HD - 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	2.31%	2.25%	1.83%	2.12%	1.96%	2.00%	324.84	337.85	318.52	344.55
Weekly	5.14%	4.88%	4.79%	4.88%	4.32%	4.39%	317.26	345.92	303.84	361.20
Monthly	9.04%	10.68%	9.03%	10.97%	9.00%	9.15%	302.77	362.48	276.71	396.61
Quarterly	17.18%	19.85%	15.67%	19.18%	15.59%	15.85%	283.46	387.16	242.55	452.47
Annual	—	—	—	—	31.18%	31.69%	242.55	452.47	177.58	618.00
Option Time Horizon	—	—	—	—	11.77%	11.96%	294.50	372.65	261.81	419.18

Calculation Notes: Computed at 2026-03-23T16:31 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $331.28 | Strike (K): $335.00 (first OTM call ≥ spot) | Observed Mid-Price: $14.0250 (Bid $13.6500 / Ask $14.4000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 2.88% | Binomial IV (Annual): 31.18% (CRR binomial tree, American, n=20 steps) | BS IV: 31.30% (European Black-Scholes) | Yahoo IV (Annual): 31.69% → 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
2026-03-12	$2.3300
2025-12-04	$2.3000
2025-09-04	$2.3000
2025-06-05	$2.3000
2025-03-13	$2.3000
2024-11-27	$2.2500
2024-08-29	$2.2500
2024-05-30	$2.2500
2024-03-06	$2.2500
2023-11-29	$2.0900
2023-08-30	$2.0900
2023-05-31	$2.0900
2023-03-08	$2.0900
2022-11-30	$1.9000
2022-08-31	$1.9000
2022-06-01	$1.9000
2022-03-09	$1.9000
2021-12-01	$1.6500
2021-09-01	$1.6500
2021-06-02	$1.6500
2021-03-10	$1.6500
2020-12-02	$1.5000
2020-09-02	$1.5000
2020-06-03	$1.5000
2020-03-11	$1.5000
2019-12-04	$1.3600
2019-09-04	$1.3600
2019-06-05	$1.3600
2019-03-13	$1.3600
2018-11-28	$1.0300
2018-08-29	$1.0300
2018-05-30	$1.0300
2018-03-07	$1.0300
2017-11-29	$0.8900
2017-08-29	$0.8900
2017-05-30	$0.8900
2017-03-07	$0.8900
2016-11-29	$0.6900
2016-08-30	$0.6900
2016-05-31	$0.6900
2016-03-08	$0.6900
2015-12-01	$0.5900
2015-09-01	$0.5900
2015-06-02	$0.5900
2015-03-10	$0.5900
2014-12-02	$0.4700
2014-09-02	$0.4700
2014-06-03	$0.4700
2014-03-11	$0.4700
2013-12-03	$0.3900
2013-09-03	$0.3900
2013-06-04	$0.3900
2013-03-12	$0.3900
2012-11-27	$0.2900
2012-08-28	$0.2900
2012-05-29	$0.2900
2012-03-06	$0.2900
2011-11-29	$0.2900
2011-08-30	$0.2500
2011-06-14	$0.2500
2011-03-08	$0.2500
2010-11-30	$0.2360
2010-08-31	$0.2360
2010-06-01	$0.2360
2010-03-09	$0.2360
2009-12-01	$0.2250
2009-09-01	$0.2250
2009-06-09	$0.2250
2009-03-10	$0.2250
2008-12-02	$0.2250
2008-09-02	$0.2250
2008-06-03	$0.2250
2008-03-11	$0.2250
2007-11-27	$0.2250
2007-08-28	$0.2250
2007-06-05	$0.2250
2007-03-06	$0.2250
2006-11-28	$0.2250
2006-09-05	$0.1500
2006-06-06	$0.1500
2006-03-07	$0.1500
2005-11-29	$0.1000
2005-08-30	$0.1000
2005-06-07	$0.1000
2005-03-08	$0.1000
2004-11-30	$0.0850
2004-08-31	$0.0850
2004-06-08	$0.0850
2004-03-09	$0.0700
2003-12-02	$0.0700
2003-09-02	$0.0700
2003-06-10	$0.0600
2003-03-11	$0.0600
2002-12-03	$0.0600
2002-09-03	$0.0500
2002-06-11	$0.0500
2002-03-12	$0.0500
2001-11-28	$0.0500
2001-11-27	$0.0500
2001-08-28	$0.0400
2001-06-12	$0.0400
2001-03-06	$0.0400
2000-11-28	$0.0400
2000-08-29	$0.0400
2000-06-13	$0.0400
2000-03-07	$0.0400
1999-11-30	$0.0400
1999-08-31	$0.0267
1999-06-08	$0.0267
1999-03-02	$0.0200
1998-12-01	$0.0200
1998-09-01	$0.0200
1998-06-09	$0.0200
1998-03-03	$0.0167
1997-12-02	$0.0167
1997-09-09	$0.0167
1997-06-10	$0.0167
1997-03-11	$0.0133
1996-12-03	$0.0133
1996-09-10	$0.0133
1996-06-07	$0.0133
1996-03-06	$0.0111
1995-12-06	$0.0111
1995-09-07	$0.0111
1995-06-08	$0.0111
1995-02-22	$0.0089
1994-12-01	$0.0089
1994-09-02	$0.0089
1994-06-06	$0.0089
1994-03-03	$0.0067
1993-11-24	$0.0067
1993-08-31	$0.0067
1993-06-10	$0.0067
1993-03-04	$0.0050
1992-11-30	$0.0050
1992-08-27	$0.0050
1992-05-22	$0.0050
1992-03-03	$0.0033
1991-11-26	$0.0033
1991-08-28	$0.0033
1991-07-03	$0.0033
1991-03-07	$0.0022
1990-11-26	$0.0022
1990-08-23	$0.0022
1990-07-16	$0.0022
1990-02-22	$0.0015
1989-11-22	$0.0015
1989-08-25	$0.0015
1989-07-11	$0.0015
1989-03-10	$0.0010
1988-12-07	$0.0010
1988-08-30	$0.0010
1988-06-01	$0.0010
1988-03-15	$0.0007
1987-11-19	$0.0007

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.86. Further, an Excess Kurtosis of 41.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.81%	47	0.43%	0.43%
-6.81% to -5.08%	90	0.83%	1.27%
-5.08% to -3.34%	280	2.59%	3.85%
-3.34% to -1.61%	1150	10.63%	14.48%
-1.61% to 0.12%	4136	38.23%	52.71%
0.12% to 1.85%	3563	32.93%	85.64%
1.85% to 3.58%	1081	9.99%	95.63%
3.58% to 5.31%	297	2.74%	98.37%
5.31% to 7.04%	90	0.83%	99.21%
Greater than 7.04%	86	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.19%	2.43%	81.55%	68.27%
±2σ	-4.50%	4.73%	95.97%	95.45%
±3σ	-6.81%	7.04%	98.77%	99.73%

Descriptive Statistics

Mean	0.118%
Standard Error	0.022%
Median	0.000%
Mode	0.000%
Standard Deviation	2.308%
Sample Variance	5.328%
Kurtosis	41.05
Skewness	1.86
Range	69.396%
Minimum	-28.736%
Maximum	40.660%
Count	10820

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.588%	5374	49.67%	0.789%
Negative	-1.448%	5016	46.36%	-0.671%
Zero	0.000%	430	3.97%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.84%
20	1 Month	2.77%
60	1 Quarter	2.43%
250	1 Year	2.16%
750	3 Years	1.96%
1,250	5 Years	2.12%
2,500	10 Years	2.00%
5,000	20 Years	2.18%
12,500	50 Years	2.74%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.15. Further, an Excess Kurtosis of 62.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.17%	0	0.00%	0.00%
-4.17% to -2.48%	0	0.00%	0.00%
-2.48% to -0.80%	0	0.00%	0.00%
-0.80% to 0.89%	507	4.69%	4.69%
0.89% to 2.58%	6645	61.41%	66.09%
2.58% to 4.26%	2423	22.39%	88.49%
4.26% to 5.95%	774	7.15%	95.64%
5.95% to 7.63%	240	2.22%	97.86%
7.63% to 9.32%	104	0.96%	98.82%
Greater than 9.32%	128	1.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.33%	4.82%	91.73%	68.27%
±2σ	-1.92%	7.07%	97.35%	95.45%
±3σ	-4.17%	9.32%	98.82%	99.73%

Descriptive Statistics

Mean	2.576%
Standard Error	0.022%
Median	2.017%
Mode	2.326%
Standard Deviation	2.248%
Sample Variance	5.052%
Kurtosis	62.22
Skewness	6.15
Range	34.346%
Minimum	0.269%
Maximum	34.615%
Count	10821

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.576%	10821	100.00%	2.576%
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 0.81. Further, an Excess Kurtosis of 12.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.47%	65	0.60%	0.60%
-5.47% to -4.10%	131	1.21%	1.81%
-4.10% to -2.73%	339	3.13%	4.94%
-2.73% to -1.36%	1242	11.48%	16.42%
-1.36% to 0.01%	3985	36.83%	53.25%
0.01% to 1.38%	3282	30.33%	83.58%
1.38% to 2.75%	1215	11.23%	94.81%
2.75% to 4.12%	365	3.37%	98.18%
4.12% to 5.49%	121	1.12%	99.30%
Greater than 5.49%	76	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.81%	1.84%	77.99%	68.27%
±2σ	-3.64%	3.67%	94.77%	95.45%
±3σ	-5.47%	5.49%	98.70%	99.73%

Descriptive Statistics

Mean	0.013%
Standard Error	0.018%
Median	0.000%
Mode	0.000%
Standard Deviation	1.827%
Sample Variance	3.338%
Kurtosis	12.46
Skewness	0.81
Range	38.453%
Minimum	-12.766%
Maximum	25.687%
Count	10821

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.345%	5066	46.82%	0.630%
Negative	-1.281%	5207	48.12%	-0.616%
Zero	0.000%	548	5.06%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.77. Further, an Excess Kurtosis of 9.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.86%	14	0.61%	0.61%
-14.86% to -11.00%	21	0.92%	1.53%
-11.00% to -7.15%	62	2.71%	4.25%
-7.15% to -3.29%	267	11.68%	15.93%
-3.29% to 0.56%	827	36.19%	52.12%
0.56% to 4.42%	761	33.30%	85.43%
4.42% to 8.27%	225	9.85%	95.27%
8.27% to 12.13%	59	2.58%	97.86%
12.13% to 15.98%	26	1.14%	98.99%
Greater than 15.98%	23	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.58%	5.70%	80.22%	68.27%
±2σ	-9.72%	10.84%	94.79%	95.45%
±3σ	-14.86%	15.98%	98.38%	99.73%

Descriptive Statistics

Mean	0.564%
Standard Error	0.108%
Median	0.350%
Mode	0.000%
Standard Deviation	5.140%
Sample Variance	26.422%
Kurtosis	9.09
Skewness	0.77
Range	76.411%
Minimum	-35.751%
Maximum	40.660%
Count	2285

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.747%	1228	53.74%	2.014%
Negative	-3.313%	1000	43.76%	-1.450%
Zero	0.000%	57	2.50%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.95%
12	1 Quarter	5.74%
52	1 Year	4.95%
156	3 Years	4.54%
260	5 Years	4.88%
520	10 Years	4.63%
1,040	20 Years	5.03%
2,600	50 Years	6.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.68. Further, an Excess Kurtosis of 24.97 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 -4.47%	0	0.00%	0.00%
-4.47% to -0.81%	0	0.00%	0.00%
-0.81% to 2.86%	284	12.42%	12.42%
2.86% to 6.52%	1200	52.49%	64.92%
6.52% to 10.19%	494	21.61%	86.53%
10.19% to 13.85%	167	7.31%	93.83%
13.85% to 17.51%	67	2.93%	96.76%
17.51% to 21.18%	35	1.53%	98.29%
Greater than 21.18%	39	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.64%	11.41%	88.58%	68.27%
±2σ	-3.25%	16.29%	96.15%	95.45%
±3σ	-8.13%	21.18%	98.29%	99.73%

Descriptive Statistics

Mean	6.522%
Standard Error	0.102%
Median	5.200%
Mode	6.977%
Standard Deviation	4.885%
Sample Variance	23.863%
Kurtosis	24.97
Skewness	3.68
Range	68.478%
Minimum	1.014%
Maximum	69.492%
Count	2286

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.522%	2286	100.00%	6.522%
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 1.74. Further, an Excess Kurtosis of 14.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.35%	8	0.35%	0.35%
-14.35% to -10.76%	22	0.96%	1.31%
-10.76% to -7.17%	62	2.71%	4.02%
-7.17% to -3.58%	268	11.72%	15.75%
-3.58% to 0.01%	878	38.41%	54.16%
0.01% to 3.60%	684	29.92%	84.08%
3.60% to 7.19%	248	10.85%	94.93%
7.19% to 10.78%	66	2.89%	97.81%
10.78% to 14.36%	30	1.31%	99.13%
Greater than 14.36%	20	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.78%	4.79%	80.27%	68.27%
±2σ	-9.56%	9.58%	94.88%	95.45%
±3σ	-14.35%	14.36%	98.78%	99.73%

Descriptive Statistics

Mean	0.009%
Standard Error	0.100%
Median	-0.191%
Mode	0.000%
Standard Deviation	4.785%
Sample Variance	22.892%
Kurtosis	14.96
Skewness	1.74
Range	75.935%
Minimum	-20.290%
Maximum	55.645%
Count	2286

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.504%	1049	45.89%	1.608%
Negative	-3.097%	1180	51.62%	-1.599%
Zero	0.000%	57	2.49%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.15. Further, an Excess Kurtosis of 2.31 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.91%	4	0.75%	0.75%
-24.91% to -18.13%	4	0.75%	1.50%
-18.13% to -11.34%	22	4.13%	5.63%
-11.34% to -4.56%	73	13.70%	19.32%
-4.56% to 2.22%	180	33.77%	53.10%
2.22% to 9.01%	143	26.83%	79.92%
9.01% to 15.79%	78	14.63%	94.56%
15.79% to 22.57%	20	3.75%	98.31%
22.57% to 29.36%	4	0.75%	99.06%
Greater than 29.36%	5	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.82%	11.27%	76.55%	68.27%
±2σ	-15.87%	20.31%	94.75%	95.45%
±3σ	-24.91%	29.36%	98.31%	99.73%

Descriptive Statistics

Mean	2.223%
Standard Error	0.392%
Median	1.832%
Mode	0.000%
Standard Deviation	9.044%
Sample Variance	81.803%
Kurtosis	2.31
Skewness	0.15
Range	77.473%
Minimum	-36.813%
Maximum	40.660%
Count	533

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.743%	313	58.72%	4.547%
Negative	-5.899%	210	39.40%	-2.324%
Zero	0.000%	10	1.88%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	13.13%
12	1 Year	10.37%
36	3 Years	10.41%
60	5 Years	10.97%
120	10 Years	10.36%
240	20 Years	10.93%
600	50 Years	14.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.74. Further, an Excess Kurtosis of 23.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.73%	0	0.00%	0.00%
-16.73% to -8.73%	0	0.00%	0.00%
-8.73% to -0.72%	0	0.00%	0.00%
-0.72% to 7.29%	65	12.17%	12.17%
7.29% to 15.30%	278	52.06%	64.23%
15.30% to 23.30%	114	21.35%	85.58%
23.30% to 31.31%	52	9.74%	95.32%
31.31% to 39.32%	12	2.25%	97.57%
39.32% to 47.33%	3	0.56%	98.13%
Greater than 47.33%	10	1.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.62%	25.97%	87.08%	68.27%
±2σ	-6.06%	36.65%	96.82%	95.45%
±3σ	-16.73%	47.33%	98.13%	99.73%

Descriptive Statistics

Mean	15.297%
Standard Error	0.462%
Median	12.768%
Mode	6.139%
Standard Deviation	10.677%
Sample Variance	114.001%
Kurtosis	23.91
Skewness	3.74
Range	113.533%
Minimum	2.962%
Maximum	116.495%
Count	534

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.297%	534	100.00%	15.297%
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 1.26. Further, an Excess Kurtosis of 5.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -28.02%	0	0.00%	0.00%
-28.02% to -21.25%	5	0.94%	0.94%
-21.25% to -14.48%	14	2.62%	3.56%
-14.48% to -7.71%	89	16.67%	20.22%
-7.71% to -0.94%	173	32.40%	52.62%
-0.94% to 5.83%	164	30.71%	83.33%
5.83% to 12.61%	56	10.49%	93.82%
12.61% to 19.38%	21	3.93%	97.75%
19.38% to 26.15%	7	1.31%	99.06%
Greater than 26.15%	5	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.96%	8.09%	76.78%	68.27%
±2σ	-18.99%	17.12%	95.32%	95.45%
±3σ	-28.02%	26.15%	99.06%	99.73%

Descriptive Statistics

Mean	-0.936%
Standard Error	0.391%
Median	-1.361%
Mode	0.000%
Standard Deviation	9.028%
Sample Variance	81.496%
Kurtosis	5.61
Skewness	1.26
Range	83.731%
Minimum	-25.470%
Maximum	58.261%
Count	534

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.108%	212	39.70%	2.822%
Negative	-6.515%	308	57.68%	-3.758%
Zero	0.000%	14	2.62%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.72. Further, an Excess Kurtosis of 2.87 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.65%	0	0.00%	0.00%
-44.65% to -31.76%	3	1.69%	1.69%
-31.76% to -18.88%	4	2.25%	3.93%
-18.88% to -5.99%	27	15.17%	19.10%
-5.99% to 6.89%	58	32.58%	51.69%
6.89% to 19.77%	51	28.65%	80.34%
19.77% to 32.66%	22	12.36%	92.70%
32.66% to 45.54%	10	5.62%	98.31%
45.54% to 58.43%	2	1.12%	99.44%
Greater than 58.43%	1	0.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.29%	24.07%	73.03%	68.27%
±2σ	-27.47%	41.25%	95.51%	95.45%
±3σ	-44.65%	58.43%	99.44%	99.73%

Descriptive Statistics

Mean	6.891%
Standard Error	1.288%
Median	6.282%
Mode	-0.956%
Standard Deviation	17.179%
Sample Variance	295.103%
Kurtosis	2.87
Skewness	0.72
Range	128.737%
Minimum	-39.011%
Maximum	89.726%
Count	178

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.678%	116	65.17%	10.217%
Negative	-9.548%	62	34.83%	-3.326%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	16.29%
12	3 Years	18.92%
20	5 Years	19.18%
40	10 Years	18.67%
80	20 Years	19.61%
200	50 Years	25.69%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.35. Further, an Excess Kurtosis of 7.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.72%	0	0.00%	0.00%
-29.72% to -14.83%	0	0.00%	0.00%
-14.83% to 0.06%	0	0.00%	0.00%
0.06% to 14.95%	30	16.76%	16.76%
14.95% to 29.83%	89	49.72%	66.48%
29.83% to 44.72%	31	17.32%	83.80%
44.72% to 59.61%	14	7.82%	91.62%
59.61% to 74.50%	8	4.47%	96.09%
74.50% to 89.39%	4	2.23%	98.32%
Greater than 89.39%	3	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.98%	49.69%	85.47%	68.27%
±2σ	-9.87%	69.54%	94.97%	95.45%
±3σ	-29.72%	89.39%	98.32%	99.73%

Descriptive Statistics

Mean	29.834%
Standard Error	1.484%
Median	24.605%
Mode	8.083%
Standard Deviation	19.852%
Sample Variance	394.097%
Kurtosis	7.61
Skewness	2.35
Range	123.532%
Minimum	8.083%
Maximum	131.615%
Count	179

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.834%	179	100.00%	29.834%
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 0.99. Further, an Excess Kurtosis of 2.81 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.49%	0	0.00%	0.00%
-50.49% to -38.74%	2	1.12%	1.12%
-38.74% to -26.99%	4	2.23%	3.35%
-26.99% to -15.24%	31	17.32%	20.67%
-15.24% to -3.48%	60	33.52%	54.19%
-3.48% to 8.27%	53	29.61%	83.80%
8.27% to 20.02%	18	10.06%	93.85%
20.02% to 31.77%	6	3.35%	97.21%
31.77% to 43.52%	2	1.12%	98.32%
Greater than 43.52%	3	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.15%	12.18%	74.86%	68.27%
±2σ	-34.82%	27.85%	94.97%	95.45%
±3σ	-50.49%	43.52%	98.32%	99.73%

Descriptive Statistics

Mean	-3.485%
Standard Error	1.171%
Median	-4.909%
Mode	-0.582%
Standard Deviation	15.668%
Sample Variance	245.495%
Kurtosis	2.81
Skewness	0.99
Range	106.202%
Minimum	-42.238%
Maximum	63.964%
Count	179

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.119%	63	35.20%	4.265%
Negative	-12.063%	115	64.25%	-7.750%
Zero	0.000%	1	0.56%	0.000%

HD Deep Analytical Report