^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%	4.53%	4.38%	6.83%
Quarterly	6.88%	7.62%	6.89%	12.24%
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 19.55 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%	1.80%
-2.30% to -1.52%	538	3.34%	5.14%
-1.52% to -0.74%	1722	10.68%	15.82%
-0.74% to 0.03%	5381	33.37%	49.19%
0.03% to 0.81%	5666	35.14%	84.33%
0.81% to 1.59%	1790	11.10%	95.44%
1.59% to 2.37%	487	3.02%	98.46%
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%	78.84%	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	0.046%
Mode	0.000%
Standard Deviation	1.039%
Sample Variance	1.079%
Kurtosis	19.55
Skewness	-0.57
Range	32.047%
Minimum	-20.467%
Maximum	11.580%
Count	16124

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.689%	8535	52.93%	0.365%
Negative	-0.709%	7538	46.75%	-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	1.53%
20	1 Month	1.50%
60	1 Quarter	1.18%
250	1 Year	1.28%
750	3 Years	1.14%
1,250	5 Years	1.30%
2,500	10 Years	1.24%
5,000	20 Years	1.34%
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 53.33 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%	3410	21.15%	21.15%
0.74% to 1.40%	5790	35.91%	57.05%
1.40% to 2.06%	4514	27.99%	85.05%
2.06% to 2.73%	1490	9.24%	94.29%
2.73% to 3.39%	519	3.22%	97.51%
3.39% to 4.05%	207	1.28%	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%	80.56%	68.27%
±2σ	-0.36%	3.17%	96.76%	95.45%
±3σ	-1.24%	4.05%	98.79%	99.73%

Descriptive Statistics

Mean	1.403%
Standard Error	0.007%
Median	1.275%
Mode	0.609%
Standard Deviation	0.882%
Sample Variance	0.778%
Kurtosis	53.33
Skewness	3.97
Range	25.593%
Minimum	0.146%
Maximum	25.739%
Count	16125

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.403%	16125	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	3.00%	4.50%
-1.50% to -0.76%	1828	11.34%	15.84%
-0.76% to -0.02%	5778	35.83%	51.67%
-0.02% to 0.72%	5208	32.30%	83.97%
0.72% to 1.46%	1720	10.67%	94.64%
1.46% to 2.19%	570	3.53%	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	16125

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.687%	7551	46.83%	0.322%
Negative	-0.644%	8517	52.82%	-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%	1.70%
-5.18% to -3.40%	139	4.15%	5.86%
-3.40% to -1.62%	406	12.13%	17.99%
-1.62% to 0.17%	997	29.79%	47.77%
0.17% to 1.95%	1186	35.43%	83.21%
1.95% to 3.73%	413	12.34%	95.55%
3.73% to 5.51%	95	2.84%	98.39%
5.51% 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%	77.68%	68.27%
±2σ	-4.59%	4.92%	95.16%	95.45%
±3σ	-6.97%	7.30%	98.83%	99.73%

Descriptive Statistics

Mean	0.165%
Standard Error	0.041%
Median	0.268%
Mode	1.262%
Standard Deviation	2.377%
Sample Variance	5.650%
Kurtosis	9.52
Skewness	-0.52
Range	44.725%
Minimum	-27.328%
Maximum	17.397%
Count	3347

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.647%	1874	55.99%	0.922%
Negative	-1.726%	1468	43.86%	-0.757%
Zero	0.000%	5	0.15%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	3.35%
12	1 Quarter	2.49%
52	1 Year	3.06%
156	3 Years	2.72%
260	5 Years	3.16%
520	10 Years	3.01%
1,040	20 Years	3.22%
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 38.15 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%	495	14.78%	14.78%
1.68% to 3.31%	1613	48.18%	62.96%
3.31% to 4.93%	757	22.61%	85.57%
4.93% to 6.56%	291	8.69%	94.27%
6.56% to 8.18%	101	3.02%	97.28%
8.18% to 9.80%	40	1.19%	98.48%
Greater than 9.80%	51	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.14%	5.47%	86.53%	68.27%
±2σ	-1.02%	7.64%	96.62%	95.45%
±3σ	-3.19%	9.80%	98.48%	99.73%

Descriptive Statistics

Mean	3.307%
Standard Error	0.037%
Median	2.779%
Mode	1.747%
Standard Deviation	2.166%
Sample Variance	4.691%
Kurtosis	38.15
Skewness	4.07
Range	39.326%
Minimum	0.571%
Maximum	39.897%
Count	3348

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.307%	3348	100.00%	3.307%
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 22.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.31%	14	0.42%	0.42%
-7.31% to -5.51%	25	0.75%	1.16%
-5.51% to -3.70%	92	2.75%	3.91%
-3.70% to -1.90%	426	12.72%	16.64%
-1.90% to -0.09%	1261	37.66%	54.30%
-0.09% to 1.71%	953	28.46%	82.77%
1.71% to 3.52%	383	11.44%	94.21%
3.52% to 5.32%	130	3.88%	98.09%
5.32% to 7.12%	41	1.22%	99.31%
Greater than 7.12%	23	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.50%	2.31%	78.35%	68.27%
±2σ	-4.91%	4.72%	95.40%	95.45%
±3σ	-7.31%	7.12%	98.89%	99.73%

Descriptive Statistics

Mean	-0.094%
Standard Error	0.042%
Median	-0.264%
Mode	0.000%
Standard Deviation	2.406%
Sample Variance	5.787%
Kurtosis	22.20
Skewness	1.73
Range	49.752%
Minimum	-12.147%
Maximum	37.605%
Count	3348

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.803%	1461	43.64%	0.787%
Negative	-1.566%	1882	56.21%	-0.880%
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 1.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.21%	4	0.52%	0.52%
-12.21% to -8.98%	13	1.69%	2.21%
-8.98% to -5.76%	40	5.19%	7.40%
-5.76% to -2.54%	86	11.17%	18.57%
-2.54% to 0.69%	211	27.40%	45.97%
0.69% to 3.91%	259	33.64%	79.61%
3.91% to 7.13%	116	15.06%	94.68%
7.13% to 10.36%	30	3.90%	98.57%
10.36% to 13.58%	10	1.30%	99.87%
Greater than 13.58%	1	0.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.61%	4.99%	73.25%	68.27%
±2σ	-7.91%	9.28%	94.29%	95.45%
±3σ	-12.21%	13.58%	99.35%	99.73%

Descriptive Statistics

Mean	0.687%
Standard Error	0.155%
Median	0.985%
Mode	1.132%
Standard Deviation	4.298%
Sample Variance	18.473%
Kurtosis	1.61
Skewness	-0.43
Range	38.068%
Minimum	-21.763%
Maximum	16.305%
Count	770

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.357%	463	60.13%	2.019%
Negative	-3.350%	306	39.74%	-1.331%
Zero	0.000%	1	0.13%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	4.17%
12	1 Year	5.76%
36	3 Years	5.82%
60	5 Years	6.83%
120	10 Years	6.67%
240	20 Years	6.89%
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 3.66. Further, an Excess Kurtosis of 23.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.44%	0	0.00%	0.00%
-6.44% to -3.04%	0	0.00%	0.00%
-3.04% to 0.36%	0	0.00%	0.00%
0.36% to 3.76%	108	14.01%	14.01%
3.76% to 7.16%	388	50.32%	64.33%
7.16% to 10.56%	172	22.31%	86.64%
10.56% to 13.96%	53	6.87%	93.51%
13.96% to 17.36%	27	3.50%	97.02%
17.36% to 20.76%	13	1.69%	98.70%
Greater than 20.76%	10	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.63%	11.70%	88.46%	68.27%
±2σ	-1.91%	16.23%	95.98%	95.45%
±3σ	-6.44%	20.76%	98.70%	99.73%

Descriptive Statistics

Mean	7.162%
Standard Error	0.163%
Median	5.999%
Mode	4.261%
Standard Deviation	4.534%
Sample Variance	20.561%
Kurtosis	23.36
Skewness	3.66
Range	49.963%
Minimum	2.000%
Maximum	51.963%
Count	771

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.162%	771	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 3.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.60%	2	0.26%	0.26%
-13.60% to -10.32%	3	0.39%	0.65%
-10.32% to -7.04%	25	3.24%	3.89%
-7.04% to -3.75%	127	16.47%	20.36%
-3.75% to -0.47%	272	35.28%	55.64%
-0.47% to 2.81%	204	26.46%	82.10%
2.81% to 6.09%	80	10.38%	92.48%
6.09% to 9.38%	37	4.80%	97.28%
9.38% to 12.66%	15	1.95%	99.22%
Greater than 12.66%	6	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.85%	3.91%	75.10%	68.27%
±2σ	-9.22%	8.28%	94.42%	95.45%
±3σ	-13.60%	12.66%	98.96%	99.73%

Descriptive Statistics

Mean	-0.471%
Standard Error	0.158%
Median	-0.931%
Mode	-4.088%
Standard Deviation	4.377%
Sample Variance	19.157%
Kurtosis	3.32
Skewness	0.91
Range	42.044%
Minimum	-14.227%
Maximum	27.817%
Count	771

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.543%	311	40.34%	1.429%
Negative	-3.192%	459	59.53%	-1.900%
Zero	0.000%	1	0.13%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.30. Further, an Excess Kurtosis of 0.98 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.62%	2	0.78%	0.78%
-18.62% to -13.46%	3	1.17%	1.95%
-13.46% to -8.30%	12	4.67%	6.61%
-8.30% to -3.13%	33	12.84%	19.46%
-3.13% to 2.03%	76	29.57%	49.03%
2.03% to 7.19%	80	31.13%	80.16%
7.19% to 12.35%	35	13.62%	93.77%
12.35% to 17.51%	14	5.45%	99.22%
17.51% to 22.67%	1	0.39%	99.61%
Greater than 22.67%	1	0.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.85%	8.91%	71.60%	68.27%
±2σ	-11.74%	15.79%	95.33%	95.45%
±3σ	-18.62%	22.67%	98.83%	99.73%

Descriptive Statistics

Mean	2.027%
Standard Error	0.429%
Median	2.278%
Mode	4.091%
Standard Deviation	6.882%
Sample Variance	47.364%
Kurtosis	0.98
Skewness	-0.30
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	-4.981%	92	35.80%	-1.783%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	10.25%
12	3 Years	12.29%
20	5 Years	12.24%
40	10 Years	12.07%
80	20 Years	12.21%
200	50 Years	11.85%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.91. Further, an Excess Kurtosis of 12.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.99%	0	0.00%	0.00%
-9.99% to -4.28%	0	0.00%	0.00%
-4.28% to 1.43%	0	0.00%	0.00%
1.43% to 7.14%	43	16.67%	16.67%
7.14% to 12.85%	122	47.29%	63.95%
12.85% to 18.56%	61	23.64%	87.60%
18.56% to 24.27%	18	6.98%	94.57%
24.27% to 29.98%	5	1.94%	96.51%
29.98% to 35.70%	2	0.78%	97.29%
Greater than 35.70%	7	2.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.23%	20.46%	88.37%	68.27%
±2σ	-2.38%	28.08%	96.12%	95.45%
±3σ	-9.99%	35.70%	97.29%	99.73%

Descriptive Statistics

Mean	12.850%
Standard Error	0.474%
Median	11.180%
Mode	11.470%
Standard Deviation	7.615%
Sample Variance	57.987%
Kurtosis	12.00
Skewness	2.91
Range	52.625%
Minimum	3.740%
Maximum	56.365%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.850%	258	100.00%	12.850%
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 0.94. Further, an Excess Kurtosis of 2.51 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.17%	0	0.00%	0.00%
-22.17% to -17.00%	1	0.39%	0.39%
-17.00% to -11.83%	7	2.71%	3.10%
-11.83% to -6.66%	43	16.67%	19.77%
-6.66% to -1.49%	92	35.66%	55.43%
-1.49% to 3.68%	69	26.74%	82.17%
3.68% to 8.85%	28	10.85%	93.02%
8.85% to 14.02%	11	4.26%	97.29%
14.02% to 19.20%	5	1.94%	99.22%
Greater than 19.20%	2	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.38%	5.41%	72.87%	68.27%
±2σ	-15.28%	12.30%	95.74%	95.45%
±3σ	-22.17%	19.20%	99.22%	99.73%

Descriptive Statistics

Mean	-1.487%
Standard Error	0.429%
Median	-2.222%
Mode	-0.111%
Standard Deviation	6.894%
Sample Variance	47.533%
Kurtosis	2.51
Skewness	0.94
Range	50.488%
Minimum	-19.451%
Maximum	31.037%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.477%	93	36.05%	1.974%
Negative	-5.412%	165	63.95%	-3.461%
Zero	0.000%	0	0.00%	0.000%

^GSPC Deep Analytical Report