%
Sample Variance	19.161%
Kurtosis	3.33
Skewness	0.91
Range	42.044%
Minimum	-14.227%
Maximum	27.817%
Count	770

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.542%	310	40.26%	1.426%
Negative	-3.192%	459	59.61%	-1.903%
Zero	0.000%	1	0.13%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.31. Further, an Excess Kurtosis of 1.01 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.57%	2	0.78%	0.78%
-18.57% to -13.41%	3	1.17%	1.95%
-13.41% to -8.26%	12	4.67%	6.61%
-8.26% to -3.11%	32	12.45%	19.07%
-3.11% to 2.04%	77	29.96%	49.03%
2.04% to 7.20%	80	31.13%	80.16%
7.20% to 12.35%	35	13.62%	93.77%
12.35% to 17.50%	14	5.45%	99.22%
17.50% to 22.66%	1	0.39%	99.61%
Greater than 22.66%	1	0.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.83%	8.91%	71.98%	68.27%
±2σ	-11.70%	15.79%	95.33%	95.45%
±3σ	-18.56%	22.66%	98.83%	99.73%

Descriptive Statistics

Mean	2.045%
Standard Error	0.429%
Median	2.278%
Mode	4.091%
Standard Deviation	6.870%
Sample Variance	47.198%
Kurtosis	1.01
Skewness	-0.31
Range	48.430%
Minimum	-23.563%
Maximum	24.867%
Count	257

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.935%	165	64.20%	3.810%
Negative	-4.932%	92	35.80%	-1.766%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	9.16%
12	3 Years	11.93%
20	5 Years	12.02%
40	10 Years	11.96%
80	20 Years	12.16%
200	50 Years	11.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.89. Further, an Excess Kurtosis of 11.90 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.07%	0	0.00%	0.00%
-10.07% to -4.34%	0	0.00%	0.00%
-4.34% to 1.38%	0	0.00%	0.00%
1.38% to 7.11%	44	17.05%	17.05%
7.11% to 12.83%	120	46.51%	63.57%
12.83% to 18.56%	62	24.03%	87.60%
18.56% to 24.28%	18	6.98%	94.57%
24.28% to 30.00%	5	1.94%	96.51%
30.00% to 35.73%	2	0.78%	97.29%
Greater than 35.73%	7	2.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.20%	20.46%	87.98%	68.27%
±2σ	-2.44%	28.10%	96.12%	95.45%
±3σ	-10.07%	35.73%	97.29%	99.73%

Descriptive Statistics

Mean	12.831%
Standard Error	0.475%
Median	11.180%
Mode	11.470%
Standard Deviation	7.633%
Sample Variance	58.258%
Kurtosis	11.90
Skewness	2.89
Range	53.148%
Minimum	3.217%
Maximum	56.365%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.831%	258	100.00%	12.831%
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 0.95. Further, an Excess Kurtosis of 2.56 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.16%	0	0.00%	0.00%
-22.16% to -16.99%	1	0.39%	0.39%
-16.99% to -11.83%	7	2.71%	3.10%
-11.83% to -6.67%	43	16.67%	19.77%
-6.67% to -1.50%	92	35.66%	55.43%
-1.50% to 3.66%	70	27.13%	82.56%
3.66% to 8.82%	27	10.47%	93.02%
8.82% to 13.98%	11	4.26%	97.29%
13.98% to 19.15%	5	1.94%	99.22%
Greater than 19.15%	2	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.39%	5.38%	72.87%	68.27%
±2σ	-15.27%	12.26%	95.74%	95.45%
±3σ	-22.16%	19.15%	99.22%	99.73%

Descriptive Statistics

Mean	-1.505%
Standard Error	0.429%
Median	-2.222%
Mode	-0.111%
Standard Deviation	6.884%
Sample Variance	47.386%
Kurtosis	2.56
Skewness	0.95
Range	50.488%
Minimum	-19.451%
Maximum	31.037%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.426%	93	36.05%	1.956%
Negative	-5.412%	165	63.95%	-3.461%
Zero	0.000%	0	0.00%	0.000%

^GSPC Deep Analytical Report