CB - 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	1.94%	1.79%	1.74%	1.87%	1.65%	1.79%	322.08	332.91	316.80	338.46
Weekly	4.20%	4.60%	4.08%	4.27%	3.64%	3.94%	315.75	339.59	304.46	352.18
Monthly	6.91%	10.09%	6.91%	9.02%	7.58%	8.21%	303.56	353.23	281.40	381.03
Quarterly	11.28%	19.07%	10.82%	14.24%	13.12%	14.22%	287.18	373.37	251.86	425.73
Annual	—	—	—	—	26.25%	28.44%	251.86	425.73	193.71	553.52
Option Time Horizon	—	—	—	—	9.91%	10.73%	296.56	361.55	268.59	399.21

Calculation Notes: Computed at 2026-03-23T16:34 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $327.45 | Strike (K): $330.00 (first OTM call ≥ spot) | Observed Mid-Price: $12.3000 (Bid $11.5000 / Ask $13.1000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.18% | Binomial IV (Annual): 26.25% (CRR binomial tree, American, n=20 steps) | BS IV: 26.30% (European Black-Scholes) | Yahoo IV (Annual): 28.44% → 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
2026-03-13	$0.9700
2025-06-13	$0.9700
2025-03-14	$0.9100
2024-12-13	$0.9100
2024-09-13	$0.9100
2024-06-14	$0.9100
2024-03-14	$0.8600
2023-12-14	$0.8600
2023-09-14	$0.8600
2023-06-15	$0.8600
2023-03-16	$0.8300
2022-12-15	$0.8300
2022-09-15	$0.8300
2022-06-16	$0.8300
2022-03-17	$0.8000
2021-12-16	$0.8000
2021-09-16	$0.8000
2021-06-17	$0.8000
2021-03-18	$0.7800
2020-12-17	$0.7800
2020-09-17	$0.7800
2020-06-18	$0.7800
2020-03-19	$0.7500
2019-12-19	$0.7500
2019-09-19	$0.7500
2019-06-20	$0.7500
2019-03-21	$0.7300
2018-12-20	$0.7300
2018-09-20	$0.7300
2018-06-21	$0.7300
2018-03-28	$0.7100
2017-12-28	$0.7100
2017-09-28	$0.7100
2017-06-28	$0.7100
2017-03-29	$0.6900
2016-12-28	$0.6900
2016-09-28	$0.6900
2016-06-28	$0.6900
2016-03-29	$0.6700
2015-12-29	$0.6700
2015-09-28	$0.6700
2015-06-26	$0.6700
2015-03-27	$0.6500
2014-12-15	$0.6500
2014-09-26	$0.6500
2014-07-21	$0.6500
2014-03-26	$0.6300
2014-01-13	$0.6300
2013-09-26	$0.5100
2013-07-19	$0.5100
2013-03-26	$0.4900
2012-12-13	$0.4900
2012-09-26	$0.4900
2012-07-27	$0.4900
2012-03-28	$0.4700
2012-01-10	$0.4700
2011-09-28	$0.3500
2011-06-28	$0.3500
2011-03-30	$0.3300
2010-12-14	$0.3300
2010-09-29	$0.3300
2010-07-23	$0.3300
2010-03-29	$0.3100
2009-12-15	$0.3100
2009-09-29	$0.3100
2009-07-24	$0.3100
2009-03-27	$0.2500
2009-01-06	$0.2700
2008-10-09	$0.2600
2008-06-26	$0.2900
2008-03-27	$0.2700
2007-12-27	$0.2700
2007-09-26	$0.2700
2007-06-27	$0.2700
2007-03-28	$0.2500
2006-12-27	$0.2500
2006-09-27	$0.2500
2006-06-28	$0.2500
2006-03-29	$0.2300
2005-12-28	$0.2300
2005-09-28	$0.2300
2005-06-28	$0.2300
2005-03-29	$0.2100
2004-12-29	$0.2100
2004-09-28	$0.2100
2004-06-28	$0.2100
2004-03-29	$0.1900
2003-12-29	$0.1900
2003-09-26	$0.1900
2003-06-26	$0.1900
2003-03-27	$0.1700
2002-12-24	$0.1700
2002-09-25	$0.1700
2002-06-26	$0.1700
2002-03-26	$0.1500
2001-12-27	$0.1500
2001-09-26	$0.1500
2001-06-27	$0.1500
2001-03-28	$0.1300
2000-12-27	$0.1300
2000-09-27	$0.1300
2000-06-28	$0.1300
2000-03-29	$0.1100
1999-12-29	$0.1100
1999-09-28	$0.1100
1999-06-28	$0.1100
1999-03-29	$0.0900
1998-12-11	$0.0900
1998-09-28	$0.0900
1998-06-26	$0.0900
1998-03-27	$0.0800
1997-12-10	$0.0800
1997-09-26	$0.0733
1997-06-26	$0.0733
1997-03-26	$0.0600
1996-12-27	$0.0600
1996-09-26	$0.0600
1996-06-12	$0.0600
1996-03-27	$0.0467
1995-12-27	$0.0467
1995-09-27	$0.0467
1995-06-28	$0.0467
1995-03-27	$0.0367
1994-12-23	$0.0367
1994-09-26	$0.0367
1994-06-24	$0.0367
1994-03-25	$0.0333
1993-12-27	$0.0333
1993-09-24	$0.0333
1993-09-02	$0.0767
1993-06-24	$0.0333

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.48. Further, an Excess Kurtosis of 12.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.75%	57	0.69%	0.69%
-5.75% to -4.29%	70	0.84%	1.53%
-4.29% to -2.84%	240	2.90%	4.43%
-2.84% to -1.39%	853	10.29%	14.72%
-1.39% to 0.07%	3061	36.92%	51.64%
0.07% to 1.52%	2845	34.32%	85.96%
1.52% to 2.98%	751	9.06%	95.02%
2.98% to 4.43%	245	2.96%	97.97%
4.43% to 5.89%	81	0.98%	98.95%
Greater than 5.89%	87	1.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.87%	2.01%	80.18%	68.27%
±2σ	-3.81%	3.95%	95.11%	95.45%
±3σ	-5.75%	5.89%	98.26%	99.73%

Descriptive Statistics

Mean	0.069%
Standard Error	0.021%
Median	0.017%
Mode	0.000%
Standard Deviation	1.939%
Sample Variance	3.758%
Kurtosis	12.30
Skewness	0.48
Range	40.511%
Minimum	-19.758%
Maximum	20.753%
Count	8290

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.324%	4173	50.34%	0.666%
Negative	-1.264%	3918	47.26%	-0.597%
Zero	0.000%	199	2.40%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.61%
20	1 Month	1.83%
60	1 Quarter	1.85%
250	1 Year	1.76%
750	3 Years	1.70%
1,250	5 Years	1.87%
2,500	10 Years	1.89%
5,000	20 Years	2.03%
12,500	50 Years	2.33%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.50. Further, an Excess Kurtosis of 22.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.14%	0	0.00%	0.00%
-3.14% to -1.79%	0	0.00%	0.00%
-1.79% to -0.45%	0	0.00%	0.00%
-0.45% to 0.89%	926	11.17%	11.17%
0.89% to 2.23%	4561	55.01%	66.18%
2.23% to 3.57%	1651	19.91%	86.09%
3.57% to 4.91%	605	7.30%	93.39%
4.91% to 6.26%	261	3.15%	96.54%
6.26% to 7.60%	119	1.44%	97.97%
Greater than 7.60%	168	2.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.44%	4.02%	88.47%	68.27%
±2σ	-1.35%	5.81%	95.80%	95.45%
±3σ	-3.14%	7.60%	97.97%	99.73%

Descriptive Statistics

Mean	2.231%
Standard Error	0.020%
Median	1.716%
Mode	0.855%
Standard Deviation	1.789%
Sample Variance	3.201%
Kurtosis	22.11
Skewness	3.50
Range	26.404%
Minimum	0.210%
Maximum	26.614%
Count	8291

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.231%	8291	100.00%	2.231%
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 0.29. Further, an Excess Kurtosis of 12.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.20%	82	0.99%	0.99%
-5.20% to -3.90%	84	1.01%	2.00%
-3.90% to -2.60%	236	2.85%	4.85%
-2.60% to -1.30%	792	9.55%	14.40%
-1.30% to 0.00%	3093	37.31%	51.71%
0.00% to 1.30%	2775	33.47%	85.18%
1.30% to 2.60%	807	9.73%	94.91%
2.60% to 3.90%	259	3.12%	98.03%
3.90% to 5.21%	98	1.18%	99.22%
Greater than 5.21%	65	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.73%	1.74%	80.05%	68.27%
±2σ	-3.47%	3.47%	94.77%	95.45%
±3σ	-5.20%	5.21%	98.23%	99.73%

Descriptive Statistics

Mean	0.001%
Standard Error	0.019%
Median	0.000%
Mode	0.000%
Standard Deviation	1.735%
Sample Variance	3.009%
Kurtosis	12.43
Skewness	0.29
Range	39.529%
Minimum	-14.483%
Maximum	25.046%
Count	8291

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.190%	4004	48.29%	0.575%
Negative	-1.176%	4046	48.80%	-0.574%
Zero	0.000%	241	2.91%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.63. Further, an Excess Kurtosis of 4.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.27%	8	0.46%	0.46%
-12.27% to -9.12%	23	1.34%	1.80%
-9.12% to -5.97%	61	3.54%	5.35%
-5.97% to -2.82%	182	10.58%	15.92%
-2.82% to 0.33%	613	35.62%	51.54%
0.33% to 3.48%	578	33.59%	85.12%
3.48% to 6.63%	162	9.41%	94.54%
6.63% to 9.78%	48	2.79%	97.33%
9.78% to 12.93%	26	1.51%	98.84%
Greater than 12.93%	20	1.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.87%	4.53%	78.73%	68.27%
±2σ	-8.07%	8.73%	94.31%	95.45%
±3σ	-12.27%	12.93%	98.37%	99.73%

Descriptive Statistics

Mean	0.330%
Standard Error	0.101%
Median	0.195%
Mode	0.000%
Standard Deviation	4.201%
Sample Variance	17.648%
Kurtosis	4.91
Skewness	0.63
Range	49.389%
Minimum	-24.857%
Maximum	24.532%
Count	1721

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.075%	896	52.06%	1.601%
Negative	-2.692%	813	47.24%	-1.272%
Zero	0.000%	12	0.70%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	4.67%
12	1 Quarter	4.26%
52	1 Year	3.98%
156	3 Years	3.87%
260	5 Years	4.27%
520	10 Years	4.32%
1,040	20 Years	4.59%
2,600	50 Years	5.51%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.90. Further, an Excess Kurtosis of 28.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.13%	0	0.00%	0.00%
-8.13% to -4.68%	0	0.00%	0.00%
-4.68% to -1.23%	0	0.00%	0.00%
-1.23% to 2.23%	163	9.47%	9.47%
2.23% to 5.68%	985	57.20%	66.67%
5.68% to 9.13%	336	19.51%	86.18%
9.13% to 12.59%	127	7.38%	93.55%
12.59% to 16.04%	60	3.48%	97.04%
16.04% to 19.49%	19	1.10%	98.14%
Greater than 19.49%	32	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.08%	10.28%	88.68%	68.27%
±2σ	-3.53%	14.89%	95.99%	95.45%
±3σ	-8.13%	19.49%	98.14%	99.73%

Descriptive Statistics

Mean	5.679%
Standard Error	0.111%
Median	4.316%
Mode	2.128%
Standard Deviation	4.604%
Sample Variance	21.193%
Kurtosis	28.09
Skewness	3.90
Range	60.143%
Minimum	0.630%
Maximum	60.773%
Count	1722

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.679%	1722	100.00%	5.679%
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 0.39. 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 -12.35%	17	0.99%	0.99%
-12.35% to -9.29%	20	1.16%	2.15%
-9.29% to -6.22%	52	3.02%	5.17%
-6.22% to -3.16%	167	9.70%	14.87%
-3.16% to -0.09%	619	35.95%	50.81%
-0.09% to 2.97%	583	33.86%	84.67%
2.97% to 6.03%	170	9.87%	94.54%
6.03% to 9.10%	58	3.37%	97.91%
9.10% to 12.16%	20	1.16%	99.07%
Greater than 12.16%	16	0.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.18%	3.99%	78.75%	68.27%
±2σ	-8.26%	8.08%	94.13%	95.45%
±3σ	-12.35%	12.16%	98.08%	99.73%

Descriptive Statistics

Mean	-0.094%
Standard Error	0.098%
Median	-0.162%
Mode	0.000%
Standard Deviation	4.085%
Sample Variance	16.684%
Kurtosis	6.91
Skewness	0.39
Range	56.433%
Minimum	-19.310%
Maximum	37.123%
Count	1722

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.849%	813	47.21%	1.345%
Negative	-2.792%	888	51.57%	-1.440%
Zero	0.000%	21	1.22%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.10. Further, an Excess Kurtosis of 1.89 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -19.43%	4	1.01%	1.01%
-19.43% to -14.25%	4	1.01%	2.02%
-14.25% to -9.07%	8	2.02%	4.04%
-9.07% to -3.89%	66	16.67%	20.71%
-3.89% to 1.29%	114	28.79%	49.49%
1.29% to 6.47%	127	32.07%	81.57%
6.47% to 11.65%	48	12.12%	93.69%
11.65% to 16.83%	19	4.80%	98.48%
16.83% to 22.01%	2	0.51%	98.99%
Greater than 22.01%	4	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.62%	8.20%	75.00%	68.27%
±2σ	-12.53%	15.11%	95.45%	95.45%
±3σ	-19.43%	22.01%	97.98%	99.73%

Descriptive Statistics

Mean	1.290%
Standard Error	0.347%
Median	1.333%
Mode	0.000%
Standard Deviation	6.908%
Sample Variance	47.718%
Kurtosis	1.89
Skewness	0.10
Range	51.122%
Minimum	-22.405%
Maximum	28.717%
Count	396

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.541%	235	59.34%	3.288%
Negative	-5.009%	158	39.90%	-1.999%
Zero	0.000%	3	0.76%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	8.42%
12	1 Year	8.20%
36	3 Years	8.02%
60	5 Years	9.02%
120	10 Years	9.19%
240	20 Years	9.45%
600	50 Years	11.62%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.37. Further, an Excess Kurtosis of 16.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.54%	0	0.00%	0.00%
-17.54% to -9.97%	0	0.00%	0.00%
-9.97% to -2.40%	0	0.00%	0.00%
-2.40% to 5.16%	36	9.07%	9.07%
5.16% to 12.73%	236	59.45%	68.51%
12.73% to 20.30%	73	18.39%	86.90%
20.30% to 27.87%	22	5.54%	92.44%
27.87% to 35.44%	17	4.28%	96.73%
35.44% to 43.01%	6	1.51%	98.24%
Greater than 43.01%	7	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.64%	22.83%	89.67%	68.27%
±2σ	-7.45%	32.92%	95.21%	95.45%
±3σ	-17.54%	43.01%	98.24%	99.73%

Descriptive Statistics

Mean	12.733%
Standard Error	0.507%
Median	9.928%
Mode	4.723%
Standard Deviation	10.092%
Sample Variance	101.856%
Kurtosis	16.43
Skewness	3.37
Range	86.350%
Minimum	2.600%
Maximum	88.950%
Count	397

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.733%	397	100.00%	12.733%
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 0.62. Further, an Excess Kurtosis of 2.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.33%	2	0.50%	0.50%
-21.33% to -16.14%	3	0.76%	1.26%
-16.14% to -10.96%	16	4.03%	5.29%
-10.96% to -5.78%	50	12.59%	17.88%
-5.78% to -0.60%	143	36.02%	53.90%
-0.60% to 4.58%	103	25.94%	79.85%
4.58% to 9.76%	63	15.87%	95.72%
9.76% to 14.95%	5	1.26%	96.98%
14.95% to 20.13%	6	1.51%	98.49%
Greater than 20.13%	6	1.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.51%	6.31%	75.82%	68.27%
±2σ	-14.42%	13.22%	95.47%	95.45%
±3σ	-21.33%	20.13%	97.98%	99.73%

Descriptive Statistics

Mean	-0.599%
Standard Error	0.347%
Median	-1.148%
Mode	-10.526%
Standard Deviation	6.909%
Sample Variance	47.741%
Kurtosis	2.61
Skewness	0.62
Range	52.891%
Minimum	-22.951%
Maximum	29.940%
Count	397

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.426%	167	42.06%	2.282%
Negative	-4.995%	229	57.68%	-2.881%
Zero	0.000%	1	0.25%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.41. Further, an Excess Kurtosis of 3.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.04%	0	0.00%	0.00%
-30.04% to -21.57%	4	3.03%	3.03%
-21.57% to -13.11%	4	3.03%	6.06%
-13.11% to -4.65%	12	9.09%	15.15%
-4.65% to 3.81%	45	34.09%	49.24%
3.81% to 12.28%	44	33.33%	82.58%
12.28% to 20.74%	16	12.12%	94.70%
20.74% to 29.20%	3	2.27%	96.97%
29.20% to 37.66%	3	2.27%	99.24%
Greater than 37.66%	1	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.47%	15.10%	80.30%	68.27%
±2σ	-18.75%	26.38%	93.94%	95.45%
±3σ	-30.04%	37.66%	99.24%	99.73%

Descriptive Statistics

Mean	3.813%
Standard Error	0.982%
Median	4.034%
Mode	5.047%
Standard Deviation	11.283%
Sample Variance	127.299%
Kurtosis	3.09
Skewness	0.41
Range	79.265%
Minimum	-28.398%
Maximum	50.867%
Count	132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.755%	93	70.45%	6.168%
Negative	-7.972%	39	29.55%	-2.355%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	12.59%
12	3 Years	13.10%
20	5 Years	14.24%
40	10 Years	15.30%
80	20 Years	15.87%
200	50 Years	19.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.65. Further, an Excess Kurtosis of 7.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.92%	0	0.00%	0.00%
-33.92% to -19.62%	0	0.00%	0.00%
-19.62% to -5.32%	0	0.00%	0.00%
-5.32% to 8.98%	8	6.02%	6.02%
8.98% to 23.28%	85	63.91%	69.92%
23.28% to 37.58%	24	18.05%	87.97%
37.58% to 51.88%	4	3.01%	90.98%
51.88% to 66.18%	7	5.26%	96.24%
66.18% to 80.48%	0	0.00%	96.24%
Greater than 80.48%	5	3.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.22%	42.35%	89.47%	68.27%
±2σ	-14.85%	61.41%	96.24%	95.45%
±3σ	-33.92%	80.48%	96.24%	99.73%

Descriptive Statistics

Mean	23.282%
Standard Error	1.653%
Median	16.712%
Mode	5.828%
Standard Deviation	19.066%
Sample Variance	363.524%
Kurtosis	7.87
Skewness	2.65
Range	110.747%
Minimum	5.828%
Maximum	116.575%
Count	133

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.282%	133	100.00%	23.282%
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 0.97. Further, an Excess Kurtosis of 3.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.44%	0	0.00%	0.00%
-34.44% to -26.32%	2	1.50%	1.50%
-26.32% to -18.21%	3	2.26%	3.76%
-18.21% to -10.09%	17	12.78%	16.54%
-10.09% to -1.98%	50	37.59%	54.14%
-1.98% to 6.14%	41	30.83%	84.96%
6.14% to 14.25%	11	8.27%	93.23%
14.25% to 22.37%	4	3.01%	96.24%
22.37% to 30.48%	2	1.50%	97.74%
Greater than 30.48%	3	2.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.80%	8.84%	79.70%	68.27%
±2σ	-23.62%	19.66%	92.48%	95.45%
±3σ	-34.44%	30.48%	97.74%	99.73%

Descriptive Statistics

Mean	-1.978%
Standard Error	0.938%
Median	-2.892%
Mode	-8.264%
Standard Deviation	10.821%
Sample Variance	117.099%
Kurtosis	3.20
Skewness	0.97
Range	73.420%
Minimum	-32.174%
Maximum	41.246%
Count	133

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.133%	48	36.09%	2.935%
Negative	-7.687%	85	63.91%	-4.913%
Zero	0.000%	0	0.00%	0.000%

CB Deep Analytical Report