MCK - 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	2.00%	1.63%	1.63%	2.13%	1.49%	1.64%	933.48	961.69	919.69	976.11
Weekly	4.20%	4.67%	4.51%	4.83%	3.28%	3.62%	916.93	979.05	887.37	1011.66
Monthly	8.38%	9.46%	9.40%	10.61%	6.82%	7.54%	885.00	1014.37	826.64	1085.99
Quarterly	15.14%	17.24%	18.04%	18.97%	11.82%	13.05%	841.89	1066.32	748.06	1200.06
Annual	—	—	—	—	23.63%	26.11%	748.06	1200.06	590.61	1519.97
Option Time Horizon	—	—	—	—	7.72%	8.53%	877.04	1023.57	811.84	1105.78

Calculation Notes: Computed at 2026-02-22T14:25 UTC | Reference Contract: Call option expiring 2026-04-02 (39 days) | Spot Price (S): $947.48 | Strike (K): $970.00 (first OTM call ≥ spot) | Observed Mid-Price: $21.2000 (Bid $19.4000 / Ask $23.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.33% | Binomial IV (Annual): 23.63% (CRR binomial tree, American, n=20 steps) | BS IV: 23.85% (European Black-Scholes) | Yahoo IV (Annual): 26.11% → 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
2025-12-01	$0.8200
2025-09-02	$0.8200
2025-06-02	$0.7100
2025-03-03	$0.7100
2024-12-02	$0.7100
2024-08-30	$0.7100
2024-06-03	$0.6200
2024-02-29	$0.6200
2023-11-30	$0.6200
2023-08-31	$0.6200
2023-05-31	$0.5400
2023-02-28	$0.5400
2022-11-30	$0.5400
2022-08-31	$0.5400
2022-05-31	$0.4700
2022-02-28	$0.4700
2021-11-30	$0.4700
2021-08-31	$0.4700
2021-05-28	$0.4200
2021-03-01	$0.4200
2020-11-30	$0.4200
2020-08-31	$0.4200
2020-05-29	$0.4100
2020-02-28	$0.4100
2019-11-29	$0.4100
2019-08-30	$0.4100
2019-05-31	$0.3900
2019-02-28	$0.3900
2018-11-30	$0.3900
2018-08-31	$0.3900
2018-05-31	$0.3400
2018-02-28	$0.3400
2017-11-30	$0.3400
2017-08-30	$0.3400
2017-06-01	$0.2800
2017-02-27	$0.2800
2016-11-29	$0.2800
2016-08-30	$0.2800
2016-06-02	$0.2800
2016-02-26	$0.2800
2015-11-27	$0.2800
2015-08-28	$0.2800
2015-06-04	$0.2400
2015-02-26	$0.2400
2014-11-26	$0.2400
2014-08-28	$0.2400
2014-06-05	$0.2400
2014-02-27	$0.2400
2013-11-27	$0.2400
2013-08-29	$0.2400
2013-06-05	$0.2000
2013-02-27	$0.2000
2012-11-29	$0.2000
2012-08-30	$0.2000
2012-06-06	$0.2000
2012-02-28	$0.2000
2011-11-29	$0.2000
2011-08-30	$0.2000
2011-06-08	$0.2000
2011-02-25	$0.1800
2010-11-29	$0.1800
2010-08-30	$0.1800
2010-06-08	$0.1800
2010-02-25	$0.1200
2009-11-27	$0.1200
2009-08-28	$0.1200
2009-06-08	$0.1200
2009-02-26	$0.1200
2008-11-26	$0.1200
2008-08-28	$0.1200
2008-06-04	$0.1200
2008-02-28	$0.0600
2007-11-29	$0.0600
2007-08-29	$0.0600
2007-06-06	$0.0600
2007-02-27	$0.0600
2006-11-29	$0.0600
2006-08-30	$0.0600
2006-06-07	$0.0600
2006-02-27	$0.0600
2005-11-29	$0.0600
2005-08-30	$0.0600
2005-06-08	$0.0600
2005-02-25	$0.0600
2004-11-29	$0.0600
2004-08-30	$0.0600
2004-06-07	$0.0600
2004-02-26	$0.0600
2003-11-26	$0.0600
2003-08-27	$0.0600
2003-06-05	$0.0600
2003-02-27	$0.0600
2002-11-27	$0.0600
2002-08-28	$0.0600
2002-06-06	$0.0600
2002-02-27	$0.0600
2001-11-29	$0.0600
2001-08-29	$0.0600
2001-05-31	$0.0600
2001-02-27	$0.0600
2000-11-29	$0.0600
2000-08-30	$0.0600
2000-05-30	$0.0600
2000-02-28	$0.0600
1999-11-29	$0.0600
1999-08-30	$0.0600
1999-05-27	$0.0600
1999-02-25	$0.0600
1998-11-27	$0.1250
1998-08-28	$0.1250
1998-05-28	$0.1250
1998-02-26	$0.1250
1997-11-26	$0.1250
1997-08-28	$0.1250
1997-05-29	$0.1250
1997-02-27	$0.1250
1996-11-27	$0.1250
1996-08-29	$0.1250
1996-05-30	$0.1250
1996-02-28	$0.1250
1995-11-29	$0.1250
1995-08-30	$0.1250
1995-05-25	$0.0625
1995-02-23	$0.0625
1994-12-09	$0.1250

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Left Skewed (Extreme Negative Tail Risk) with a Skewness factor of -1.80. Further, an Excess Kurtosis of 50.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.91%	52	0.66%	0.66%
-5.91% to -4.41%	70	0.89%	1.55%
-4.41% to -2.92%	206	2.62%	4.17%
-2.92% to -1.42%	834	10.60%	14.76%
-1.42% to 0.08%	2763	35.11%	49.87%
0.08% to 1.57%	2790	35.45%	85.32%
1.57% to 3.07%	817	10.38%	95.71%
3.07% to 4.57%	200	2.54%	98.25%
4.57% to 6.06%	66	0.84%	99.09%
Greater than 6.06%	72	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.92%	2.07%	80.90%	68.27%
±2σ	-3.91%	4.07%	95.64%	95.45%
±3σ	-5.91%	6.06%	98.42%	99.73%

Descriptive Statistics

Mean	0.076%
Standard Error	0.022%
Median	0.079%
Mode	0.000%
Standard Deviation	1.995%
Sample Variance	3.981%
Kurtosis	50.21
Skewness	-1.80
Range	64.050%
Minimum	-47.529%
Maximum	16.521%
Count	7870

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.323%	4074	51.77%	0.685%
Negative	-1.301%	3684	46.81%	-0.609%
Zero	0.000%	112	1.42%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.95%
20	1 Month	3.44%
60	1 Quarter	2.44%
250	1 Year	2.34%
750	3 Years	2.05%
1,250	5 Years	2.13%
2,500	10 Years	2.38%
5,000	20 Years	2.29%
12,500	50 Years	2.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.41. Further, an Excess Kurtosis of 22.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.55%	0	0.00%	0.00%
-2.55% to -1.33%	0	0.00%	0.00%
-1.33% to -0.11%	0	0.00%	0.00%
-0.11% to 1.12%	1092	13.87%	13.87%
1.12% to 2.34%	3993	50.73%	64.60%
2.34% to 3.56%	1667	21.18%	85.78%
3.56% to 4.78%	621	7.89%	93.67%
4.78% to 6.01%	244	3.10%	96.77%
6.01% to 7.23%	118	1.50%	98.27%
Greater than 7.23%	136	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.71%	3.97%	86.89%	68.27%
±2σ	-0.92%	5.60%	95.99%	95.45%
±3σ	-2.55%	7.23%	98.27%	99.73%

Descriptive Statistics

Mean	2.339%
Standard Error	0.018%
Median	1.914%
Mode	1.189%
Standard Deviation	1.630%
Sample Variance	2.657%
Kurtosis	22.26
Skewness	3.41
Range	26.102%
Minimum	0.244%
Maximum	26.346%
Count	7871

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.339%	7871	100.00%	2.339%
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 0.49. Further, an Excess Kurtosis of 8.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.93%	61	0.77%	0.77%
-4.93% to -3.70%	67	0.85%	1.63%
-3.70% to -2.48%	249	3.16%	4.79%
-2.48% to -1.25%	962	12.22%	17.01%
-1.25% to -0.03%	2634	33.46%	50.48%
-0.03% to 1.20%	2576	32.73%	83.20%
1.20% to 2.42%	898	11.41%	94.61%
2.42% to 3.65%	268	3.40%	98.02%
3.65% to 4.87%	96	1.22%	99.24%
Greater than 4.87%	60	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.66%	1.61%	77.89%	68.27%
±2σ	-3.30%	3.24%	94.98%	95.45%
±3σ	-4.93%	4.87%	98.46%	99.73%

Descriptive Statistics

Mean	-0.028%
Standard Error	0.018%
Median	-0.045%
Mode	0.000%
Standard Deviation	1.634%
Sample Variance	2.671%
Kurtosis	8.33
Skewness	0.49
Range	30.923%
Minimum	-10.733%
Maximum	20.190%
Count	7871

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.184%	3687	46.84%	0.555%
Negative	-1.138%	4028	51.17%	-0.582%
Zero	0.000%	156	1.98%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.78. Further, an Excess Kurtosis of 11.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.23%	10	0.61%	0.61%
-12.23% to -9.08%	15	0.92%	1.53%
-9.08% to -5.94%	61	3.74%	5.27%
-5.94% to -2.79%	182	11.15%	16.42%
-2.79% to 0.36%	536	32.84%	49.26%
0.36% to 3.50%	560	34.31%	83.58%
3.50% to 6.65%	183	11.21%	94.79%
6.65% to 9.80%	49	3.00%	97.79%
9.80% to 12.95%	26	1.59%	99.39%
Greater than 12.95%	10	0.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.84%	4.55%	77.57%	68.27%
±2σ	-8.04%	8.75%	94.55%	95.45%
±3σ	-12.23%	12.94%	98.77%	99.73%

Descriptive Statistics

Mean	0.357%
Standard Error	0.104%
Median	0.416%
Mode	0.000%
Standard Deviation	4.196%
Sample Variance	17.604%
Kurtosis	11.69
Skewness	-0.78
Range	65.711%
Minimum	-46.471%
Maximum	19.240%
Count	1632

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.003%	893	54.72%	1.643%
Negative	-2.864%	733	44.91%	-1.286%
Zero	0.000%	6	0.37%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.08%
12	1 Quarter	5.60%
52	1 Year	5.18%
156	3 Years	4.67%
260	5 Years	4.83%
520	10 Years	5.52%
1,040	20 Years	5.22%
2,600	50 Years	5.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.55. Further, an Excess Kurtosis of 131.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.07%	0	0.00%	0.00%
-8.07% to -4.57%	0	0.00%	0.00%
-4.57% to -1.06%	0	0.00%	0.00%
-1.06% to 2.44%	130	7.96%	7.96%
2.44% to 5.95%	932	57.07%	65.03%
5.95% to 9.45%	374	22.90%	87.94%
9.45% to 12.95%	98	6.00%	93.94%
12.95% to 16.46%	58	3.55%	97.49%
16.46% to 19.96%	15	0.92%	98.41%
Greater than 19.96%	26	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.27%	10.62%	90.88%	68.27%
±2σ	-3.40%	15.29%	96.75%	95.45%
±3σ	-8.07%	19.96%	98.41%	99.73%

Descriptive Statistics

Mean	5.946%
Standard Error	0.116%
Median	4.854%
Mode	2.861%
Standard Deviation	4.672%
Sample Variance	21.830%
Kurtosis	131.03
Skewness	7.55
Range	104.206%
Minimum	1.263%
Maximum	105.469%
Count	1633

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.946%	1633	100.00%	5.946%
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 5.27. Further, an Excess Kurtosis of 98.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.66%	2	0.12%	0.12%
-13.66% to -10.28%	19	1.16%	1.29%
-10.28% to -6.89%	35	2.14%	3.43%
-6.89% to -3.51%	193	11.82%	15.25%
-3.51% to -0.13%	617	37.78%	53.03%
-0.13% to 3.25%	540	33.07%	86.10%
3.25% to 6.64%	149	9.12%	95.22%
6.64% to 10.02%	51	3.12%	98.35%
10.02% to 13.40%	19	1.16%	99.51%
Greater than 13.40%	8	0.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.64%	4.38%	81.87%	68.27%
±2σ	-9.15%	8.89%	95.96%	95.45%
±3σ	-13.66%	13.40%	99.39%	99.73%

Descriptive Statistics

Mean	-0.129%
Standard Error	0.112%
Median	-0.379%
Mode	0.000%
Standard Deviation	4.510%
Sample Variance	20.342%
Kurtosis	98.27
Skewness	5.27
Range	106.623%
Minimum	-16.879%
Maximum	89.744%
Count	1633

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.009%	741	45.38%	1.365%
Negative	-2.757%	885	54.20%	-1.494%
Zero	0.000%	7	0.43%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.63. 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 -23.59%	4	1.07%	1.07%
-23.59% to -17.31%	2	0.53%	1.60%
-17.31% to -11.03%	10	2.67%	4.27%
-11.03% to -4.74%	57	15.20%	19.47%
-4.74% to 1.54%	113	30.13%	49.60%
1.54% to 7.82%	111	29.60%	79.20%
7.82% to 14.11%	59	15.73%	94.93%
14.11% to 20.39%	12	3.20%	98.13%
20.39% to 26.67%	6	1.60%	99.73%
Greater than 26.67%	1	0.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.84%	9.92%	73.07%	68.27%
±2σ	-15.22%	18.30%	95.73%	95.45%
±3σ	-23.59%	26.67%	98.67%	99.73%

Descriptive Statistics

Mean	1.539%
Standard Error	0.433%
Median	1.671%
Mode	1.671%
Standard Deviation	8.378%
Sample Variance	70.199%
Kurtosis	3.79
Skewness	-0.63
Range	74.346%
Minimum	-46.970%
Maximum	27.376%
Count	375

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.844%	217	57.87%	3.960%
Negative	-5.747%	158	42.13%	-2.421%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.94%
12	1 Year	10.96%
36	3 Years	10.58%
60	5 Years	10.61%
120	10 Years	12.14%
240	20 Years	11.31%
600	50 Years	12.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.45. Further, an Excess Kurtosis of 37.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.45%	0	0.00%	0.00%
-14.45% to -7.35%	0	0.00%	0.00%
-7.35% to -0.25%	0	0.00%	0.00%
-0.25% to 6.84%	47	12.50%	12.50%
6.84% to 13.94%	197	52.39%	64.89%
13.94% to 21.04%	81	21.54%	86.44%
21.04% to 28.14%	26	6.91%	93.35%
28.14% to 35.24%	13	3.46%	96.81%
35.24% to 42.33%	8	2.13%	98.94%
Greater than 42.33%	4	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.48%	23.41%	88.56%	68.27%
±2σ	-4.99%	32.87%	96.28%	95.45%
±3σ	-14.45%	42.33%	98.94%	99.73%

Descriptive Statistics

Mean	13.942%
Standard Error	0.488%
Median	11.764%
Mode	7.550%
Standard Deviation	9.464%
Sample Variance	89.561%
Kurtosis	37.89
Skewness	4.45
Range	112.771%
Minimum	3.635%
Maximum	116.406%
Count	376

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.942%	376	100.00%	13.942%
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 3.22. Further, an Excess Kurtosis of 26.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.82%	0	0.00%	0.00%
-28.82% to -21.77%	1	0.27%	0.27%
-21.77% to -14.72%	8	2.13%	2.39%
-14.72% to -7.67%	58	15.43%	17.82%
-7.67% to -0.62%	137	36.44%	54.26%
-0.62% to 6.42%	115	30.59%	84.84%
6.42% to 13.47%	43	11.44%	96.28%
13.47% to 20.52%	8	2.13%	98.40%
20.52% to 27.57%	2	0.53%	98.94%
Greater than 27.57%	4	1.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.02%	8.77%	79.79%	68.27%
±2σ	-19.42%	18.17%	97.87%	95.45%
±3σ	-28.82%	27.57%	98.94%	99.73%

Descriptive Statistics

Mean	-0.625%
Standard Error	0.485%
Median	-1.612%
Mode	-7.343%
Standard Deviation	9.397%
Sample Variance	88.310%
Kurtosis	26.34
Skewness	3.22
Range	113.519%
Minimum	-22.090%
Maximum	91.429%
Count	376

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.793%	159	42.29%	2.873%
Negative	-6.089%	216	57.45%	-3.498%
Zero	0.000%	1	0.27%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.44. Further, an Excess Kurtosis of 1.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.82%	1	0.80%	0.80%
-40.82% to -29.46%	3	2.40%	3.20%
-29.46% to -18.10%	4	3.20%	6.40%
-18.10% to -6.74%	13	10.40%	16.80%
-6.74% to 4.62%	39	31.20%	48.00%
4.62% to 15.98%	39	31.20%	79.20%
15.98% to 27.34%	20	16.00%	95.20%
27.34% to 38.69%	4	3.20%	98.40%
38.69% to 50.05%	2	1.60%	100.00%
Greater than 50.05%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.53%	19.76%	75.20%	68.27%
±2σ	-25.67%	34.91%	94.40%	95.45%
±3σ	-40.82%	50.05%	99.20%	99.73%

Descriptive Statistics

Mean	4.618%
Standard Error	1.355%
Median	5.165%
Mode	-53.294%
Standard Deviation	15.145%
Sample Variance	229.381%
Kurtosis	1.94
Skewness	-0.44
Range	101.291%
Minimum	-53.294%
Maximum	47.997%
Count	125

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.330%	78	62.40%	8.318%
Negative	-9.841%	47	37.60%	-3.700%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	17.98%
12	3 Years	19.76%
20	5 Years	18.97%
40	10 Years	20.97%
80	20 Years	19.96%
200	50 Years	22.63%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.12. Further, an Excess Kurtosis of 14.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.55%	0	0.00%	0.00%
-25.55% to -12.62%	0	0.00%	0.00%
-12.62% to 0.31%	0	0.00%	0.00%
0.31% to 13.24%	17	13.49%	13.49%
13.24% to 26.17%	66	52.38%	65.87%
26.17% to 39.10%	26	20.63%	86.51%
39.10% to 52.03%	9	7.14%	93.65%
52.03% to 64.96%	3	2.38%	96.03%
64.96% to 77.89%	3	2.38%	98.41%
Greater than 77.89%	2	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.93%	43.41%	90.48%	68.27%
±2σ	-8.31%	60.65%	95.24%	95.45%
±3σ	-25.54%	77.89%	98.41%	99.73%

Descriptive Statistics

Mean	26.172%
Standard Error	1.536%
Median	21.576%
Mode	9.247%
Standard Deviation	17.239%
Sample Variance	297.175%
Kurtosis	14.76
Skewness	3.12
Range	128.448%
Minimum	9.247%
Maximum	137.695%
Count	126

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.172%	126	100.00%	26.172%
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 2.92. Further, an Excess Kurtosis of 14.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.78%	0	0.00%	0.00%
-55.78% to -42.25%	0	0.00%	0.00%
-42.25% to -28.72%	1	0.79%	0.79%
-28.72% to -15.19%	15	11.90%	12.70%
-15.19% to -1.66%	60	47.62%	60.32%
-1.66% to 11.87%	35	27.78%	88.10%
11.87% to 25.40%	10	7.94%	96.03%
25.40% to 38.93%	1	0.79%	96.83%
38.93% to 52.46%	1	0.79%	97.62%
Greater than 52.46%	3	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.70%	16.38%	84.92%	68.27%
±2σ	-37.74%	34.42%	96.83%	95.45%
±3σ	-55.78%	52.46%	97.62%	99.73%

Descriptive Statistics

Mean	-1.664%
Standard Error	1.607%
Median	-4.764%
Mode	-31.388%
Standard Deviation	18.040%
Sample Variance	325.425%
Kurtosis	14.45
Skewness	2.92
Range	145.495%
Minimum	-31.388%
Maximum	114.107%
Count	126

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.508%	48	38.09%	5.146%
Negative	-11.001%	78	61.91%	-6.810%
Zero	0.000%	0	0.00%	0.000%

MCK Deep Analytical Report