MA - Detail Report

Quick Overview

Timeframe	C-C DoR σ (Historical)	H-L DoR σ (Historical)	O-C DoR σ (Historical)	5Y ATRP (Avg)	Binomial IV (Period)	Yahoo IV (Period)	1σ Lower (68.27%)	1σ Upper	2σ Lower (95.45%)	2σ Upper
Daily	2.04%	1.85%	1.71%	2.07%	—	1.88%	495.18	513.36	486.34	522.70
Weekly	4.34%	4.74%	4.32%	4.84%	—	4.14%	484.58	524.60	465.73	545.83
Monthly	8.18%	9.07%	7.85%	10.24%	—	8.62%	464.22	547.60	427.42	594.75
Quarterly	14.42%	16.21%	13.04%	16.37%	—	14.92%	436.98	581.74	378.73	671.21
Annual	—	—	—	—	—	29.85%	378.73	671.21	284.49	893.55
Option Time Horizon	—	—	—	—	—	11.27%	452.58	561.69	406.25	625.75

Calculation Notes: Computed at 2026-03-23T16:43 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $504.19 | Strike (K): $505.00 (first OTM call ≥ spot) | Observed Mid-Price: $22.3750 (Bid $22.0500 / Ask $22.7000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.63% | Binomial IV (Annual): 0.00% (CRR binomial tree, American, n=20 steps) | BS IV: 28.61% (European Black-Scholes) | Yahoo IV (Annual): 29.85% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2026-01-09	$0.8700
2025-10-09	$0.7600
2025-07-09	$0.7600
2025-04-09	$0.7600
2025-01-10	$0.7600
2024-10-09	$0.6600
2024-07-09	$0.6600
2024-04-08	$0.6600
2024-01-08	$0.6600
2023-10-05	$0.5700
2023-07-06	$0.5700
2023-04-05	$0.5700
2023-01-06	$0.5700
2022-10-06	$0.4900
2022-07-07	$0.4900
2022-04-07	$0.4900
2022-01-06	$0.4900
2021-10-07	$0.4400
2021-07-08	$0.4400
2021-04-08	$0.4400
2021-01-07	$0.4400
2020-10-08	$0.4000
2020-07-08	$0.4000
2020-04-08	$0.4000
2020-01-08	$0.4000
2019-10-08	$0.3300
2019-07-08	$0.3300
2019-04-08	$0.3300
2019-01-08	$0.3300
2018-10-05	$0.2500
2018-07-06	$0.2500
2018-04-06	$0.2500
2018-01-08	$0.2500
2017-10-05	$0.2200
2017-07-05	$0.2200
2017-04-05	$0.2200
2017-01-05	$0.2200
2016-10-05	$0.1900
2016-07-06	$0.1900
2016-04-06	$0.1900
2016-01-06	$0.1900
2015-10-07	$0.1600
2015-07-07	$0.1600
2015-04-07	$0.1600
2015-01-07	$0.1600
2014-10-07	$0.1100
2014-07-07	$0.1100
2014-04-07	$0.1100
2014-01-07	$0.1100
2013-10-07	$0.0600
2013-07-05	$0.0600
2013-04-05	$0.0600
2013-01-07	$0.0300
2012-10-05	$0.0300
2012-07-05	$0.0300
2012-04-04	$0.0300
2012-01-05	$0.0150
2011-10-05	$0.0150
2011-07-06	$0.0150
2011-04-06	$0.0150
2011-01-06	$0.0150
2010-10-07	$0.0150
2010-07-01	$0.0150
2010-04-07	$0.0150
2010-01-06	$0.0150
2009-10-07	$0.0150
2009-07-08	$0.0150
2009-04-08	$0.0150
2009-01-07	$0.0150
2008-10-08	$0.0150
2008-07-09	$0.0150
2008-04-07	$0.0150
2008-01-09	$0.0150
2007-10-17	$0.0150
2007-06-29	$0.0150
2007-04-04	$0.0150
2007-01-10	$0.0090
2006-10-05	$0.0090

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 10.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.01%	36	0.72%	0.72%
-6.01% to -4.48%	58	1.16%	1.89%
-4.48% to -2.95%	163	3.27%	5.15%
-2.95% to -1.41%	480	9.63%	14.78%
-1.41% to 0.12%	1744	34.98%	49.76%
0.12% to 1.65%	1791	35.92%	85.68%
1.65% to 3.18%	496	9.95%	95.63%
3.18% to 4.71%	119	2.39%	98.01%
4.71% to 6.24%	51	1.02%	99.04%
Greater than 6.24%	48	0.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.92%	2.16%	80.37%	68.27%
±2σ	-3.97%	4.20%	94.83%	95.45%
±3σ	-6.01%	6.24%	98.32%	99.73%

Descriptive Statistics

Mean	0.117%
Standard Error	0.029%
Median	0.123%
Mode	-0.083%
Standard Deviation	2.042%
Sample Variance	4.169%
Kurtosis	10.48
Skewness	0.67
Range	33.571%
Minimum	-12.725%
Maximum	20.846%
Count	4986

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.353%	2684	53.83%	0.728%
Negative	-1.330%	2293	45.99%	-0.612%
Zero	0.000%	9	0.18%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.28%
20	1 Month	2.21%
60	1 Quarter	2.26%
250	1 Year	2.05%
750	3 Years	1.71%
1,250	5 Years	2.07%
2,500	10 Years	2.10%
5,000	20 Years	2.54%
12,500	50 Years	2.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.13. Further, an Excess Kurtosis of 15.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.16%	0	0.00%	0.00%
-3.16% to -1.77%	0	0.00%	0.00%
-1.77% to -0.38%	0	0.00%	0.00%
-0.38% to 1.01%	594	11.91%	11.91%
1.01% to 2.40%	2702	54.18%	66.09%
2.40% to 3.79%	994	19.93%	86.02%
3.79% to 5.18%	360	7.22%	93.24%
5.18% to 6.58%	154	3.09%	96.33%
6.58% to 7.97%	88	1.76%	98.10%
Greater than 7.97%	95	1.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.55%	4.26%	89.07%	68.27%
±2σ	-1.31%	6.11%	95.61%	95.45%
±3σ	-3.16%	7.97%	98.10%	99.73%

Descriptive Statistics

Mean	2.403%
Standard Error	0.026%
Median	1.858%
Mode	1.351%
Standard Deviation	1.855%
Sample Variance	3.442%
Kurtosis	15.62
Skewness	3.13
Range	20.954%
Minimum	0.410%
Maximum	21.364%
Count	4987

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.403%	4987	100.00%	2.403%
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 Fairly Symmetrical with a Skewness factor of 0.25. Further, an Excess Kurtosis of 6.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.17%	49	0.98%	0.98%
-5.17% to -3.88%	42	0.84%	1.82%
-3.88% to -2.60%	129	2.59%	4.41%
-2.60% to -1.32%	528	10.59%	15.00%
-1.32% to -0.03%	1837	36.84%	51.83%
-0.03% to 1.25%	1631	32.71%	84.54%
1.25% to 2.54%	513	10.29%	94.83%
2.54% to 3.82%	146	2.93%	97.75%
3.82% to 5.11%	65	1.30%	99.06%
Greater than 5.11%	47	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.74%	1.68%	79.45%	68.27%
±2σ	-3.46%	3.40%	94.69%	95.45%
±3σ	-5.17%	5.11%	98.07%	99.73%

Descriptive Statistics

Mean	-0.031%
Standard Error	0.024%
Median	-0.080%
Mode	0.000%
Standard Deviation	1.713%
Sample Variance	2.936%
Kurtosis	6.91
Skewness	0.25
Range	26.320%
Minimum	-12.391%
Maximum	13.929%
Count	4987

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.197%	2341	46.94%	0.562%
Negative	-1.120%	2639	52.92%	-0.593%
Zero	0.000%	7	0.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 6.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.47%	10	0.97%	0.97%
-12.47% to -9.22%	8	0.77%	1.74%
-9.22% to -5.96%	36	3.48%	5.22%
-5.96% to -2.70%	114	11.03%	16.25%
-2.70% to 0.56%	337	32.59%	48.84%
0.56% to 3.82%	383	37.04%	85.88%
3.82% to 7.08%	96	9.28%	95.16%
7.08% to 10.34%	29	2.80%	97.97%
10.34% to 13.60%	8	0.77%	98.74%
Greater than 13.60%	13	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.78%	4.90%	77.66%	68.27%
±2σ	-8.13%	9.25%	94.49%	95.45%
±3σ	-12.47%	13.60%	97.78%	99.73%

Descriptive Statistics

Mean	0.560%
Standard Error	0.135%
Median	0.623%
Mode	-1.888%
Standard Deviation	4.345%
Sample Variance	18.880%
Kurtosis	6.52
Skewness	0.67
Range	49.727%
Minimum	-16.973%
Maximum	32.754%
Count	1034

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.965%	617	59.67%	1.769%
Negative	-2.999%	417	40.33%	-1.209%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	5.24%
12	1 Quarter	5.48%
52	1 Year	4.75%
156	3 Years	3.90%
260	5 Years	4.84%
520	10 Years	4.87%
1,040	20 Years	5.94%
2,600	50 Years	5.94%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.70. Further, an Excess Kurtosis of 10.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.05%	0	0.00%	0.00%
-8.05% to -4.50%	0	0.00%	0.00%
-4.50% to -0.95%	0	0.00%	0.00%
-0.95% to 2.60%	132	12.75%	12.75%
2.60% to 6.16%	561	54.20%	66.96%
6.16% to 9.71%	197	19.03%	85.99%
9.71% to 13.26%	74	7.15%	93.14%
13.26% to 16.81%	30	2.90%	96.04%
16.81% to 20.36%	15	1.45%	97.49%
Greater than 20.36%	26	2.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.42%	10.89%	88.21%	68.27%
±2σ	-3.32%	15.63%	95.07%	95.45%
±3σ	-8.05%	20.36%	97.49%	99.73%

Descriptive Statistics

Mean	6.156%
Standard Error	0.147%
Median	4.726%
Mode	3.376%
Standard Deviation	4.736%
Sample Variance	22.427%
Kurtosis	10.11
Skewness	2.70
Range	37.042%
Minimum	1.076%
Maximum	38.118%
Count	1035

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.156%	1035	100.00%	6.156%
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 0.58. Further, an Excess Kurtosis of 5.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.19%	9	0.87%	0.87%
-13.19% to -9.96%	10	0.97%	1.84%
-9.96% to -6.72%	27	2.61%	4.44%
-6.72% to -3.48%	107	10.34%	14.78%
-3.48% to -0.25%	411	39.71%	54.49%
-0.25% to 2.99%	310	29.95%	84.44%
2.99% to 6.23%	104	10.05%	94.49%
6.23% to 9.46%	32	3.09%	97.58%
9.46% to 12.70%	11	1.06%	98.65%
Greater than 12.70%	14	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.56%	4.07%	79.23%	68.27%
±2σ	-8.88%	8.39%	94.20%	95.45%
±3σ	-13.19%	12.70%	97.78%	99.73%

Descriptive Statistics

Mean	-0.246%
Standard Error	0.134%
Median	-0.510%
Mode	-2.117%
Standard Deviation	4.316%
Sample Variance	18.627%
Kurtosis	5.35
Skewness	0.58
Range	46.993%
Minimum	-24.507%
Maximum	22.486%
Count	1035

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.176%	438	42.32%	1.344%
Negative	-2.756%	597	57.68%	-1.590%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.49. Further, an Excess Kurtosis of 2.77 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.16%	1	0.42%	0.42%
-22.16% to -16.03%	3	1.26%	1.68%
-16.03% to -9.90%	10	4.20%	5.88%
-9.90% to -3.77%	37	15.55%	21.43%
-3.77% to 2.37%	72	30.25%	51.68%
2.37% to 8.50%	76	31.93%	83.61%
8.50% to 14.63%	26	10.92%	94.54%
14.63% to 20.76%	7	2.94%	97.48%
20.76% to 26.89%	3	1.26%	98.74%
Greater than 26.89%	3	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.81%	10.54%	78.57%	68.27%
±2σ	-13.98%	18.72%	94.96%	95.45%
±3σ	-22.16%	26.89%	98.32%	99.73%

Descriptive Statistics

Mean	2.366%
Standard Error	0.530%
Median	2.208%
Mode	-6.177%
Standard Deviation	8.175%
Sample Variance	66.823%
Kurtosis	2.77
Skewness	0.49
Range	64.203%
Minimum	-26.889%
Maximum	37.314%
Count	238

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.956%	148	62.19%	4.326%
Negative	-5.181%	90	37.81%	-1.959%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.19%
12	1 Year	9.52%
36	3 Years	8.39%
60	5 Years	10.24%
120	10 Years	10.59%
240	20 Years	12.63%
600	50 Years	12.63%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.42. Further, an Excess Kurtosis of 8.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.55%	0	0.00%	0.00%
-13.55% to -6.75%	0	0.00%	0.00%
-6.75% to 0.06%	0	0.00%	0.00%
0.06% to 6.86%	41	17.15%	17.15%
6.86% to 13.66%	115	48.12%	65.27%
13.66% to 20.46%	47	19.67%	84.94%
20.46% to 27.26%	22	9.21%	94.14%
27.26% to 34.06%	6	2.51%	96.65%
34.06% to 40.86%	3	1.26%	97.91%
Greater than 40.86%	5	2.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.59%	22.73%	87.03%	68.27%
±2σ	-4.48%	31.79%	95.40%	95.45%
±3σ	-13.55%	40.86%	97.91%	99.73%

Descriptive Statistics

Mean	13.658%
Standard Error	0.587%
Median	10.598%
Mode	5.946%
Standard Deviation	9.068%
Sample Variance	82.225%
Kurtosis	8.27
Skewness	2.42
Range	61.730%
Minimum	2.945%
Maximum	64.675%
Count	239

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.658%	239	100.00%	13.658%
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 0.76. Further, an Excess Kurtosis of 3.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.11%	1	0.42%	0.42%
-25.11% to -19.22%	3	1.26%	1.67%
-19.22% to -13.34%	7	2.93%	4.60%
-13.34% to -7.45%	30	12.55%	17.15%
-7.45% to -1.56%	83	34.73%	51.88%
-1.56% to 4.32%	70	29.29%	81.17%
4.32% to 10.21%	30	12.55%	93.72%
10.21% to 16.09%	9	3.77%	97.49%
16.09% to 21.98%	3	1.26%	98.74%
Greater than 21.98%	3	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.41%	6.28%	76.57%	68.27%
±2σ	-17.26%	14.13%	94.98%	95.45%
±3σ	-25.11%	21.98%	98.33%	99.73%

Descriptive Statistics

Mean	-1.565%
Standard Error	0.508%
Median	-1.922%
Mode	-0.913%
Standard Deviation	7.848%
Sample Variance	61.592%
Kurtosis	3.50
Skewness	0.76
Range	64.301%
Minimum	-25.644%
Maximum	38.657%
Count	239

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.190%	84	35.15%	2.176%
Negative	-5.767%	155	64.85%	-3.740%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.85. Further, an Excess Kurtosis of 3.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.07%	1	1.27%	1.27%
-36.07% to -25.25%	0	0.00%	1.27%
-25.25% to -14.44%	1	1.27%	2.53%
-14.44% to -3.62%	10	12.66%	15.19%
-3.62% to 7.20%	29	36.71%	51.90%
7.20% to 18.01%	28	35.44%	87.34%
18.01% to 28.83%	5	6.33%	93.67%
28.83% to 39.64%	2	2.53%	96.20%
39.64% to 50.46%	1	1.27%	97.47%
Greater than 50.46%	2	2.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.23%	21.62%	83.54%	68.27%
±2σ	-21.65%	36.04%	94.94%	95.45%
±3σ	-36.07%	50.46%	96.20%	99.73%

Descriptive Statistics

Mean	7.195%
Standard Error	1.623%
Median	6.781%
Mode	-39.398%
Standard Deviation	14.422%
Sample Variance	207.985%
Kurtosis	3.79
Skewness	0.85
Range	101.151%
Minimum	-39.398%
Maximum	61.753%
Count	79

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.264%	55	69.62%	9.234%
Negative	-6.712%	24	30.38%	-2.039%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	12.34%
12	3 Years	14.54%
20	5 Years	16.37%
40	10 Years	18.21%
80	20 Years	22.44%
200	50 Years	22.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.55. Further, an Excess Kurtosis of 8.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.36%	0	0.00%	0.00%
-23.36% to -11.20%	0	0.00%	0.00%
-11.20% to 0.96%	0	0.00%	0.00%
0.96% to 13.11%	13	16.25%	16.25%
13.11% to 25.27%	41	51.25%	67.50%
25.27% to 37.43%	16	20.00%	87.50%
37.43% to 49.58%	3	3.75%	91.25%
49.58% to 61.74%	3	3.75%	95.00%
61.74% to 73.90%	3	3.75%	98.75%
Greater than 73.90%	1	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.06%	41.48%	87.50%	68.27%
±2σ	-7.15%	57.69%	95.00%	95.45%
±3σ	-23.36%	73.90%	98.75%	99.73%

Descriptive Statistics

Mean	25.271%
Standard Error	1.812%
Median	21.372%
Mode	8.860%
Standard Deviation	16.209%
Sample Variance	262.723%
Kurtosis	8.48
Skewness	2.55
Range	97.772%
Minimum	8.860%
Maximum	106.632%
Count	80

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.271%	80	100.00%	25.271%
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 1.56. Further, an Excess Kurtosis of 8.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.05%	0	0.00%	0.00%
-44.05% to -34.27%	1	1.25%	1.25%
-34.27% to -24.48%	3	3.75%	5.00%
-24.48% to -14.70%	7	8.75%	13.75%
-14.70% to -4.92%	33	41.25%	55.00%
-4.92% to 4.86%	25	31.25%	86.25%
4.86% to 14.64%	7	8.75%	95.00%
14.64% to 24.42%	3	3.75%	98.75%
24.42% to 34.20%	0	0.00%	98.75%
Greater than 34.20%	1	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.96%	8.12%	82.50%	68.27%
±2σ	-31.00%	21.16%	97.50%	95.45%
±3σ	-44.05%	34.20%	98.75%	99.73%

Descriptive Statistics

Mean	-4.921%
Standard Error	1.458%
Median	-6.606%
Mode	-38.030%
Standard Deviation	13.042%
Sample Variance	170.082%
Kurtosis	8.45
Skewness	1.56
Range	100.708%
Minimum	-38.030%
Maximum	62.678%
Count	80

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.759%	27	33.75%	2.619%
Negative	-11.380%	53	66.25%	-7.539%
Zero	0.000%	0	0.00%	0.000%

MA Deep Analytical Report