Markets Data Volatility Heatmap Portfolio Calculator

LLY Deep Analytical Report

Eli Lilly and Company | Category: Equity Mega Cap | Ann. Div Yield: 0.59% ($6.00) | Last Updated: 2026-02-22 | Data Range: 1972-06-01 → 2026-02-01 (645 months)
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 1.73% 1.31% 1.48% 2.64% 2.18% 2.33% 987.70 1031.82 966.36 1054.61
Weekly 3.89% 3.36% 3.89% 6.46% 4.81% 5.13% 962.12 1059.26 916.94 1111.44
Monthly 7.55% 6.79% 7.43% 14.28% 10.01% 10.67% 913.35 1115.82 826.34 1233.31
Quarterly 11.84% 11.03% 10.99% 24.86% 17.34% 18.48% 848.80 1200.67 713.67 1428.00
Annual — — — — 34.68% 36.96% 713.67 1428.00 504.53 2019.97
Option Time Horizon — — — — 13.34% 14.22% 883.45 1153.58 773.13 1318.19
Calculation Notes: Computed at 2026-02-22T14:16 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $1009.52  |  Strike (K): $1020.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $51.0500 (Bid $49.1500 / Ask $52.9500)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.59%  |  Binomial IV (Annual): 34.68% (CRR binomial tree, American, n=20 steps)  |  BS IV: 34.74% (European Black-Scholes)  |  Yahoo IV (Annual): 36.96% → period-scaled as σperiod = σannual·√h  |  Price bands: Upper = S·e+σ√h, Lower = S·e−σ√h
Historical Dividend Payouts
Ex-Dividend Date Amount
2026-02-13 $1.7300
2025-11-14 $1.5000
2025-08-15 $1.5000
2025-05-16 $1.5000
2025-02-14 $1.5000
2024-11-15 $1.3000
2024-08-15 $1.3000
2024-05-15 $1.3000
2024-02-14 $1.3000
2023-11-14 $1.1300
2023-08-14 $1.1300
2023-05-12 $1.1300
2023-02-14 $1.1300
2022-11-14 $0.9800
2022-08-12 $0.9800
2022-05-13 $0.9800
2022-02-14 $0.9800
2021-11-12 $0.8500
2021-08-12 $0.8500
2021-05-13 $0.8500
2021-02-11 $0.8500
2020-11-12 $0.7400
2020-08-13 $0.7400
2020-05-14 $0.7400
2020-02-13 $0.7400
2019-11-14 $0.6450
2019-08-14 $0.6450
2019-05-16 $0.6450
2019-02-14 $0.6450
2018-11-14 $0.5630
2018-08-14 $0.5630
2018-05-16 $0.5630
2018-02-14 $0.5630
2017-11-14 $0.5200
2017-08-11 $0.5200
2017-05-11 $0.5200
2017-02-13 $0.5200
2016-11-10 $0.5100
2016-08-11 $0.5100
2016-05-11 $0.5100
2016-02-10 $0.5100
2015-11-10 $0.5000
2015-08-12 $0.5000
2015-05-14 $0.5000
2015-02-11 $0.5000
2014-11-12 $0.4900
2014-08-13 $0.4900
2014-05-13 $0.4900
2014-02-12 $0.4900
2013-11-13 $0.4900
2013-08-13 $0.4900
2013-05-14 $0.4900
2013-02-13 $0.4900
2012-11-13 $0.4900
2012-08-13 $0.4900
2012-05-11 $0.4900
2012-02-13 $0.4900
2011-11-10 $0.4900
2011-08-11 $0.4900
2011-05-11 $0.4900
2011-02-11 $0.4900
2010-11-10 $0.4900
2010-08-11 $0.4900
2010-05-12 $0.4900
2010-02-10 $0.4900
2009-11-10 $0.4900
2009-08-12 $0.4900
2009-05-13 $0.4900
2009-02-11 $0.4900
2008-11-12 $0.4700
2008-08-13 $0.4700
2008-05-13 $0.4700
2008-02-13 $0.4700
2007-11-13 $0.4250
2007-08-13 $0.4250
2007-05-11 $0.4250
2007-02-13 $0.4250
2006-11-13 $0.4000
2006-08-11 $0.4000
2006-05-11 $0.4000
2006-02-13 $0.4000
2005-11-10 $0.3800
2005-08-11 $0.3800
2005-05-11 $0.3800
2005-02-11 $0.3800
2004-11-10 $0.3550
2004-08-11 $0.3550
2004-05-12 $0.3550
2004-02-11 $0.3550
2003-11-12 $0.3350
2003-08-13 $0.3350
2003-05-13 $0.3350
2003-02-12 $0.3350
2002-11-13 $0.3100
2002-08-13 $0.3100
2002-05-13 $0.3100
2002-02-13 $0.3100
2001-11-13 $0.2800
2001-08-13 $0.2800
2001-05-11 $0.2800
2001-02-13 $0.2800
2000-11-13 $0.2600
2000-08-11 $0.2600
2000-05-11 $0.2600
2000-02-11 $0.2600
1999-11-10 $0.2300
1999-08-11 $0.2300
1999-05-12 $0.2300
1999-02-10 $0.2300
1998-11-10 $0.2000
1998-08-12 $0.2000
1998-05-13 $0.2000
1998-02-11 $0.2000
1997-11-12 $0.2000
1997-08-13 $0.1800
1997-05-13 $0.1800
1997-02-12 $0.1800
1996-11-13 $0.1710
1996-08-13 $0.1710
1996-05-13 $0.1710
1996-02-13 $0.1710
1995-11-13 $0.1713
1995-08-11 $0.1613
1995-05-09 $0.1613
1995-02-09 $0.1613
1994-11-08 $0.1562
1994-08-09 $0.1562
1994-05-09 $0.1562
1994-02-09 $0.1562
1993-11-08 $0.1512
1993-08-09 $0.1512
1993-05-10 $0.1512
1993-02-09 $0.1512
1992-11-06 $0.1375
1992-08-10 $0.1375
1992-05-11 $0.1375
1992-02-10 $0.1375
1991-11-08 $0.1250
1991-08-09 $0.1250
1991-05-09 $0.1250
1991-02-07 $0.1250
1990-11-08 $0.1025
1990-08-09 $0.1025
1990-05-09 $0.1025
1990-02-09 $0.1025
1989-11-09 $0.0843
1989-08-09 $0.0843
1989-05-09 $0.0843
1989-02-09 $0.0844
1988-11-08 $0.0719
1988-08-09 $0.0719
1988-05-09 $0.0719
1988-02-09 $0.0719
1987-11-06 $0.0625
1987-08-10 $0.0625
1987-05-11 $0.0625
1987-02-09 $0.0625
1986-11-07 $0.0563
1986-08-11 $0.0563
1986-05-09 $0.0563
1986-02-10 $0.0563
1985-11-08 $0.0500
1985-08-09 $0.0500
1985-05-09 $0.0500
1985-02-08 $0.0500
1984-11-08 $0.0500
1984-08-09 $0.0453
1984-05-09 $0.0453
1984-02-08 $0.0453
1983-11-07 $0.0453
1983-08-09 $0.0453
1983-05-09 $0.0406
1983-02-09 $0.0406
1982-11-05 $0.0406
1982-08-09 $0.0406
1982-05-10 $0.0406
1982-02-08 $0.0406
1981-11-06 $0.0359
1981-08-10 $0.0359
1981-05-11 $0.0359
1981-02-05 $0.0359
1980-11-07 $0.0359
1980-08-11 $0.0359
1980-05-12 $0.0328
1980-02-08 $0.0328
1979-11-02 $0.0328
1979-08-06 $0.0328
1979-05-07 $0.0281
1979-02-05 $0.0281
1978-11-03 $0.0281
1978-08-07 $0.0250
1978-05-08 $0.0250
1978-02-06 $0.0250
1977-11-03 $0.0222
1977-08-08 $0.0222
1977-05-09 $0.0222
1977-02-04 $0.0222
1976-11-05 $0.0203
1976-08-09 $0.0203
1976-05-10 $0.0187
1976-02-06 $0.0187
1975-11-07 $0.0172
1975-08-11 $0.0172
1975-05-12 $0.0172
1975-02-07 $0.0172
1974-11-08 $0.0156
1974-08-12 $0.0156
1974-05-13 $0.0147
1974-02-08 $0.0147
1973-11-12 $0.0129
1973-08-13 $0.0129
1973-05-14 $0.0118
1973-02-09 $0.0118
1972-11-13 $0.0114
1972-08-07 $0.0114
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.23. Further, an Excess Kurtosis of 14.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.13%740.55%0.55%
-5.13% to -3.83%1280.95%1.49%
-3.83% to -2.53%4673.45%4.94%
-2.53% to -1.23%166012.26%17.20%
-1.23% to 0.07%464934.34%51.54%
0.07% to 1.37%425931.46%83.00%
1.37% to 2.67%160311.84%94.84%
2.67% to 3.97%4603.40%98.23%
3.97% to 5.27%1441.06%99.30%
Greater than 5.27%950.70%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.67%1.80% 77.41%68.27%
±2σ -3.40%3.53% 95.35%95.45%
±3σ -5.13%5.27% 98.75%99.73%
Descriptive Statistics
Mean0.067%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.733%
Sample Variance3.005%
Kurtosis14.94
Skewness-0.23
Range45.716%
Minimum-29.178%
Maximum16.538%
Count13539
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.287% 6701 49.49% 0.637%
Negative -1.222% 6319 46.67% -0.570%
Zero 0.000% 519 3.83% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.58%
20 1 Month 3.77%
60 1 Quarter 3.14%
250 1 Year 3.19%
750 3 Years 2.75%
1,250 5 Years 2.64%
2,500 10 Years 2.36%
5,000 20 Years 2.15%
12,500 50 Years 2.20%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.05. Further, an Excess Kurtosis of 93.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.86%00.00%0.00%
-1.86% to -0.87%00.00%0.00%
-0.87% to 0.11%00.00%0.00%
0.11% to 1.09%230717.04%17.04%
1.09% to 2.08%600344.34%61.37%
2.08% to 3.06%315923.33%84.70%
3.06% to 4.05%12138.96%93.66%
4.05% to 5.03%4793.54%97.20%
5.03% to 6.01%1901.40%98.60%
Greater than 6.01%1891.40%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.77%3.39% 84.18%68.27%
±2σ -0.55%4.70% 96.34%95.45%
±3σ -1.86%6.01% 98.60%99.73%
Descriptive Statistics
Mean2.078%
Standard Error0.011%
Median1.784%
Mode1.266%
Standard Deviation1.312%
Sample Variance1.721%
Kurtosis93.81
Skewness5.05
Range43.322%
Minimum0.167%
Maximum43.489%
Count13540
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.078% 13540 100.00% 2.078%
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 1.44. Further, an Excess Kurtosis of 40.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.46%740.55%0.55%
-4.46% to -3.35%1491.10%1.65%
-3.35% to -2.24%4983.68%5.32%
-2.24% to -1.13%168812.47%17.79%
-1.13% to -0.03%410030.28%48.07%
-0.03% to 1.08%467434.52%82.59%
1.08% to 2.19%164712.16%94.76%
2.19% to 3.30%4903.62%98.38%
3.30% to 4.41%1401.03%99.41%
Greater than 4.41%800.59%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.50%1.45% 76.68%68.27%
±2σ -2.98%2.93% 95.07%95.45%
±3σ -4.46%4.41% 98.86%99.73%
Descriptive Statistics
Mean-0.025%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.478%
Sample Variance2.183%
Kurtosis40.49
Skewness1.44
Range50.136%
Minimum-10.949%
Maximum39.187%
Count13540
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.090% 6302 46.54% 0.507%
Negative -1.100% 6551 48.38% -0.532%
Zero 0.000% 687 5.07% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.19. Further, an Excess Kurtosis of 4.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.35%200.71%0.71%
-11.35% to -8.43%230.82%1.53%
-8.43% to -5.51%1033.67%5.21%
-5.51% to -2.59%39013.91%19.12%
-2.59% to 0.33%89131.79%50.91%
0.33% to 3.25%86230.75%81.66%
3.25% to 6.17%36112.88%94.54%
6.17% to 9.09%1013.60%98.14%
9.09% to 12.01%311.11%99.25%
Greater than 12.01%210.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.57%4.22% 75.03%68.27%
±2σ -7.46%8.11% 95.01%95.45%
±3σ -11.35%12.01% 98.54%99.73%
Descriptive Statistics
Mean0.327%
Standard Error0.074%
Median0.261%
Mode0.000%
Standard Deviation3.893%
Sample Variance15.154%
Kurtosis4.29
Skewness-0.19
Range51.160%
Minimum-32.425%
Maximum18.735%
Count2803
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.000% 1488 53.09% 1.593%
Negative -2.779% 1276 45.52% -1.265%
Zero 0.000% 39 1.39% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 7.31%
12 1 Quarter 6.75%
52 1 Year 7.81%
156 3 Years 6.77%
260 5 Years 6.46%
520 10 Years 5.66%
1,040 20 Years 5.00%
2,600 50 Years 5.29%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.60. Further, an Excess Kurtosis of 30.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.62%00.00%0.00%
-4.62% to -2.10%00.00%0.00%
-2.10% to 0.42%00.00%0.00%
0.42% to 2.94%49817.76%17.76%
2.94% to 5.46%122743.76%61.52%
5.46% to 7.98%65323.29%84.81%
7.98% to 10.50%2549.06%93.87%
10.50% to 13.02%923.28%97.15%
13.02% to 15.54%411.46%98.61%
Greater than 15.54%391.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.10%8.82% 83.56%68.27%
±2σ -1.26%12.18% 96.43%95.45%
±3σ -4.62%15.54% 98.61%99.73%
Descriptive Statistics
Mean5.459%
Standard Error0.063%
Median4.740%
Mode2.863%
Standard Deviation3.360%
Sample Variance11.287%
Kurtosis30.31
Skewness3.60
Range53.196%
Minimum1.013%
Maximum54.209%
Count2804
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.459% 2804 100.00% 5.459%
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 1.47. Further, an Excess Kurtosis of 15.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.77%70.25%0.25%
-11.77% to -8.85%281.00%1.25%
-8.85% to -5.93%893.17%4.42%
-5.93% to -3.02%39113.94%18.37%
-3.02% to -0.10%94533.70%52.07%
-0.10% to 2.82%82829.53%81.60%
2.82% to 5.74%36412.98%94.58%
5.74% to 8.66%1013.60%98.18%
8.66% to 11.58%260.93%99.11%
Greater than 11.58%250.89%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.99%3.79% 76.14%68.27%
±2σ -7.88%7.68% 95.65%95.45%
±3σ -11.77%11.58% 98.86%99.73%
Descriptive Statistics
Mean-0.097%
Standard Error0.073%
Median-0.217%
Mode0.000%
Standard Deviation3.891%
Sample Variance15.140%
Kurtosis15.18
Skewness1.47
Range66.404%
Minimum-15.194%
Maximum51.210%
Count2804
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.943% 1278 45.58% 1.341%
Negative -2.733% 1476 52.64% -1.439%
Zero 0.000% 50 1.78% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.21. Further, an Excess Kurtosis of 1.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -21.28%20.31%0.31%
-21.28% to -15.61%60.93%1.24%
-15.61% to -9.95%264.04%5.28%
-9.95% to -4.29%9614.91%20.19%
-4.29% to 1.37%20832.30%52.48%
1.37% to 7.04%17427.02%79.50%
7.04% to 12.70%9114.13%93.63%
12.70% to 18.36%284.35%97.98%
18.36% to 24.02%91.40%99.38%
Greater than 24.02%40.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.18%8.92% 72.20%68.27%
±2σ -13.73%16.47% 94.41%95.45%
±3σ -21.28%24.02% 99.07%99.73%
Descriptive Statistics
Mean1.374%
Standard Error0.297%
Median0.982%
Mode0.000%
Standard Deviation7.550%
Sample Variance56.998%
Kurtosis1.18
Skewness0.21
Range60.669%
Minimum-29.470%
Maximum31.199%
Count644
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.385% 361 56.06% 3.579%
Negative -5.090% 279 43.32% -2.205%
Zero 0.000% 4 0.62% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 11.34%
12 1 Year 16.31%
36 3 Years 15.35%
60 5 Years 14.28%
120 10 Years 12.53%
240 20 Years 10.79%
600 50 Years 11.49%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.78. Further, an Excess Kurtosis of 15.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.92%00.00%0.00%
-7.92% to -2.83%00.00%0.00%
-2.83% to 2.26%00.00%0.00%
2.26% to 7.35%12018.60%18.60%
7.35% to 12.45%27142.02%60.62%
12.45% to 17.54%14622.64%83.26%
17.54% to 22.63%6510.08%93.33%
22.63% to 27.72%243.72%97.05%
27.72% to 32.81%101.55%98.60%
Greater than 32.81%91.40%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 5.66%19.23% 81.24%68.27%
±2σ -1.13%26.02% 96.59%95.45%
±3σ -7.92%32.81% 98.60%99.73%
Descriptive Statistics
Mean12.446%
Standard Error0.267%
Median10.803%
Mode5.612%
Standard Deviation6.789%
Sample Variance46.097%
Kurtosis15.86
Skewness2.78
Range71.801%
Minimum3.307%
Maximum75.108%
Count645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.446% 645 100.00% 12.446%
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 0.54. Further, an Excess Kurtosis of 2.32 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -22.81%10.16%0.16%
-22.81% to -17.24%71.09%1.24%
-17.24% to -11.67%304.65%5.89%
-11.67% to -6.10%9414.57%20.47%
-6.10% to -0.53%19229.77%50.23%
-0.53% to 5.04%20131.16%81.40%
5.04% to 10.61%7912.25%93.64%
10.61% to 16.18%284.34%97.98%
16.18% to 21.75%81.24%99.22%
Greater than 21.75%50.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.96%6.90% 71.63%68.27%
±2σ -15.38%14.32% 95.35%95.45%
±3σ -22.81%21.75% 99.07%99.73%
Descriptive Statistics
Mean-0.529%
Standard Error0.292%
Median-0.558%
Mode0.000%
Standard Deviation7.427%
Sample Variance55.158%
Kurtosis2.32
Skewness0.54
Range65.510%
Minimum-22.904%
Maximum42.606%
Count645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.723% 288 44.65% 2.555%
Negative -5.701% 349 54.11% -3.085%
Zero 0.000% 8 1.24% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.51. Further, an Excess Kurtosis of 1.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.59%00.00%0.00%
-31.59% to -22.71%10.47%0.47%
-22.71% to -13.84%94.19%4.65%
-13.84% to -4.96%3415.81%20.47%
-4.96% to 3.92%6429.77%50.23%
3.92% to 12.79%6630.70%80.93%
12.79% to 21.67%2813.02%93.95%
21.67% to 30.55%104.65%98.60%
30.55% to 39.42%20.93%99.53%
Greater than 39.42%10.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.92%15.75% 69.77%68.27%
±2σ -19.75%27.59% 96.28%95.45%
±3σ -31.59%39.42% 99.53%99.73%
Descriptive Statistics
Mean3.916%
Standard Error0.807%
Median3.912%
Mode-27.519%
Standard Deviation11.835%
Sample Variance140.056%
Kurtosis1.82
Skewness0.51
Range87.751%
Minimum-27.519%
Maximum60.232%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.693% 136 63.26% 6.764%
Negative -7.751% 79 36.74% -2.848%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 24.60%
12 3 Years 25.72%
20 5 Years 24.86%
40 10 Years 22.32%
80 20 Years 18.93%
200 50 Years 19.89%
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 8.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.82%00.00%0.00%
-10.82% to -2.54%00.00%0.00%
-2.54% to 5.73%00.00%0.00%
5.73% to 14.01%4420.37%20.37%
14.01% to 22.28%8639.81%60.19%
22.28% to 30.55%5625.93%86.11%
30.55% to 38.83%167.41%93.52%
38.83% to 47.10%83.70%97.22%
47.10% to 55.38%10.46%97.69%
Greater than 55.38%52.31%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 11.25%33.31% 82.41%68.27%
±2σ 0.21%44.34% 96.76%95.45%
±3σ -10.82%55.38% 97.69%99.73%
Descriptive Statistics
Mean22.279%
Standard Error0.751%
Median19.422%
Mode7.190%
Standard Deviation11.032%
Sample Variance121.702%
Kurtosis8.00
Skewness2.25
Range79.390%
Minimum7.190%
Maximum86.580%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 22.279% 216 100.00% 22.279%
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 0.40. Further, an Excess Kurtosis of 0.65 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -34.87%10.46%0.46%
-34.87% to -26.63%00.00%0.46%
-26.63% to -18.39%94.17%4.63%
-18.39% to -10.14%3415.74%20.37%
-10.14% to -1.90%7333.80%54.17%
-1.90% to 6.34%5525.46%79.63%
6.34% to 14.58%2511.57%91.20%
14.58% to 22.82%156.94%98.15%
22.82% to 31.07%31.39%99.54%
Greater than 31.07%10.46%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -12.89%9.09% 68.52%68.27%
±2σ -23.88%20.08% 95.37%95.45%
±3σ -34.87%31.07% 99.07%99.73%
Descriptive Statistics
Mean-1.902%
Standard Error0.748%
Median-3.074%
Mode0.000%
Standard Deviation10.990%
Sample Variance120.771%
Kurtosis0.65
Skewness0.40
Range75.566%
Minimum-36.270%
Maximum39.296%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.589% 87 40.28% 3.459%
Negative -9.118% 127 58.80% -5.361%
Zero 0.000% 2 0.93% 0.000%