Markets Data Volatility Heatmap Portfolio Calculator

LLY Deep Analytical Report

Eli Lilly and Company | Category: Equity Mega Cap | Ann. Div Yield: 0.66% ($6.00) | Last Updated: 2026-03-24 | Data Range: 1972-06-01 → 2026-03-01 (646 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% 2.65% 3.01% 3.08% 890.90 946.23 864.45 975.18
Weekly 3.89% 3.36% 3.89% 6.45% 6.63% 6.78% 859.22 981.12 804.08 1048.40
Monthly 7.56% 6.79% 7.44% 14.27% 13.81% 14.11% 799.73 1054.10 696.59 1210.17
Quarterly 11.87% 11.01% 11.03% 25.32% 23.92% 24.43% 722.85 1166.22 569.09 1481.31
Annual — — — — 47.83% 48.87% 569.09 1481.31 352.73 2389.89
Option Time Horizon — — — — 18.05% 18.44% 766.49 1099.82 639.88 1317.43
Calculation Notes: Computed at 2026-03-23T16:30 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $918.15  |  Strike (K): $920.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $66.3250 (Bid $64.7500 / Ask $67.9000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.66%  |  Binomial IV (Annual): 47.83% (CRR binomial tree, American, n=20 steps)  |  BS IV: 47.35% (European Black-Scholes)  |  Yahoo IV (Annual): 48.87% → 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 14.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.14%750.55%0.55%
-5.14% to -3.84%1280.94%1.50%
-3.84% to -2.54%4673.44%4.94%
-2.54% to -1.23%166612.29%17.23%
-1.23% to 0.07%465534.33%51.56%
0.07% to 1.37%426131.42%82.98%
1.37% to 2.67%160711.85%94.83%
2.67% to 3.97%4613.40%98.23%
3.97% to 5.27%1451.07%99.30%
Greater than 5.27%950.70%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.67%1.80% 77.44%68.27%
±2σ -3.40%3.53% 95.35%95.45%
±3σ -5.14%5.27% 98.75%99.73%
Descriptive Statistics
Mean0.066%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.734%
Sample Variance3.008%
Kurtosis14.89
Skewness-0.23
Range45.716%
Minimum-29.178%
Maximum16.538%
Count13560
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.288% 6708 49.47% 0.637%
Negative -1.222% 6333 46.70% -0.571%
Zero 0.000% 519 3.83% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 3.16%
20 1 Month 2.80%
60 1 Quarter 3.19%
250 1 Year 3.18%
750 3 Years 2.77%
1,250 5 Years 2.65%
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 5.04. Further, an Excess Kurtosis of 93.70 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%231517.07%17.07%
1.09% to 2.08%600544.28%61.35%
2.08% to 3.06%316723.35%84.71%
3.06% to 4.05%12148.95%93.66%
4.05% to 5.03%4803.54%97.20%
5.03% to 6.01%1901.40%98.60%
Greater than 6.01%1901.40%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.77%3.39% 84.13%68.27%
±2σ -0.54%4.70% 96.34%95.45%
±3σ -1.86%6.02% 98.60%99.73%
Descriptive Statistics
Mean2.079%
Standard Error0.011%
Median1.786%
Mode1.266%
Standard Deviation1.312%
Sample Variance1.721%
Kurtosis93.70
Skewness5.04
Range43.322%
Minimum0.167%
Maximum43.489%
Count13561
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.079% 13561 100.00% 2.079%
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 40.40 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%1.64%
-3.35% to -2.24%4993.68%5.32%
-2.24% to -1.13%169012.46%17.79%
-1.13% to -0.03%410430.26%48.05%
-0.03% to 1.08%468534.55%82.60%
1.08% to 2.19%164812.15%94.75%
2.19% to 3.30%4913.62%98.37%
3.30% to 4.41%1401.03%99.40%
Greater than 4.41%810.60%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.50%1.45% 76.67%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 Variance2.184%
Kurtosis40.40
Skewness1.44
Range50.136%
Minimum-10.949%
Maximum39.187%
Count13561
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.090% 6316 46.58% 0.508%
Negative -1.100% 6558 48.36% -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 4.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.36%200.71%0.71%
-11.36% to -8.44%230.82%1.53%
-8.44% to -5.51%1043.71%5.24%
-5.51% to -2.60%39013.89%19.13%
-2.60% to 0.32%89131.74%50.87%
0.32% to 3.24%86530.82%81.69%
3.24% to 6.16%36112.86%94.55%
6.16% to 9.08%1013.60%98.15%
9.08% to 12.00%311.10%99.25%
Greater than 12.00%210.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.57%4.22% 74.99%68.27%
±2σ -7.46%8.11% 95.01%95.45%
±3σ -11.35%12.00% 98.54%99.73%
Descriptive Statistics
Mean0.324%
Standard Error0.073%
Median0.256%
Mode0.000%
Standard Deviation3.893%
Sample Variance15.157%
Kurtosis4.28
Skewness-0.19
Range51.160%
Minimum-32.425%
Maximum18.735%
Count2807
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.999% 1489 53.05% 1.591%
Negative -2.781% 1279 45.56% -1.267%
Zero 0.000% 39 1.39% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 5.83%
12 1 Quarter 6.77%
52 1 Year 7.71%
156 3 Years 6.80%
260 5 Years 6.45%
520 10 Years 5.67%
1,040 20 Years 5.01%
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 30.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.61%00.00%0.00%
-4.61% to -2.10%00.00%0.00%
-2.10% to 0.42%00.00%0.00%
0.42% to 2.94%50017.81%17.81%
2.94% to 5.46%122743.70%61.50%
5.46% to 7.98%65423.29%84.79%
7.98% to 10.50%2549.05%93.84%
10.50% to 13.02%933.31%97.15%
13.02% to 15.53%411.46%98.61%
Greater than 15.53%391.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.10%8.82% 83.51%68.27%
±2σ -1.26%12.18% 96.44%95.45%
±3σ -4.61%15.53% 98.61%99.73%
Descriptive Statistics
Mean5.460%
Standard Error0.063%
Median4.740%
Mode2.863%
Standard Deviation3.358%
Sample Variance11.276%
Kurtosis30.32
Skewness3.60
Range53.196%
Minimum1.013%
Maximum54.209%
Count2808
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.460% 2808 100.00% 5.460%
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 15.17 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 -3.01%39113.92%18.34%
-3.01% to -0.10%94633.69%52.03%
-0.10% to 2.82%83129.59%81.62%
2.82% to 5.74%36312.93%94.55%
5.74% to 8.66%1023.63%98.18%
8.66% to 11.57%260.93%99.11%
Greater than 11.57%250.89%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.99%3.79% 76.18%68.27%
±2σ -7.88%7.69% 95.66%95.45%
±3σ -11.77%11.57% 98.86%99.73%
Descriptive Statistics
Mean-0.095%
Standard Error0.073%
Median-0.216%
Mode0.000%
Standard Deviation3.890%
Sample Variance15.133%
Kurtosis15.17
Skewness1.47
Range66.404%
Minimum-15.194%
Maximum51.210%
Count2808
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.943% 1281 45.62% 1.343%
Negative -2.732% 1477 52.60% -1.437%
Zero 0.000% 50 1.78% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.20. Further, an Excess Kurtosis of 1.17 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -21.33%20.31%0.31%
-21.33% to -15.66%60.93%1.24%
-15.66% to -9.98%274.19%5.43%
-9.98% to -4.31%9514.73%20.16%
-4.31% to 1.36%20832.25%52.40%
1.36% to 7.03%17527.13%79.53%
7.03% to 12.70%9114.11%93.64%
12.70% to 18.37%284.34%97.98%
18.37% to 24.05%91.40%99.38%
Greater than 24.05%40.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.20%8.92% 72.09%68.27%
±2σ -13.77%16.48% 94.42%95.45%
±3σ -21.33%24.05% 99.07%99.73%
Descriptive Statistics
Mean1.359%
Standard Error0.298%
Median0.992%
Mode0.000%
Standard Deviation7.562%
Sample Variance57.186%
Kurtosis1.17
Skewness0.20
Range60.669%
Minimum-29.470%
Maximum31.199%
Count645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.372% 362 56.12% 3.576%
Negative -5.126% 279 43.26% -2.217%
Zero 0.000% 4 0.62% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 12.90%
12 1 Year 16.23%
36 3 Years 15.46%
60 5 Years 14.27%
120 10 Years 12.57%
240 20 Years 10.82%
600 50 Years 11.50%
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 15.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.91%00.00%0.00%
-7.91% to -2.82%00.00%0.00%
-2.82% to 2.27%00.00%0.00%
2.27% to 7.36%12018.58%18.58%
7.36% to 12.45%27141.95%60.53%
12.45% to 17.54%14722.76%83.28%
17.54% to 22.64%6510.06%93.34%
22.64% to 27.73%243.72%97.06%
27.73% to 32.81%101.55%98.61%
Greater than 32.81%91.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 5.67%19.24% 81.27%68.27%
±2σ -1.12%26.03% 96.59%95.45%
±3σ -7.91%32.81% 98.61%99.73%
Descriptive Statistics
Mean12.454%
Standard Error0.267%
Median10.812%
Mode5.612%
Standard Deviation6.787%
Sample Variance46.064%
Kurtosis15.84
Skewness2.78
Range71.801%
Minimum3.307%
Maximum75.108%
Count646
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.454% 646 100.00% 12.454%
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 2.28 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -22.84%10.15%0.15%
-22.84% to -17.26%71.08%1.24%
-17.26% to -11.68%304.64%5.88%
-11.68% to -6.09%9614.86%20.74%
-6.09% to -0.51%19129.57%50.31%
-0.51% to 5.07%20030.96%81.27%
5.07% to 10.65%7912.23%93.50%
10.65% to 16.23%294.49%97.99%
16.23% to 21.81%81.24%99.23%
Greater than 21.81%50.77%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.96%6.93% 71.67%68.27%
±2σ -15.40%14.37% 95.36%95.45%
±3σ -22.84%21.81% 99.07%99.73%
Descriptive Statistics
Mean-0.514%
Standard Error0.293%
Median-0.569%
Mode0.000%
Standard Deviation7.441%
Sample Variance55.363%
Kurtosis2.28
Skewness0.54
Range65.510%
Minimum-22.904%
Maximum42.606%
Count646
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.761% 288 44.58% 2.568%
Negative -5.689% 350 54.18% -3.082%
Zero 0.000% 8 1.24% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.50. Further, an Excess Kurtosis of 1.78 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.74%00.00%0.00%
-31.74% to -22.83%10.47%0.47%
-22.83% to -13.93%94.19%4.65%
-13.93% to -5.03%3516.28%20.93%
-5.03% to 3.88%6228.84%49.77%
3.88% to 12.78%6731.16%80.93%
12.78% to 21.68%2813.02%93.95%
21.68% to 30.59%104.65%98.60%
30.59% to 39.49%20.93%99.53%
Greater than 39.49%10.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.00%15.75% 69.30%68.27%
±2σ -19.87%27.62% 96.28%95.45%
±3σ -31.74%39.49% 99.53%99.73%
Descriptive Statistics
Mean3.876%
Standard Error0.810%
Median3.912%
Mode-27.519%
Standard Deviation11.871%
Sample Variance140.921%
Kurtosis1.78
Skewness0.50
Range87.751%
Minimum-27.519%
Maximum60.232%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.693% 136 63.26% 6.764%
Negative -7.860% 79 36.74% -2.888%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 26.87%
12 3 Years 26.48%
20 5 Years 25.32%
40 10 Years 22.54%
80 20 Years 19.04%
200 50 Years 19.94%
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 8.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.70%00.00%0.00%
-10.70% to -2.44%00.00%0.00%
-2.44% to 5.82%00.00%0.00%
5.82% to 14.08%4319.91%19.91%
14.08% to 22.33%8639.81%59.72%
22.33% to 30.59%5726.39%86.11%
30.59% to 38.85%167.41%93.52%
38.85% to 47.11%83.70%97.22%
47.11% to 55.37%10.46%97.69%
Greater than 55.37%52.31%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 11.32%33.34% 81.94%68.27%
±2σ 0.31%44.36% 96.76%95.45%
±3σ -10.70%55.37% 97.69%99.73%
Descriptive Statistics
Mean22.334%
Standard Error0.749%
Median19.681%
Mode7.190%
Standard Deviation11.011%
Sample Variance121.231%
Kurtosis8.04
Skewness2.25
Range79.390%
Minimum7.190%
Maximum86.580%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 22.334% 216 100.00% 22.334%
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 0.39. Further, an Excess Kurtosis of 0.61 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -34.95%10.46%0.46%
-34.95% to -26.67%00.00%0.46%
-26.67% to -18.40%94.17%4.63%
-18.40% to -10.13%3415.74%20.37%
-10.13% to -1.86%7333.80%54.17%
-1.86% to 6.42%5525.46%79.63%
6.42% to 14.69%2712.50%92.13%
14.69% to 22.96%136.02%98.15%
22.96% to 31.23%31.39%99.54%
Greater than 31.23%10.46%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -12.89%9.17% 68.06%68.27%
±2σ -23.92%20.20% 95.37%95.45%
±3σ -34.95%31.23% 99.07%99.73%
Descriptive Statistics
Mean-1.856%
Standard Error0.751%
Median-3.074%
Mode0.000%
Standard Deviation11.030%
Sample Variance121.669%
Kurtosis0.61
Skewness0.39
Range75.566%
Minimum-36.270%
Maximum39.296%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.703% 87 40.28% 3.505%
Negative -9.118% 127 58.80% -5.361%
Zero 0.000% 2 0.93% 0.000%