DIS - 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	1.98%	1.53%	1.67%	2.34%	2.22%	2.32%	96.68	101.08	94.55	103.35
Weekly	4.49%	4.02%	4.44%	5.66%	4.90%	5.10%	94.13	103.82	89.63	109.03
Monthly	8.91%	8.72%	9.04%	12.74%	10.19%	10.61%	89.28	109.46	80.62	121.21
Quarterly	15.60%	16.10%	14.64%	22.53%	17.65%	18.38%	82.86	117.94	69.45	140.72
Annual	—	—	—	—	35.31%	36.76%	69.45	140.72	48.79	200.31
Option Time Horizon	—	—	—	—	13.33%	13.87%	86.52	112.95	75.72	129.05

Calculation Notes: Computed at 2026-03-23T16:32 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $98.86 | Strike (K): $100.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.8750 (Bid $4.7000 / Ask $5.0500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.51% | Binomial IV (Annual): 35.31% (CRR binomial tree, American, n=20 steps) | BS IV: 35.41% (European Black-Scholes) | Yahoo IV (Annual): 36.76% → 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
2025-12-15	$0.7500
2025-06-24	$0.5000
2024-12-16	$0.5000
2024-07-08	$0.4500
2023-12-08	$0.3000
2019-12-13	$0.8800
2019-07-05	$0.8800
2018-12-07	$0.8800
2018-07-06	$0.8400
2017-12-08	$0.8400
2017-07-06	$0.7800
2016-12-08	$0.7800
2016-07-07	$0.7100
2015-12-10	$0.7100
2015-07-01	$0.6600
2014-12-11	$1.1500
2013-12-12	$0.8600
2012-12-06	$0.7500
2011-12-14	$0.6000
2010-12-09	$0.4000
2009-12-10	$0.3500
2008-12-11	$0.3500
2007-12-05	$0.3500
2006-12-13	$0.3058
2005-12-08	$0.2664
2004-12-08	$0.2368
2003-12-10	$0.2072
2002-12-11	$0.2072
2001-12-05	$0.2072
2000-12-06	$0.2072
1999-11-12	$0.2072
1999-10-07	$0.0523
1998-10-07	$0.0513
1998-07-22	$0.0513
1998-04-07	$0.0520
1998-01-07	$0.0434
1997-10-15	$0.0434
1997-07-09	$0.0434
1997-04-09	$0.0434
1997-01-08	$0.0362
1996-10-09	$0.0362
1996-07-10	$0.0362
1996-04-10	$0.0362
1995-12-29	$0.0296
1995-10-11	$0.0296
1995-07-06	$0.0296
1995-04-07	$0.0296
1995-01-03	$0.0247
1994-10-07	$0.0247
1994-07-05	$0.0247
1994-04-11	$0.0247
1994-01-04	$0.0204
1993-10-06	$0.0204
1993-07-02	$0.0204
1993-04-05	$0.0204
1993-01-05	$0.0171
1992-10-05	$0.0171
1992-07-06	$0.0171
1992-04-06	$0.0173
1992-01-06	$0.0144
1991-10-07	$0.0144
1991-07-08	$0.0144
1991-04-08	$0.0144
1991-01-14	$0.0119
1990-10-05	$0.0119
1990-07-09	$0.0119
1990-04-06	$0.0119
1990-01-08	$0.0099
1989-10-06	$0.0099
1989-07-10	$0.0099
1989-04-10	$0.0099
1989-01-09	$0.0082
1988-10-07	$0.0082
1988-07-11	$0.0082
1988-04-13	$0.0082
1988-01-12	$0.0066
1987-09-16	$0.0066
1987-06-01	$0.0066
1987-03-09	$0.0066
1986-12-02	$0.0066
1986-09-15	$0.0066
1986-06-02	$0.0066
1986-03-12	$0.0066
1985-12-09	$0.0062
1985-09-10	$0.0062
1985-05-30	$0.0062
1985-03-05	$0.0062
1984-12-04	$0.0062
1984-09-13	$0.0062
1984-06-07	$0.0062
1984-03-08	$0.0062
1983-12-12	$0.0062
1983-10-07	$0.0062
1983-07-01	$0.0062
1983-03-07	$0.0062
1982-11-29	$0.0062
1982-09-27	$0.0062
1982-06-28	$0.0062
1982-03-08	$0.0062
1969-11-24	$0.0004
1969-09-09	$0.0004
1969-06-10	$0.0004
1969-03-06	$0.0004
1968-11-25	$0.0004
1968-09-10	$0.0004
1968-03-11	$0.0004
1967-12-01	$0.0004
1967-09-08	$0.0003
1967-06-09	$0.0003
1967-03-10	$0.0003
1966-11-25	$0.0003
1966-09-09	$0.0003
1966-06-10	$0.0003
1966-03-09	$0.0003
1965-11-26	$0.0003
1965-09-10	$0.0003
1965-06-11	$0.0003
1965-03-12	$0.0003
1964-11-30	$0.0003
1964-06-12	$0.0003
1964-03-13	$0.0003
1963-12-13	$0.0003
1963-09-06	$0.0003
1963-06-07	$0.0003
1963-03-12	$0.0003
1962-12-18	$0.0003
1962-09-11	$0.0002
1962-06-12	$0.0002
1962-03-13	$0.0002

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.00. Further, an Excess Kurtosis of 9.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.87%	105	0.65%	0.65%
-5.87% to -4.39%	127	0.79%	1.44%
-4.39% to -2.90%	546	3.38%	4.82%
-2.90% to -1.42%	1925	11.93%	16.75%
-1.42% to 0.07%	5740	35.56%	52.31%
0.07% to 1.55%	5003	31.00%	83.31%
1.55% to 3.04%	1788	11.08%	94.39%
3.04% to 4.52%	576	3.57%	97.96%
4.52% to 6.01%	210	1.30%	99.26%
Greater than 6.01%	120	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.91%	2.05%	77.51%	68.27%
±2σ	-3.89%	4.03%	95.03%	95.45%
±3σ	-5.87%	6.01%	98.61%	99.73%

Descriptive Statistics

Mean	0.066%
Standard Error	0.016%
Median	0.000%
Mode	0.000%
Standard Deviation	1.980%
Sample Variance	3.922%
Kurtosis	9.36
Skewness	0.00
Range	48.189%
Minimum	-29.094%
Maximum	19.095%
Count	16140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.488%	7821	48.46%	0.721%
Negative	-1.385%	7635	47.30%	-0.655%
Zero	0.000%	684	4.24%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.98%
20	1 Month	2.09%
60	1 Quarter	2.37%
250	1 Year	2.28%
750	3 Years	2.12%
1,250	5 Years	2.34%
2,500	10 Years	2.18%
5,000	20 Years	2.20%
12,500	50 Years	2.38%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.88. Further, an Excess Kurtosis of 17.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.30%	0	0.00%	0.00%
-2.30% to -1.15%	0	0.00%	0.00%
-1.15% to 0.00%	0	0.00%	0.00%
0.00% to 1.16%	2824	17.50%	17.50%
1.16% to 2.31%	7346	45.51%	63.01%
2.31% to 3.46%	3488	21.61%	84.62%
3.46% to 4.61%	1374	8.51%	93.13%
4.61% to 5.76%	581	3.60%	96.73%
5.76% to 6.91%	231	1.43%	98.16%
Greater than 6.91%	297	1.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.77%	3.84%	83.63%	68.27%
±2σ	-0.76%	5.38%	95.76%	95.45%
±3σ	-2.30%	6.91%	98.16%	99.73%

Descriptive Statistics

Mean	2.306%
Standard Error	0.012%
Median	1.911%
Mode	2.326%
Standard Deviation	1.535%
Sample Variance	2.357%
Kurtosis	17.86
Skewness	2.88
Range	26.610%
Minimum	0.166%
Maximum	26.776%
Count	16141

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.306%	16141	100.00%	2.306%
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 0.37. Further, an Excess Kurtosis of 8.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.03%	106	0.66%	0.66%
-5.03% to -3.78%	194	1.20%	1.86%
-3.78% to -2.52%	633	3.92%	5.78%
-2.52% to -1.27%	1857	11.50%	17.29%
-1.27% to -0.02%	4843	30.00%	47.29%
-0.02% to 1.23%	5729	35.49%	82.78%
1.23% to 2.48%	1926	11.93%	94.72%
2.48% to 3.73%	587	3.64%	98.35%
3.73% to 4.99%	163	1.01%	99.36%
Greater than 4.99%	103	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.69%	1.65%	76.38%	68.27%
±2σ	-3.36%	3.32%	95.00%	95.45%
±3σ	-5.03%	4.99%	98.71%	99.73%

Descriptive Statistics

Mean	-0.021%
Standard Error	0.013%
Median	0.000%
Mode	0.000%
Standard Deviation	1.669%
Sample Variance	2.784%
Kurtosis	8.38
Skewness	0.37
Range	37.352%
Minimum	-11.265%
Maximum	26.087%
Count	16141

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.231%	7595	47.05%	0.579%
Negative	-1.264%	7663	47.48%	-0.600%
Zero	0.000%	883	5.47%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.11. Further, an Excess Kurtosis of 3.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.15%	18	0.54%	0.54%
-13.15% to -9.78%	27	0.81%	1.34%
-9.78% to -6.41%	111	3.31%	4.66%
-6.41% to -3.04%	463	13.82%	18.48%
-3.04% to 0.32%	1118	33.37%	51.85%
0.32% to 3.69%	998	29.79%	81.64%
3.69% to 7.06%	400	11.94%	93.58%
7.06% to 10.43%	146	4.36%	97.94%
10.43% to 13.80%	42	1.25%	99.19%
Greater than 13.80%	27	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.17%	4.81%	75.55%	68.27%
±2σ	-8.66%	9.30%	94.81%	95.45%
±3σ	-13.15%	13.80%	98.63%	99.73%

Descriptive Statistics

Mean	0.323%
Standard Error	0.078%
Median	0.184%
Mode	0.000%
Standard Deviation	4.491%
Sample Variance	20.166%
Kurtosis	3.82
Skewness	0.11
Range	61.118%
Minimum	-36.661%
Maximum	24.457%
Count	3350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.487%	1718	51.28%	1.788%
Negative	-3.098%	1584	47.28%	-1.465%
Zero	0.000%	48	1.43%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	4.12%
12	1 Quarter	4.98%
52	1 Year	5.21%
156	3 Years	5.06%
260	5 Years	5.66%
520	10 Years	5.17%
1,040	20 Years	5.17%
2,600	50 Years	5.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 21.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.87%	0	0.00%	0.00%
-5.87% to -2.86%	0	0.00%	0.00%
-2.86% to 0.15%	0	0.00%	0.00%
0.15% to 3.17%	571	17.04%	17.04%
3.17% to 6.18%	1541	45.99%	63.03%
6.18% to 9.19%	741	22.11%	85.14%
9.19% to 12.21%	282	8.42%	93.55%
12.21% to 15.22%	107	3.19%	96.75%
15.22% to 18.23%	49	1.46%	98.21%
Greater than 18.23%	60	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.16%	10.20%	83.71%	68.27%
±2σ	-1.85%	14.21%	96.33%	95.45%
±3σ	-5.87%	18.23%	98.21%	99.73%

Descriptive Statistics

Mean	6.180%
Standard Error	0.069%
Median	5.202%
Mode	5.263%
Standard Deviation	4.017%
Sample Variance	16.134%
Kurtosis	21.16
Skewness	3.09
Range	62.485%
Minimum	0.903%
Maximum	63.388%
Count	3351

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.180%	3351	100.00%	6.180%
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 11.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.40%	16	0.48%	0.48%
-13.40% to -10.08%	34	1.01%	1.49%
-10.08% to -6.75%	138	4.12%	5.61%
-6.75% to -3.42%	428	12.77%	18.38%
-3.42% to -0.10%	1087	32.44%	50.82%
-0.10% to 3.23%	1059	31.60%	82.42%
3.23% to 6.56%	408	12.18%	94.60%
6.56% to 9.88%	118	3.52%	98.12%
9.88% to 13.21%	36	1.07%	99.19%
Greater than 13.21%	27	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.53%	4.34%	76.04%	68.27%
±2σ	-8.97%	8.78%	95.20%	95.45%
±3σ	-13.40%	13.21%	98.72%	99.73%

Descriptive Statistics

Mean	-0.096%
Standard Error	0.077%
Median	-0.192%
Mode	0.000%
Standard Deviation	4.436%
Sample Variance	19.674%
Kurtosis	11.70
Skewness	0.99
Range	78.347%
Minimum	-19.651%
Maximum	58.696%
Count	3351

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.258%	1577	47.06%	1.533%
Negative	-3.176%	1719	51.30%	-1.629%
Zero	0.000%	55	1.64%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.11. Further, an Excess Kurtosis of 1.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.36%	4	0.52%	0.52%
-25.36% to -18.68%	5	0.65%	1.17%
-18.68% to -12.00%	33	4.29%	5.45%
-12.00% to -5.31%	112	14.55%	20.00%
-5.31% to 1.37%	234	30.39%	50.39%
1.37% to 8.05%	232	30.13%	80.52%
8.05% to 14.73%	104	13.51%	94.03%
14.73% to 21.41%	31	4.03%	98.05%
21.41% to 28.10%	10	1.30%	99.35%
Greater than 28.10%	5	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.54%	10.28%	72.34%	68.27%
±2σ	-16.45%	19.19%	94.16%	95.45%
±3σ	-25.36%	28.10%	98.83%	99.73%

Descriptive Statistics

Mean	1.368%
Standard Error	0.321%
Median	1.276%
Mode	0.000%
Standard Deviation	8.910%
Sample Variance	79.396%
Kurtosis	1.79
Skewness	0.11
Range	79.440%
Minimum	-37.919%
Maximum	41.521%
Count	770

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.127%	438	56.88%	4.054%
Negative	-6.305%	328	42.60%	-2.686%
Zero	0.000%	4	0.52%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	8.35%
12	1 Year	10.90%
36	3 Years	11.17%
60	5 Years	12.74%
120	10 Years	11.59%
240	20 Years	11.10%
600	50 Years	12.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.96. Further, an Excess Kurtosis of 16.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.86%	0	0.00%	0.00%
-11.86% to -5.31%	0	0.00%	0.00%
-5.31% to 1.23%	0	0.00%	0.00%
1.23% to 7.77%	134	17.38%	17.38%
7.77% to 14.32%	341	44.23%	61.61%
14.32% to 20.86%	171	22.18%	83.79%
20.86% to 27.40%	75	9.73%	93.51%
27.40% to 33.95%	29	3.76%	97.28%
33.95% to 40.49%	11	1.43%	98.70%
Greater than 40.49%	10	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.59%	23.04%	82.88%	68.27%
±2σ	-3.13%	31.77%	96.63%	95.45%
±3σ	-11.86%	40.49%	98.70%	99.73%

Descriptive Statistics

Mean	14.317%
Standard Error	0.314%
Median	12.212%
Mode	15.789%
Standard Deviation	8.724%
Sample Variance	76.113%
Kurtosis	16.84
Skewness	2.96
Range	90.798%
Minimum	3.141%
Maximum	93.939%
Count	771

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.317%	771	100.00%	14.317%
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 1.11. Further, an Excess Kurtosis of 5.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.55%	1	0.13%	0.13%
-27.55% to -20.77%	4	0.52%	0.65%
-20.77% to -13.99%	33	4.28%	4.93%
-13.99% to -7.21%	110	14.27%	19.20%
-7.21% to -0.42%	265	34.37%	53.57%
-0.42% to 6.36%	213	27.63%	81.19%
6.36% to 13.14%	100	12.97%	94.16%
13.14% to 19.93%	27	3.50%	97.67%
19.93% to 26.71%	13	1.69%	99.35%
Greater than 26.71%	5	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.47%	8.62%	74.32%	68.27%
±2σ	-18.51%	17.67%	95.07%	95.45%
±3σ	-27.55%	26.71%	99.22%	99.73%

Descriptive Statistics

Mean	-0.422%
Standard Error	0.326%
Median	-0.988%
Mode	0.000%
Standard Deviation	9.044%
Sample Variance	81.789%
Kurtosis	5.52
Skewness	1.11
Range	89.437%
Minimum	-28.926%
Maximum	60.511%
Count	771

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.233%	329	42.67%	3.086%
Negative	-6.205%	436	56.55%	-3.509%
Zero	0.000%	6	0.78%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.59. Further, an Excess Kurtosis of 1.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.71%	0	0.00%	0.00%
-42.71% to -31.01%	2	0.78%	0.78%
-31.01% to -19.32%	12	4.67%	5.45%
-19.32% to -7.62%	48	18.68%	24.12%
-7.62% to 4.08%	64	24.90%	49.03%
4.08% to 15.78%	87	33.85%	82.88%
15.78% to 27.48%	25	9.73%	92.61%
27.48% to 39.17%	13	5.06%	97.67%
39.17% to 50.87%	3	1.17%	98.83%
Greater than 50.87%	3	1.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.52%	19.68%	74.32%	68.27%
±2σ	-27.11%	35.27%	94.94%	95.45%
±3σ	-42.71%	50.87%	98.83%	99.73%

Descriptive Statistics

Mean	4.080%
Standard Error	0.973%
Median	4.939%
Mode	-36.861%
Standard Deviation	15.597%
Sample Variance	243.253%
Kurtosis	1.24
Skewness	0.59
Range	100.073%
Minimum	-36.861%
Maximum	63.212%
Count	257

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.139%	150	58.37%	8.252%
Negative	-10.023%	107	41.63%	-4.173%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.84%
12	3 Years	21.53%
20	5 Years	22.53%
40	10 Years	20.92%
80	20 Years	19.70%
200	50 Years	22.01%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.25. Further, an Excess Kurtosis of 6.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.02%	0	0.00%	0.00%
-21.02% to -8.94%	0	0.00%	0.00%
-8.94% to 3.13%	0	0.00%	0.00%
3.13% to 15.21%	43	16.67%	16.67%
15.21% to 27.28%	115	44.57%	61.24%
27.28% to 39.36%	64	24.81%	86.05%
39.36% to 51.44%	17	6.59%	92.64%
51.44% to 63.51%	8	3.10%	95.74%
63.51% to 75.59%	4	1.55%	97.29%
Greater than 75.59%	7	2.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.18%	43.38%	85.66%	68.27%
±2σ	-4.92%	59.49%	94.96%	95.45%
±3σ	-21.02%	75.59%	97.29%	99.73%

Descriptive Statistics

Mean	27.284%
Standard Error	1.002%
Median	22.807%
Mode	23.420%
Standard Deviation	16.101%
Sample Variance	259.253%
Kurtosis	6.50
Skewness	2.25
Range	98.699%
Minimum	6.926%
Maximum	105.625%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.284%	258	100.00%	27.284%
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 0.59. Further, an Excess Kurtosis of 1.34 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.42%	0	0.00%	0.00%
-45.42% to -34.44%	2	0.78%	0.78%
-34.44% to -23.46%	9	3.49%	4.26%
-23.46% to -12.48%	40	15.50%	19.77%
-12.48% to -1.50%	91	35.27%	55.04%
-1.50% to 9.48%	64	24.81%	79.84%
9.48% to 20.46%	33	12.79%	92.64%
20.46% to 31.44%	15	5.81%	98.45%
31.44% to 42.42%	1	0.39%	98.84%
Greater than 42.42%	3	1.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.14%	13.14%	75.19%	68.27%
±2σ	-30.78%	27.78%	94.57%	95.45%
±3σ	-45.42%	42.42%	98.84%	99.73%

Descriptive Statistics

Mean	-1.497%
Standard Error	0.911%
Median	-3.965%
Mode	-11.491%
Standard Deviation	14.640%
Sample Variance	214.334%
Kurtosis	1.34
Skewness	0.59
Range	96.457%
Minimum	-38.636%
Maximum	57.821%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.918%	109	42.25%	5.035%
Negative	-11.387%	148	57.36%	-6.532%
Zero	0.000%	1	0.39%	0.000%

DIS Deep Analytical Report