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%	1.54%	1.67%	2.35%	1.64%	1.69%	103.86	107.33	102.17	109.11
Weekly	4.49%	4.02%	4.44%	5.68%	3.62%	3.71%	101.83	109.47	98.21	113.50
Monthly	8.91%	8.72%	9.05%	12.81%	7.53%	7.73%	97.92	113.84	90.82	122.74
Quarterly	15.58%	16.11%	14.63%	22.41%	13.04%	13.39%	92.67	120.29	81.34	137.05
Annual	—	—	—	—	26.08%	26.77%	81.34	137.05	62.66	177.89
Option Time Horizon	—	—	—	—	10.03%	10.30%	95.50	116.72	86.38	129.04

Calculation Notes: Computed at 2026-02-22T14:17 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $105.58 | Strike (K): $110.00 (first OTM call ≥ spot) | Observed Mid-Price: $2.5550 (Bid $2.5100 / Ask $2.6000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.42% | Binomial IV (Annual): 26.08% (CRR binomial tree, American, n=20 steps) | BS IV: 25.95% (European Black-Scholes) | Yahoo IV (Annual): 26.77% → 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 9.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.88%	104	0.65%	0.65%
-5.88% to -4.39%	128	0.79%	1.44%
-4.39% to -2.91%	545	3.38%	4.82%
-2.91% to -1.42%	1922	11.92%	16.74%
-1.42% to 0.07%	5729	35.54%	52.29%
0.07% to 1.55%	4999	31.01%	83.30%
1.55% to 3.04%	1790	11.10%	94.40%
3.04% to 4.52%	572	3.55%	97.95%
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	-1.92%	2.05%	77.49%	68.27%
±2σ	-3.90%	4.03%	95.02%	95.45%
±3σ	-5.88%	6.01%	98.61%	99.73%

Descriptive Statistics

Mean	0.066%
Standard Error	0.016%
Median	0.000%
Mode	0.000%
Standard Deviation	1.981%
Sample Variance	3.926%
Kurtosis	9.35
Skewness	0.00
Range	48.189%
Minimum	-29.094%
Maximum	19.095%
Count	16119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.489%	7815	48.48%	0.722%
Negative	-1.387%	7620	47.27%	-0.656%
Zero	0.000%	684	4.24%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.56%
20	1 Month	3.10%
60	1 Quarter	2.31%
250	1 Year	2.33%
750	3 Years	2.13%
1,250	5 Years	2.35%
2,500	10 Years	2.17%
5,000	20 Years	2.19%
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 17.84 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	17.52%	17.52%
1.16% to 2.31%	7332	45.48%	63.00%
2.31% to 3.46%	3483	21.61%	84.61%
3.46% to 4.61%	1372	8.51%	93.12%
4.61% to 5.76%	583	3.62%	96.74%
5.76% to 6.92%	229	1.42%	98.16%
Greater than 6.92%	297	1.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.77%	3.84%	83.64%	68.27%
±2σ	-0.77%	5.38%	95.75%	95.45%
±3σ	-2.30%	6.92%	98.16%	99.73%

Descriptive Statistics

Mean	2.307%
Standard Error	0.012%
Median	1.911%
Mode	2.326%
Standard Deviation	1.536%
Sample Variance	2.359%
Kurtosis	17.84
Skewness	2.88
Range	26.610%
Minimum	0.166%
Maximum	26.776%
Count	16120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.307%	16120	100.00%	2.307%
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 8.37 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%	193	1.20%	1.85%
-3.78% to -2.53%	632	3.92%	5.78%
-2.53% to -1.27%	1858	11.53%	17.30%
-1.27% to -0.02%	4835	29.99%	47.30%
-0.02% to 1.23%	5717	35.47%	82.76%
1.23% to 2.48%	1926	11.95%	94.71%
2.48% to 3.74%	587	3.64%	98.35%
3.74% 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%	76.36%	68.27%
±2σ	-3.36%	3.32%	94.99%	95.45%
±3σ	-5.03%	4.99%	98.70%	99.73%

Descriptive Statistics

Mean	-0.021%
Standard Error	0.013%
Median	0.000%
Mode	0.000%
Standard Deviation	1.670%
Sample Variance	2.787%
Kurtosis	8.37
Skewness	0.37
Range	37.352%
Minimum	-11.265%
Maximum	26.087%
Count	16120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.232%	7583	47.04%	0.580%
Negative	-1.265%	7654	47.48%	-0.601%
Zero	0.000%	883	5.48%	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	3.32%	4.66%
-6.41% to -3.04%	464	13.87%	18.53%
-3.04% to 0.33%	1114	33.29%	51.82%
0.33% to 3.70%	997	29.80%	81.62%
3.70% to 7.07%	400	11.95%	93.57%
7.07% to 10.44%	146	4.36%	97.94%
10.44% to 13.80%	42	1.26%	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%	4.82%	75.52%	68.27%
±2σ	-8.66%	9.31%	94.80%	95.45%
±3σ	-13.15%	13.81%	98.66%	99.73%

Descriptive Statistics

Mean	0.326%
Standard Error	0.078%
Median	0.189%
Mode	0.000%
Standard Deviation	4.493%
Sample Variance	20.184%
Kurtosis	3.82
Skewness	0.11
Range	61.118%
Minimum	-36.661%
Maximum	24.457%
Count	3346

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.487%	1718	51.34%	1.790%
Negative	-3.101%	1580	47.22%	-1.464%
Zero	0.000%	48	1.44%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.78%
12	1 Quarter	4.73%
52	1 Year	5.37%
156	3 Years	5.10%
260	5 Years	5.68%
520	10 Years	5.16%
1,040	20 Years	5.16%
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 21.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.88%	0	0.00%	0.00%
-5.88% to -2.86%	0	0.00%	0.00%
-2.86% to 0.15%	0	0.00%	0.00%
0.15% to 3.17%	570	17.03%	17.03%
3.17% to 6.18%	1539	45.98%	63.01%
6.18% to 9.20%	740	22.11%	85.12%
9.20% to 12.21%	283	8.46%	93.58%
12.21% to 15.22%	106	3.17%	96.74%
15.22% to 18.24%	49	1.46%	98.21%
Greater than 18.24%	60	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.16%	10.20%	83.66%	68.27%
±2σ	-1.86%	14.22%	96.33%	95.45%
±3σ	-5.88%	18.24%	98.21%	99.73%

Descriptive Statistics

Mean	6.182%
Standard Error	0.069%
Median	5.213%
Mode	5.263%
Standard Deviation	4.019%
Sample Variance	16.149%
Kurtosis	21.14
Skewness	3.09
Range	62.485%
Minimum	0.903%
Maximum	63.388%
Count	3347

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.182%	3347	100.00%	6.182%
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 11.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.41%	16	0.48%	0.48%
-13.41% to -10.08%	34	1.02%	1.49%
-10.08% to -6.75%	138	4.12%	5.62%
-6.75% to -3.43%	428	12.79%	18.40%
-3.43% to -0.10%	1087	32.48%	50.88%
-0.10% to 3.23%	1055	31.52%	82.40%
3.23% to 6.56%	408	12.19%	94.59%
6.56% to 9.89%	118	3.53%	98.12%
9.89% to 13.22%	36	1.08%	99.19%
Greater than 13.22%	27	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.54%	4.34%	76.04%	68.27%
±2σ	-8.97%	8.78%	95.19%	95.45%
±3σ	-13.41%	13.22%	98.72%	99.73%

Descriptive Statistics

Mean	-0.098%
Standard Error	0.077%
Median	-0.193%
Mode	0.000%
Standard Deviation	4.438%
Sample Variance	19.693%
Kurtosis	11.69
Skewness	0.99
Range	78.347%
Minimum	-19.651%
Maximum	58.696%
Count	3347

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.262%	1573	47.00%	1.533%
Negative	-3.176%	1719	51.36%	-1.631%
Zero	0.000%	55	1.64%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.10. 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 -18.67%	5	0.65%	1.17%
-18.67% to -11.99%	33	4.29%	5.46%
-11.99% to -5.31%	111	14.43%	19.90%
-5.31% to 1.38%	235	30.56%	50.46%
1.38% to 8.06%	231	30.04%	80.49%
8.06% to 14.75%	104	13.52%	94.02%
14.75% to 21.43%	31	4.03%	98.05%
21.43% to 28.11%	10	1.30%	99.35%
Greater than 28.11%	5	0.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.53%	10.29%	72.30%	68.27%
±2σ	-16.45%	19.20%	94.15%	95.45%
±3σ	-25.36%	28.11%	98.83%	99.73%

Descriptive Statistics

Mean	1.378%
Standard Error	0.321%
Median	1.315%
Mode	0.000%
Standard Deviation	8.912%
Sample Variance	79.425%
Kurtosis	1.79
Skewness	0.10
Range	79.440%
Minimum	-37.919%
Maximum	41.521%
Count	769

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.127%	438	56.96%	4.059%
Negative	-6.305%	327	42.52%	-2.681%
Zero	0.000%	4	0.52%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	9.35%
12	1 Year	11.75%
36	3 Years	11.31%
60	5 Years	12.81%
120	10 Years	11.57%
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 -11.85%	0	0.00%	0.00%
-11.85% to -5.30%	0	0.00%	0.00%
-5.30% to 1.24%	0	0.00%	0.00%
1.24% to 7.78%	134	17.40%	17.40%
7.78% to 14.33%	341	44.29%	61.69%
14.33% to 20.87%	170	22.08%	83.77%
20.87% to 27.41%	75	9.74%	93.51%
27.41% to 33.96%	29	3.77%	97.27%
33.96% to 40.50%	11	1.43%	98.70%
Greater than 40.50%	10	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.60%	23.05%	82.86%	68.27%
±2σ	-3.12%	31.78%	96.62%	95.45%
±3σ	-11.85%	40.50%	98.70%	99.73%

Descriptive Statistics

Mean	14.327%
Standard Error	0.314%
Median	12.212%
Mode	15.789%
Standard Deviation	8.725%
Sample Variance	76.129%
Kurtosis	16.84
Skewness	2.96
Range	90.798%
Minimum	3.141%
Maximum	93.939%
Count	770

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.327%	770	100.00%	14.327%
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 1.12. 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 -27.57%	1	0.13%	0.13%
-27.57% to -20.79%	4	0.52%	0.65%
-20.79% to -14.00%	33	4.29%	4.94%
-14.00% to -7.21%	110	14.29%	19.22%
-7.21% to -0.43%	265	34.42%	53.64%
-0.43% to 6.36%	212	27.53%	81.17%
6.36% to 13.14%	100	12.99%	94.16%
13.14% to 19.93%	27	3.51%	97.66%
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	-9.48%	8.62%	74.55%	68.27%
±2σ	-18.52%	17.66%	95.06%	95.45%
±3σ	-27.57%	26.71%	99.22%	99.73%

Descriptive Statistics

Mean	-0.430%
Standard Error	0.326%
Median	-1.008%
Mode	0.000%
Standard Deviation	9.047%
Sample Variance	81.846%
Kurtosis	5.52
Skewness	1.12
Range	89.437%
Minimum	-28.926%
Maximum	60.511%
Count	770

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.238%	328	42.60%	3.083%
Negative	-6.204%	436	56.62%	-3.513%
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 1.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.63%	0	0.00%	0.00%
-42.63% to -30.95%	2	0.78%	0.78%
-30.95% to -19.26%	12	4.67%	5.45%
-19.26% to -7.58%	47	18.29%	23.74%
-7.58% to 4.10%	65	25.29%	49.03%
4.10% to 15.79%	87	33.85%	82.88%
15.79% to 27.47%	25	9.73%	92.61%
27.47% to 39.15%	13	5.06%	97.67%
39.15% to 50.83%	3	1.17%	98.83%
Greater than 50.83%	3	1.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.47%	19.68%	74.71%	68.27%
±2σ	-27.05%	35.26%	94.94%	95.45%
±3σ	-42.63%	50.83%	98.83%	99.73%

Descriptive Statistics

Mean	4.102%
Standard Error	0.972%
Median	4.939%
Mode	-36.861%
Standard Deviation	15.577%
Sample Variance	242.647%
Kurtosis	1.26
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	-9.968%	107	41.63%	-4.150%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.21%
12	3 Years	21.32%
20	5 Years	22.41%
40	10 Years	20.86%
80	20 Years	19.67%
200	50 Years	21.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.24. Further, an Excess Kurtosis of 6.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.07%	0	0.00%	0.00%
-21.07% to -8.98%	0	0.00%	0.00%
-8.98% to 3.10%	0	0.00%	0.00%
3.10% to 15.19%	43	16.67%	16.67%
15.19% to 27.27%	115	44.57%	61.24%
27.27% to 39.36%	64	24.81%	86.05%
39.36% to 51.44%	17	6.59%	92.64%
51.44% to 63.53%	8	3.10%	95.74%
63.53% to 75.61%	4	1.55%	97.29%
Greater than 75.61%	7	2.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.16%	43.39%	85.27%	68.27%
±2σ	-4.95%	59.50%	94.96%	95.45%
±3σ	-21.07%	75.61%	97.29%	99.73%

Descriptive Statistics

Mean	27.273%
Standard Error	1.003%
Median	22.807%
Mode	23.420%
Standard Deviation	16.113%
Sample Variance	259.615%
Kurtosis	6.49
Skewness	2.24
Range	98.699%
Minimum	6.926%
Maximum	105.625%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.273%	258	100.00%	27.273%
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 0.60. Further, an Excess Kurtosis of 1.35 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 -34.45%	2	0.78%	0.78%
-34.45% to -23.47%	9	3.49%	4.26%
-23.47% to -12.50%	40	15.50%	19.77%
-12.50% to -1.52%	91	35.27%	55.04%
-1.52% to 9.45%	64	24.81%	79.84%
9.45% to 20.43%	33	12.79%	92.64%
20.43% to 31.41%	15	5.81%	98.45%
31.41% to 42.38%	1	0.39%	98.84%
Greater than 42.38%	3	1.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.16%	13.11%	75.19%	68.27%
±2σ	-30.79%	27.75%	94.57%	95.45%
±3σ	-45.42%	42.38%	98.84%	99.73%

Descriptive Statistics

Mean	-1.522%
Standard Error	0.911%
Median	-3.965%
Mode	-11.491%
Standard Deviation	14.634%
Sample Variance	214.168%
Kurtosis	1.35
Skewness	0.60
Range	96.457%
Minimum	-38.636%
Maximum	57.821%
Count	258

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.982%	108	41.86%	5.016%
Negative	-11.321%	149	57.75%	-6.538%
Zero	0.000%	1	0.39%	0.000%

DIS Deep Analytical Report