LIN - 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	1.74%	1.44%	1.51%	1.76%	—	1.95%	470.90	487.78	462.68	496.45
Weekly	3.70%	3.50%	3.62%	4.06%	—	4.29%	461.05	498.21	443.52	517.91
Monthly	6.70%	6.92%	6.58%	9.01%	—	8.93%	442.11	519.55	407.84	563.21
Quarterly	10.57%	12.14%	9.82%	14.36%	—	15.47%	416.75	551.16	362.39	633.84
Annual	—	—	—	—	—	30.94%	362.39	633.84	274.02	838.27
Option Time Horizon	—	—	—	—	—	11.68%	431.28	532.60	388.09	591.87

Calculation Notes: Computed at 2026-03-23T16:31 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $479.27 | Strike (K): $480.00 (first OTM call ≥ spot) | Observed Mid-Price: $20.6000 (Bid $18.8000 / Ask $22.4000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.23% | Binomial IV (Annual): 0.00% (CRR binomial tree, American, n=20 steps) | BS IV: 27.95% (European Black-Scholes) | Yahoo IV (Annual): 30.94% → 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
2026-03-11	$1.6000
2025-12-03	$1.5000
2025-09-04	$1.5000
2025-06-04	$1.5000
2025-03-13	$1.5000
2024-12-03	$1.3900
2024-09-04	$1.3900
2024-06-04	$1.3900
2024-03-13	$1.3900
2023-12-01	$1.2750
2023-09-01	$1.2750
2023-06-01	$1.2750
2023-03-13	$1.2750
2022-12-01	$1.1700
2022-09-01	$1.1700
2022-06-02	$1.1700
2022-03-10	$1.1700
2021-12-02	$1.0600
2021-09-02	$1.0600
2021-06-02	$1.0600
2021-03-04	$1.0600
2020-12-02	$0.9630
2020-09-02	$0.9630
2020-06-02	$0.9630
2020-03-05	$0.9630
2019-12-02	$0.8750
2019-08-30	$0.8750
2019-05-31	$0.8750
2019-03-07	$0.8750
2018-12-17	$0.8250
2018-08-03	$0.8250
2018-06-06	$0.8250
2018-03-06	$0.8250
2017-12-06	$0.7880
2017-09-07	$0.7880
2017-06-05	$0.7880
2017-03-03	$0.7880
2016-12-05	$0.7500
2016-09-06	$0.7500
2016-06-03	$0.7500
2016-03-03	$0.7500
2015-12-03	$0.7150
2015-09-03	$0.7150
2015-06-03	$0.7150
2015-03-04	$0.7150
2014-12-03	$0.6500
2014-09-04	$0.6500
2014-06-04	$0.6500
2014-03-05	$0.6500
2013-12-04	$0.6000
2013-09-04	$0.6000
2013-06-05	$0.6000
2013-03-05	$0.6000
2012-12-05	$0.5500
2012-09-05	$0.5500
2012-06-05	$0.5500
2012-03-05	$0.5500
2011-12-05	$0.5000
2011-09-02	$0.5000
2011-06-03	$0.5000
2011-03-03	$0.5000
2010-12-03	$0.4500
2010-09-02	$0.4500
2010-06-03	$0.4500
2010-03-03	$0.4500
2009-12-03	$0.4000
2009-09-02	$0.4000
2009-06-03	$0.4000
2009-03-04	$0.4000
2008-12-03	$0.3750
2008-09-03	$0.3750
2008-06-04	$0.3750
2008-03-05	$0.3750
2007-12-05	$0.3000
2007-09-05	$0.3000
2007-06-05	$0.3000
2007-03-05	$0.3000
2006-12-05	$0.2500
2006-09-05	$0.2500
2006-06-05	$0.2500
2006-03-03	$0.2500
2005-12-05	$0.1800
2005-09-02	$0.1800
2005-06-03	$0.1800
2005-03-03	$0.1800
2004-12-03	$0.1500
2004-09-02	$0.1500
2004-06-03	$0.1500
2004-03-03	$0.1500
2003-12-03	$0.1350
2003-09-03	$0.1075
2003-06-04	$0.1075
2003-03-05	$0.1075
2002-12-04	$0.0950
2002-09-04	$0.0950
2002-06-05	$0.0950
2002-03-05	$0.0950
2001-12-05	$0.0850
2001-09-05	$0.0850
2001-06-05	$0.0850
2001-03-05	$0.0850
2000-12-05	$0.0775
2000-09-06	$0.0775
2000-06-05	$0.0775
2000-03-03	$0.0775
1999-12-03	$0.0700
1999-09-02	$0.0700
1999-06-03	$0.0700
1999-03-03	$0.0700
1998-12-03	$0.0625
1998-09-03	$0.0625
1998-06-03	$0.0625
1998-03-04	$0.0625
1997-12-03	$0.0550
1997-09-04	$0.0550
1997-06-04	$0.0550
1997-03-05	$0.0550
1996-12-04	$0.0475
1996-09-05	$0.0475
1996-06-05	$0.0475
1996-03-05	$0.0475
1995-12-05	$0.0400
1995-09-06	$0.0400
1995-06-01	$0.0400
1995-03-01	$0.0400
1994-12-01	$0.0350
1994-09-01	$0.0350
1994-06-01	$0.0350
1994-03-01	$0.0350
1993-12-06	$0.0310
1993-09-02	$0.0310
1993-06-01	$0.0310
1993-03-01	$0.0310
1992-12-01	$0.0310
1992-09-01	$0.0310

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.21. Further, an Excess Kurtosis of 5.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.15%	46	0.54%	0.54%
-5.15% to -3.84%	93	1.09%	1.64%
-3.84% to -2.54%	307	3.61%	5.25%
-2.54% to -1.23%	1029	12.11%	17.36%
-1.23% to 0.07%	2898	34.10%	51.46%
0.07% to 1.37%	2685	31.60%	83.05%
1.37% to 2.68%	971	11.43%	94.48%
2.68% to 3.98%	316	3.72%	98.20%
3.98% to 5.29%	84	0.99%	99.19%
Greater than 5.29%	69	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.67%	1.81%	77.19%	68.27%
±2σ	-3.41%	3.55%	94.78%	95.45%
±3σ	-5.15%	5.29%	98.65%	99.73%

Descriptive Statistics

Mean	0.070%
Standard Error	0.019%
Median	0.022%
Mode	0.000%
Standard Deviation	1.739%
Sample Variance	3.023%
Kurtosis	5.99
Skewness	0.21
Range	28.848%
Minimum	-13.986%
Maximum	14.862%
Count	8498

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.273%	4293	50.52%	0.643%
Negative	-1.221%	3990	46.95%	-0.573%
Zero	0.000%	215	2.53%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.65%
20	1 Month	2.03%
60	1 Quarter	1.81%
250	1 Year	1.73%
750	3 Years	1.57%
1,250	5 Years	1.76%
2,500	10 Years	1.83%
5,000	20 Years	1.98%
12,500	50 Years	2.28%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.89. Further, an Excess Kurtosis of 15.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.16%	0	0.00%	0.00%
-2.16% to -1.08%	0	0.00%	0.00%
-1.08% to -0.00%	0	0.00%	0.00%
-0.00% to 1.07%	1482	17.44%	17.44%
1.07% to 2.15%	3886	45.72%	63.16%
2.15% to 3.23%	1829	21.52%	84.68%
3.23% to 4.31%	705	8.30%	92.98%
4.31% to 5.38%	312	3.67%	96.65%
5.38% to 6.46%	138	1.62%	98.27%
Greater than 6.46%	147	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.72%	3.59%	85.40%	68.27%
±2σ	-0.72%	5.02%	95.93%	95.45%
±3σ	-2.16%	6.46%	98.27%	99.73%

Descriptive Statistics

Mean	2.152%
Standard Error	0.016%
Median	1.761%
Mode	1.639%
Standard Deviation	1.436%
Sample Variance	2.063%
Kurtosis	15.69
Skewness	2.89
Range	19.065%
Minimum	0.327%
Maximum	19.392%
Count	8499

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.152%	8499	100.00%	2.152%
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 0.02. Further, an Excess Kurtosis of 5.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.59%	64	0.75%	0.75%
-4.59% to -3.46%	99	1.16%	1.92%
-3.46% to -2.33%	332	3.91%	5.82%
-2.33% to -1.19%	944	11.11%	16.93%
-1.19% to -0.06%	2710	31.89%	48.82%
-0.06% to 1.07%	2918	34.33%	83.15%
1.07% to 2.20%	968	11.39%	94.54%
2.20% to 3.33%	300	3.53%	98.07%
3.33% to 4.46%	107	1.26%	99.33%
Greater than 4.46%	57	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.57%	1.45%	76.89%	68.27%
±2σ	-3.08%	2.96%	94.51%	95.45%
±3σ	-4.59%	4.46%	98.58%	99.73%

Descriptive Statistics

Mean	-0.062%
Standard Error	0.016%
Median	-0.026%
Mode	0.000%
Standard Deviation	1.509%
Sample Variance	2.279%
Kurtosis	5.01
Skewness	0.02
Range	24.502%
Minimum	-11.494%
Maximum	13.008%
Count	8499

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.075%	3948	46.45%	0.499%
Negative	-1.105%	4317	50.79%	-0.561%
Zero	0.000%	234	2.75%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.14. Further, an Excess Kurtosis of 7.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.76%	12	0.68%	0.68%
-10.76% to -7.98%	19	1.08%	1.76%
-7.98% to -5.21%	59	3.35%	5.11%
-5.21% to -2.44%	214	12.15%	17.26%
-2.44% to 0.34%	581	32.99%	50.26%
0.34% to 3.11%	572	32.48%	82.74%
3.11% to 5.88%	210	11.93%	94.66%
5.88% to 8.66%	64	3.63%	98.30%
8.66% to 11.43%	14	0.80%	99.09%
Greater than 11.43%	16	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.36%	4.04%	77.12%	68.27%
±2σ	-7.06%	7.73%	95.46%	95.45%
±3σ	-10.76%	11.43%	98.41%	99.73%

Descriptive Statistics

Mean	0.337%
Standard Error	0.088%
Median	0.330%
Mode	0.000%
Standard Deviation	3.698%
Sample Variance	13.677%
Kurtosis	7.07
Skewness	0.14
Range	55.585%
Minimum	-29.513%
Maximum	26.072%
Count	1761

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.707%	952	54.06%	1.463%
Negative	-2.498%	794	45.09%	-1.126%
Zero	0.000%	15	0.85%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	4.68%
12	1 Quarter	4.62%
52	1 Year	3.89%
156	3 Years	3.47%
260	5 Years	4.06%
520	10 Years	4.28%
1,040	20 Years	4.52%
2,600	50 Years	5.23%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.05. Further, an Excess Kurtosis of 17.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.15%	0	0.00%	0.00%
-5.15% to -2.52%	0	0.00%	0.00%
-2.52% to 0.10%	0	0.00%	0.00%
0.10% to 2.73%	316	17.93%	17.93%
2.73% to 5.35%	759	43.08%	61.01%
5.35% to 7.98%	426	24.18%	85.19%
7.98% to 10.60%	156	8.85%	94.04%
10.60% to 13.23%	49	2.78%	96.82%
13.23% to 15.85%	23	1.31%	98.13%
Greater than 15.85%	33	1.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.85%	8.85%	86.15%	68.27%
±2σ	-1.65%	12.35%	96.14%	95.45%
±3σ	-5.15%	15.85%	98.13%	99.73%

Descriptive Statistics

Mean	5.354%
Standard Error	0.083%
Median	4.484%
Mode	3.846%
Standard Deviation	3.500%
Sample Variance	12.249%
Kurtosis	17.62
Skewness	3.05
Range	40.153%
Minimum	0.946%
Maximum	41.099%
Count	1762

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.354%	1762	100.00%	5.354%
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 1.07. Further, an Excess Kurtosis of 12.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.02%	11	0.62%	0.62%
-11.02% to -8.30%	15	0.85%	1.48%
-8.30% to -5.58%	54	3.06%	4.54%
-5.58% to -2.87%	230	13.05%	17.59%
-2.87% to -0.15%	606	34.39%	51.99%
-0.15% to 2.57%	556	31.56%	83.54%
2.57% to 5.29%	200	11.35%	94.89%
5.29% to 8.00%	50	2.84%	97.73%
8.00% to 10.72%	24	1.36%	99.09%
Greater than 10.72%	16	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.77%	3.47%	77.13%	68.27%
±2σ	-7.40%	7.10%	95.23%	95.45%
±3σ	-11.02%	10.72%	98.47%	99.73%

Descriptive Statistics

Mean	-0.149%
Standard Error	0.086%
Median	-0.283%
Mode	0.000%
Standard Deviation	3.623%
Sample Variance	13.124%
Kurtosis	12.44
Skewness	1.07
Range	62.144%
Minimum	-21.073%
Maximum	41.071%
Count	1762

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.637%	789	44.78%	1.181%
Negative	-2.475%	947	53.75%	-1.330%
Zero	0.000%	26	1.48%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.56. Further, an Excess Kurtosis of 4.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.73%	3	0.74%	0.74%
-18.73% to -13.70%	3	0.74%	1.48%
-13.70% to -8.68%	13	3.21%	4.69%
-8.68% to -3.65%	58	14.32%	19.01%
-3.65% to 1.38%	126	31.11%	50.12%
1.38% to 6.40%	136	33.58%	83.70%
6.40% to 11.43%	42	10.37%	94.07%
11.43% to 16.46%	19	4.69%	98.77%
16.46% to 21.48%	1	0.25%	99.01%
Greater than 21.48%	4	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.33%	8.08%	76.30%	68.27%
±2σ	-12.03%	14.78%	95.06%	95.45%
±3σ	-18.73%	21.48%	98.27%	99.73%

Descriptive Statistics

Mean	1.377%
Standard Error	0.333%
Median	1.295%
Mode	-4.589%
Standard Deviation	6.702%
Sample Variance	44.923%
Kurtosis	4.98
Skewness	0.56
Range	70.658%
Minimum	-27.157%
Maximum	43.501%
Count	405

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.270%	243	60.00%	3.162%
Negative	-4.518%	160	39.51%	-1.785%
Zero	0.000%	2	0.49%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.15%
12	1 Year	8.58%
36	3 Years	7.71%
60	5 Years	9.01%
120	10 Years	9.31%
240	20 Years	9.37%
600	50 Years	10.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.31. Further, an Excess Kurtosis of 7.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.15%	0	0.00%	0.00%
-9.15% to -3.96%	0	0.00%	0.00%
-3.96% to 1.23%	0	0.00%	0.00%
1.23% to 6.42%	61	15.02%	15.02%
6.42% to 11.60%	200	49.26%	64.29%
11.60% to 16.79%	84	20.69%	84.98%
16.79% to 21.98%	38	9.36%	94.33%
21.98% to 27.17%	7	1.72%	96.06%
27.17% to 32.36%	6	1.48%	97.54%
Greater than 32.36%	10	2.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.69%	18.52%	84.48%	68.27%
±2σ	-2.23%	25.44%	95.32%	95.45%
±3σ	-9.15%	32.36%	97.54%	99.73%

Descriptive Statistics

Mean	11.604%
Standard Error	0.343%
Median	9.348%
Mode	16.667%
Standard Deviation	6.918%
Sample Variance	47.854%
Kurtosis	7.29
Skewness	2.31
Range	46.456%
Minimum	2.504%
Maximum	48.960%
Count	406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.604%	406	100.00%	11.604%
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 0.58. Further, an Excess Kurtosis of 4.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.57%	1	0.25%	0.25%
-20.57% to -15.63%	4	0.99%	1.23%
-15.63% to -10.69%	17	4.19%	5.42%
-10.69% to -5.75%	47	11.58%	17.00%
-5.75% to -0.81%	154	37.93%	54.93%
-0.81% to 4.12%	107	26.35%	81.28%
4.12% to 9.06%	53	13.05%	94.33%
9.06% to 14.00%	17	4.19%	98.52%
14.00% to 18.94%	2	0.49%	99.01%
Greater than 18.94%	4	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.40%	5.77%	76.35%	68.27%
±2σ	-13.98%	12.35%	95.57%	95.45%
±3σ	-20.56%	18.94%	98.77%	99.73%

Descriptive Statistics

Mean	-0.813%
Standard Error	0.327%
Median	-1.188%
Mode	4.762%
Standard Deviation	6.584%
Sample Variance	43.346%
Kurtosis	4.42
Skewness	0.58
Range	67.624%
Minimum	-31.039%
Maximum	36.585%
Count	406

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.134%	160	39.41%	2.023%
Negative	-4.720%	244	60.10%	-2.837%
Zero	0.000%	2	0.49%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.97. Further, an Excess Kurtosis of 6.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.64%	1	0.74%	0.74%
-27.64% to -19.71%	1	0.74%	1.48%
-19.71% to -11.78%	4	2.96%	4.44%
-11.78% to -3.85%	16	11.85%	16.30%
-3.85% to 4.08%	45	33.33%	49.63%
4.08% to 12.01%	48	35.56%	85.19%
12.01% to 19.94%	14	10.37%	95.56%
19.94% to 27.87%	4	2.96%	98.52%
27.87% to 35.80%	1	0.74%	99.26%
Greater than 35.80%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.49%	14.66%	77.78%	68.27%
±2σ	-17.06%	25.23%	94.81%	95.45%
±3σ	-27.64%	35.80%	98.52%	99.73%

Descriptive Statistics

Mean	4.082%
Standard Error	0.910%
Median	4.114%
Mode	-1.855%
Standard Deviation	10.573%
Sample Variance	111.795%
Kurtosis	6.27
Skewness	0.97
Range	91.014%
Minimum	-30.197%
Maximum	60.817%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.786%	93	68.89%	6.053%
Negative	-6.334%	42	31.11%	-1.971%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	14.27%
12	3 Years	13.13%
20	5 Years	14.36%
40	10 Years	15.42%
80	20 Years	15.60%
200	50 Years	18.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.29. Further, an Excess Kurtosis of 7.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.08%	0	0.00%	0.00%
-16.08% to -6.98%	0	0.00%	0.00%
-6.98% to 2.13%	0	0.00%	0.00%
2.13% to 11.23%	24	17.65%	17.65%
11.23% to 20.34%	65	47.79%	65.44%
20.34% to 29.45%	27	19.85%	85.29%
29.45% to 38.55%	9	6.62%	91.91%
38.55% to 47.66%	6	4.41%	96.32%
47.66% to 56.76%	2	1.47%	97.79%
Greater than 56.76%	3	2.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.20%	32.48%	83.82%	68.27%
±2σ	-3.94%	44.62%	96.32%	95.45%
±3σ	-16.08%	56.76%	97.79%	99.73%

Descriptive Statistics

Mean	20.339%
Standard Error	1.041%
Median	16.787%
Mode	5.319%
Standard Deviation	12.141%
Sample Variance	147.411%
Kurtosis	7.62
Skewness	2.29
Range	82.221%
Minimum	5.319%
Maximum	87.540%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.339%	136	100.00%	20.339%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.76. Further, an Excess Kurtosis of 4.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.87%	1	0.74%	0.74%
-31.87% to -24.50%	1	0.74%	1.47%
-24.50% to -17.13%	4	2.94%	4.41%
-17.13% to -9.77%	17	12.50%	16.91%
-9.77% to -2.40%	51	37.50%	54.41%
-2.40% to 4.97%	42	30.88%	85.29%
4.97% to 12.33%	12	8.82%	94.12%
12.33% to 19.70%	4	2.94%	97.06%
19.70% to 27.07%	3	2.21%	99.26%
Greater than 27.07%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.22%	7.42%	77.21%	68.27%
±2σ	-22.05%	17.25%	95.59%	95.45%
±3σ	-31.87%	27.07%	98.53%	99.73%

Descriptive Statistics

Mean	-2.400%
Standard Error	0.842%
Median	-3.274%
Mode	-37.198%
Standard Deviation	9.823%
Sample Variance	96.501%
Kurtosis	4.16
Skewness	0.76
Range	80.329%
Minimum	-37.198%
Maximum	43.131%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.290%	47	34.56%	2.519%
Negative	-7.517%	89	65.44%	-4.919%
Zero	0.000%	0	0.00%	0.000%

LIN Deep Analytical Report