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%	1.33%	1.57%	489.94	503.17	483.45	509.92
Weekly	3.70%	3.50%	3.62%	4.06%	2.93%	3.45%	482.15	511.29	468.21	526.52
Monthly	6.70%	6.92%	6.58%	9.12%	6.11%	7.18%	467.09	527.78	439.42	561.02
Quarterly	10.58%	12.15%	9.83%	14.23%	10.58%	12.44%	446.67	551.91	401.83	613.49
Annual	—	—	—	—	21.16%	24.88%	401.83	613.49	325.21	758.04
Option Time Horizon	—	—	—	—	8.14%	9.57%	457.71	538.60	421.93	584.27

Calculation Notes: Computed at 2026-02-22T14:17 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $496.51 | Strike (K): $500.00 (first OTM call ≥ spot) | Observed Mid-Price: $15.3500 (Bid $13.2000 / Ask $17.5000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 1.22% | Binomial IV (Annual): 21.16% (CRR binomial tree, American, n=20 steps) | BS IV: 21.22% (European Black-Scholes) | Yahoo IV (Annual): 24.88% → 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
2025-12-03	$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 5.98 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	1.10%	1.64%
-3.84% to -2.54%	307	3.62%	5.26%
-2.54% to -1.23%	1026	12.10%	17.36%
-1.23% to 0.07%	2892	34.11%	51.47%
0.07% to 1.38%	2684	31.66%	83.13%
1.38% to 2.68%	962	11.35%	94.48%
2.68% to 3.99%	315	3.72%	98.20%
3.99% 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%	94.76%	95.45%
±3σ	-5.15%	5.29%	98.64%	99.73%

Descriptive Statistics

Mean	0.071%
Standard Error	0.019%
Median	0.022%
Mode	0.000%
Standard Deviation	1.740%
Sample Variance	3.027%
Kurtosis	5.98
Skewness	0.21
Range	28.848%
Minimum	-13.986%
Maximum	14.862%
Count	8478

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.274%	4283	50.52%	0.644%
Negative	-1.221%	3980	46.95%	-0.573%
Zero	0.000%	215	2.54%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.92%
20	1 Month	2.00%
60	1 Quarter	1.73%
250	1 Year	1.71%
750	3 Years	1.59%
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 2.88. Further, an Excess Kurtosis of 15.65 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	17.48%	17.48%
1.07% to 2.15%	3877	45.72%	63.20%
2.15% to 3.23%	1819	21.45%	84.66%
3.23% to 4.31%	705	8.31%	92.97%
4.31% to 5.39%	312	3.68%	96.65%
5.39% to 6.47%	137	1.62%	98.27%
Greater than 6.47%	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%	5.03%	95.93%	95.45%
±3σ	-2.16%	6.47%	98.27%	99.73%

Descriptive Statistics

Mean	2.153%
Standard Error	0.016%
Median	1.760%
Mode	1.639%
Standard Deviation	1.438%
Sample Variance	2.067%
Kurtosis	15.65
Skewness	2.88
Range	19.065%
Minimum	0.327%
Maximum	19.392%
Count	8479

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.153%	8479	100.00%	2.153%
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 5.00 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%	98	1.16%	1.91%
-3.46% to -2.33%	329	3.88%	5.79%
-2.33% to -1.20%	942	11.11%	16.90%
-1.20% to -0.06%	2705	31.90%	48.80%
-0.06% to 1.07%	2913	34.36%	83.16%
1.07% to 2.20%	966	11.39%	94.55%
2.20% to 3.34%	299	3.53%	98.08%
3.34% to 4.47%	106	1.25%	99.33%
Greater than 4.47%	57	0.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.57%	1.45%	76.92%	68.27%
±2σ	-3.08%	2.96%	94.52%	95.45%
±3σ	-4.59%	4.47%	98.57%	99.73%

Descriptive Statistics

Mean	-0.062%
Standard Error	0.016%
Median	-0.026%
Mode	0.000%
Standard Deviation	1.511%
Sample Variance	2.282%
Kurtosis	5.00
Skewness	0.02
Range	24.502%
Minimum	-11.494%
Maximum	13.008%
Count	8479

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.075%	3939	46.46%	0.499%
Negative	-1.106%	4306	50.78%	-0.562%
Zero	0.000%	234	2.76%	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 7.08 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 -7.99%	19	1.08%	1.76%
-7.99% to -5.21%	59	3.36%	5.12%
-5.21% to -2.44%	213	12.12%	17.25%
-2.44% to 0.34%	580	33.01%	50.26%
0.34% to 3.11%	571	32.50%	82.75%
3.11% to 5.89%	209	11.90%	94.65%
5.89% to 8.66%	64	3.64%	98.29%
8.66% to 11.44%	14	0.80%	99.09%
Greater than 11.44%	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%	7.74%	95.50%	95.45%
±3σ	-10.76%	11.43%	98.41%	99.73%

Descriptive Statistics

Mean	0.338%
Standard Error	0.088%
Median	0.330%
Mode	0.000%
Standard Deviation	3.699%
Sample Variance	13.682%
Kurtosis	7.08
Skewness	0.14
Range	55.585%
Minimum	-29.513%
Maximum	26.072%
Count	1757

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.707%	950	54.07%	1.464%
Negative	-2.496%	792	45.08%	-1.125%
Zero	0.000%	15	0.85%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	5.55%
12	1 Quarter	4.49%
52	1 Year	3.76%
156	3 Years	3.49%
260	5 Years	4.06%
520	10 Years	4.27%
1,040	20 Years	4.51%
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 17.58 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 -2.53%	0	0.00%	0.00%
-2.53% to 0.10%	0	0.00%	0.00%
0.10% to 2.73%	316	17.97%	17.97%
2.73% to 5.36%	756	43.00%	60.98%
5.36% to 7.98%	426	24.23%	85.21%
7.98% to 10.61%	155	8.82%	94.03%
10.61% to 13.24%	49	2.79%	96.81%
13.24% to 15.87%	23	1.31%	98.12%
Greater than 15.87%	33	1.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.85%	8.86%	86.12%	68.27%
±2σ	-1.65%	12.36%	96.13%	95.45%
±3σ	-5.15%	15.87%	98.12%	99.73%

Descriptive Statistics

Mean	5.356%
Standard Error	0.084%
Median	4.481%
Mode	3.846%
Standard Deviation	3.503%
Sample Variance	12.272%
Kurtosis	17.58
Skewness	3.05
Range	40.153%
Minimum	0.946%
Maximum	41.099%
Count	1758

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.356%	1758	100.00%	5.356%
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 12.45 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	0.63%	0.63%
-11.02% to -8.30%	15	0.85%	1.48%
-8.30% to -5.58%	54	3.07%	4.55%
-5.58% to -2.87%	229	13.03%	17.58%
-2.87% to -0.15%	605	34.41%	51.99%
-0.15% to 2.57%	555	31.57%	83.56%
2.57% to 5.29%	199	11.32%	94.88%
5.29% to 8.01%	50	2.84%	97.72%
8.01% to 10.72%	24	1.37%	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%	3.48%	77.13%	68.27%
±2σ	-7.40%	7.10%	95.22%	95.45%
±3σ	-11.02%	10.72%	98.46%	99.73%

Descriptive Statistics

Mean	-0.149%
Standard Error	0.086%
Median	-0.283%
Mode	0.000%
Standard Deviation	3.624%
Sample Variance	13.135%
Kurtosis	12.45
Skewness	1.07
Range	62.144%
Minimum	-21.073%
Maximum	41.071%
Count	1758

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.637%	787	44.77%	1.181%
Negative	-2.474%	945	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 5.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.72%	3	0.74%	0.74%
-18.72% to -13.69%	3	0.74%	1.49%
-13.69% to -8.67%	13	3.22%	4.70%
-8.67% to -3.64%	58	14.36%	19.06%
-3.64% to 1.38%	125	30.94%	50.00%
1.38% to 6.41%	136	33.66%	83.66%
6.41% to 11.43%	42	10.40%	94.06%
11.43% to 16.46%	19	4.70%	98.76%
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	-5.32%	8.08%	76.24%	68.27%
±2σ	-12.02%	14.78%	95.05%	95.45%
±3σ	-18.72%	21.48%	98.27%	99.73%

Descriptive Statistics

Mean	1.384%
Standard Error	0.333%
Median	1.364%
Mode	-4.589%
Standard Deviation	6.700%
Sample Variance	44.884%
Kurtosis	5.00
Skewness	0.56
Range	70.658%
Minimum	-27.157%
Maximum	43.501%
Count	404

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.261%	243	60.15%	3.164%
Negative	-4.524%	159	39.36%	-1.780%
Zero	0.000%	2	0.49%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.09%
12	1 Year	8.16%
36	3 Years	7.73%
60	5 Years	9.12%
120	10 Years	9.33%
240	20 Years	9.36%
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 -9.16%	0	0.00%	0.00%
-9.16% to -3.97%	0	0.00%	0.00%
-3.97% to 1.22%	0	0.00%	0.00%
1.22% to 6.41%	61	15.06%	15.06%
6.41% to 11.61%	199	49.14%	64.20%
11.61% to 16.80%	84	20.74%	84.94%
16.80% to 21.99%	38	9.38%	94.32%
21.99% to 27.18%	7	1.73%	96.05%
27.18% to 32.37%	6	1.48%	97.53%
Greater than 32.37%	10	2.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.68%	18.53%	84.44%	68.27%
±2σ	-2.24%	25.45%	95.31%	95.45%
±3σ	-9.16%	32.37%	97.53%	99.73%

Descriptive Statistics

Mean	11.605%
Standard Error	0.344%
Median	9.373%
Mode	16.667%
Standard Deviation	6.922%
Sample Variance	47.917%
Kurtosis	7.29
Skewness	2.31
Range	46.456%
Minimum	2.504%
Maximum	48.960%
Count	405

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.605%	405	100.00%	11.605%
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 4.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.56%	1	0.25%	0.25%
-20.56% to -15.63%	4	0.99%	1.23%
-15.63% to -10.69%	17	4.20%	5.43%
-10.69% to -5.76%	47	11.60%	17.04%
-5.76% to -0.82%	154	38.02%	55.06%
-0.82% to 4.12%	106	26.17%	81.23%
4.12% to 9.05%	53	13.09%	94.32%
9.05% to 13.99%	17	4.20%	98.52%
13.99% to 18.92%	2	0.49%	99.01%
Greater than 18.92%	4	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.40%	5.76%	76.30%	68.27%
±2σ	-13.98%	12.34%	95.56%	95.45%
±3σ	-20.56%	18.92%	98.77%	99.73%

Descriptive Statistics

Mean	-0.820%
Standard Error	0.327%
Median	-1.206%
Mode	4.762%
Standard Deviation	6.581%
Sample Variance	43.314%
Kurtosis	4.45
Skewness	0.58
Range	67.624%
Minimum	-31.039%
Maximum	36.585%
Count	405

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.141%	159	39.26%	2.018%
Negative	-4.711%	244	60.25%	-2.838%
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 0.96. Further, an Excess Kurtosis of 6.25 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 -19.70%	1	0.74%	1.48%
-19.70% to -11.77%	4	2.96%	4.44%
-11.77% to -3.84%	16	11.85%	16.30%
-3.84% to 4.10%	45	33.33%	49.63%
4.10% to 12.03%	48	35.56%	85.19%
12.03% to 19.96%	14	10.37%	95.56%
19.96% to 27.90%	4	2.96%	98.52%
27.90% to 35.83%	1	0.74%	99.26%
Greater than 35.83%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.48%	14.67%	77.78%	68.27%
±2σ	-17.06%	25.25%	94.81%	95.45%
±3σ	-27.64%	35.83%	98.52%	99.73%

Descriptive Statistics

Mean	4.096%
Standard Error	0.910%
Median	4.114%
Mode	-1.855%
Standard Deviation	10.578%
Sample Variance	111.895%
Kurtosis	6.25
Skewness	0.96
Range	91.014%
Minimum	-30.197%
Maximum	60.817%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.806%	93	68.89%	6.066%
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	13.60%
12	3 Years	12.91%
20	5 Years	14.23%
40	10 Years	15.35%
80	20 Years	15.56%
200	50 Years	18.05%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.28. Further, an Excess Kurtosis of 7.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.14%	0	0.00%	0.00%
-16.14% to -7.03%	0	0.00%	0.00%
-7.03% to 2.09%	0	0.00%	0.00%
2.09% to 11.20%	24	17.65%	17.65%
11.20% to 20.32%	65	47.79%	65.44%
20.32% to 29.43%	27	19.85%	85.29%
29.43% to 38.55%	9	6.62%	91.91%
38.55% to 47.66%	6	4.41%	96.32%
47.66% to 56.78%	2	1.47%	97.79%
Greater than 56.78%	3	2.21%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.17%	32.47%	83.82%	68.27%
±2σ	-3.99%	44.62%	96.32%	95.45%
±3σ	-16.14%	56.78%	97.79%	99.73%

Descriptive Statistics

Mean	20.318%
Standard Error	1.042%
Median	16.787%
Mode	5.319%
Standard Deviation	12.153%
Sample Variance	147.686%
Kurtosis	7.59
Skewness	2.28
Range	82.221%
Minimum	5.319%
Maximum	87.540%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.318%	136	100.00%	20.318%
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 0.77. Further, an Excess Kurtosis of 4.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.90%	1	0.74%	0.74%
-31.90% to -24.53%	1	0.74%	1.47%
-24.53% to -17.16%	4	2.94%	4.41%
-17.16% to -9.78%	17	12.50%	16.91%
-9.78% to -2.41%	51	37.50%	54.41%
-2.41% to 4.96%	42	30.88%	85.29%
4.96% 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	-12.24%	7.42%	77.21%	68.27%
±2σ	-22.07%	17.25%	95.59%	95.45%
±3σ	-31.90%	27.08%	98.53%	99.73%

Descriptive Statistics

Mean	-2.412%
Standard Error	0.843%
Median	-3.274%
Mode	-37.198%
Standard Deviation	9.829%
Sample Variance	96.601%
Kurtosis	4.15
Skewness	0.77
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	-7.535%	89	65.44%	-4.931%
Zero	0.000%	0	0.00%	0.000%

LIN Deep Analytical Report