Markets Data Volatility Heatmap Portfolio Calculator

DUK Deep Analytical Report

Duke Energy Corporation | Category: Equity Mega Cap | Ann. Div Yield: 3.33% ($4.22) | Last Updated: 2026-03-24 | Data Range: 1980-03-01 → 2026-03-01 (553 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 1.34% 1.19% 1.19% 1.71% 1.55% 1.77% 125.36 129.29 123.43 131.31
Weekly 2.96% 3.03% 2.97% 3.87% 3.40% 3.89% 123.05 131.72 118.93 136.28
Monthly 5.38% 6.23% 5.59% 7.93% 7.09% 8.11% 118.60 136.66 110.48 146.70
Quarterly 8.55% 11.65% 8.76% 13.22% 12.28% 14.04% 112.60 143.94 99.59 162.74
Annual — — — — 24.55% 28.08% 99.59 162.74 77.91 208.03
Option Time Horizon — — — — 9.27% 10.60% 116.04 139.67 105.77 153.23
Calculation Notes: Computed at 2026-03-23T16:33 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $127.31  |  Strike (K): $130.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.6000 (Bid $2.9000 / Ask $4.3000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.33%  |  Binomial IV (Annual): 24.55% (CRR binomial tree, American, n=20 steps)  |  BS IV: 24.86% (European Black-Scholes)  |  Yahoo IV (Annual): 28.08% → 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 $1.0650
2025-11-14 $1.0650
2025-08-15 $1.0650
2025-05-16 $1.0450
2025-02-14 $1.0450
2024-11-15 $1.0450
2024-08-16 $1.0450
2024-05-16 $1.0250
2024-02-15 $1.0250
2023-11-16 $1.0250
2023-08-17 $1.0250
2023-05-11 $1.0050
2023-02-16 $1.0050
2022-11-17 $1.0050
2022-08-11 $1.0050
2022-05-12 $0.9850
2022-02-17 $0.9850
2021-11-10 $0.9850
2021-08-12 $0.9850
2021-05-13 $0.9650
2021-02-11 $0.9650
2020-11-12 $0.9650
2020-08-13 $0.9650
2020-05-14 $0.9450
2020-02-13 $0.9450
2019-11-14 $0.9450
2019-08-15 $0.9450
2019-05-16 $0.9280
2019-02-14 $0.9280
2018-11-15 $0.9280
2018-08-16 $0.9280
2018-05-17 $0.8900
2018-02-15 $0.8900
2017-11-16 $0.8900
2017-08-16 $0.8900
2017-05-17 $0.8550
2017-02-15 $0.8550
2016-11-16 $0.8550
2016-08-10 $0.8550
2016-05-18 $0.8250
2016-02-10 $0.8250
2015-11-10 $0.8250
2015-08-12 $0.8250
2015-05-13 $0.7950
2015-02-11 $0.7950
2014-11-12 $0.7950
2014-08-13 $0.7950
2014-05-14 $0.7800
2014-02-12 $0.7800
2013-11-13 $0.7800
2013-08-14 $0.7800
2013-05-15 $0.7650
2013-02-13 $0.7650
2012-11-14 $0.7650
2012-08-15 $0.7650
2012-05-16 $0.7500
2012-02-15 $0.7500
2011-11-16 $0.7500
2011-08-10 $0.7500
2011-05-18 $0.7350
2011-02-09 $0.7350
2010-11-09 $0.7350
2010-08-11 $0.7350
2010-05-19 $0.7200
2010-02-10 $0.7200
2009-11-10 $0.7200
2009-08-12 $0.7200
2009-05-14 $0.6900
2009-02-11 $0.6900
2008-11-12 $0.6900
2008-08-13 $0.6900
2008-05-15 $0.6600
2008-02-13 $0.6600
2007-11-14 $0.6600
2007-08-15 $0.6600
2007-05-09 $0.6300
2007-02-14 $0.6300
2006-11-15 $0.5579
2006-08-09 $0.5579
2006-05-10 $0.5404
2006-02-15 $0.5404
2005-11-09 $0.5404
2005-08-10 $1.6213
2005-05-11 $0.4794
2005-02-09 $0.4794
2004-11-09 $0.4794
2004-08-11 $0.4794
2004-05-12 $0.4794
2004-02-11 $0.4794
2003-11-12 $0.4794
2003-08-13 $0.4794
2003-05-14 $0.4794
2003-02-12 $0.4794
2002-11-13 $0.4794
2002-08-14 $0.4794
2002-05-15 $0.4794
2002-02-13 $0.4794
2001-11-14 $0.4794
2001-08-15 $0.4794
2001-05-09 $0.4794
2001-02-14 $0.4794
2000-11-15 $0.4794
2000-08-09 $0.4794
2000-05-10 $0.4794
2000-02-09 $0.4794
1999-11-09 $0.4794
1999-08-11 $0.4794
1999-05-12 $0.4794
1999-02-10 $0.4794
1998-11-10 $0.4794
1998-08-12 $0.4794
1998-05-13 $0.4794
1998-02-11 $0.4794
1997-11-12 $0.4794
1997-08-13 $0.4794
1997-05-14 $0.4620
1997-02-12 $0.4620
1996-11-13 $0.4620
1996-08-14 $0.4620
1996-05-15 $0.4445
1996-02-14 $0.4445
1995-11-15 $0.4445
1995-08-16 $0.4445
1995-05-08 $0.4271
1995-02-13 $0.4271
1994-11-14 $0.4271
1994-08-08 $0.4271
1994-05-09 $0.4097
1994-02-07 $0.4097
1993-11-05 $0.4097
1993-08-09 $0.4097
1993-05-10 $0.3922
1993-02-08 $0.3922
1992-11-06 $0.3922
1992-08-10 $0.3922
1992-05-11 $0.3748
1992-02-10 $0.3748
1991-11-08 $0.3748
1991-08-12 $0.3748
1991-05-13 $0.3574
1991-02-11 $0.3574
1990-11-09 $0.3574
1990-08-13 $0.3574
1990-05-14 $0.3399
1990-02-12 $0.3399
1989-11-13 $0.3399
1989-08-14 $0.3399
1989-05-08 $0.3225
1989-02-13 $0.3225
1988-11-14 $0.3225
1988-08-08 $0.3225
1988-05-09 $0.3051
1988-02-08 $0.3051
1987-11-06 $0.3051
1987-08-10 $0.3051
1987-05-11 $0.2920
1987-02-09 $0.2920
1986-11-07 $0.2920
1986-08-11 $0.2920
1986-05-12 $0.2833
1986-02-14 $0.2833
1985-11-04 $0.2833
1985-08-12 $0.2702
1985-05-13 $0.2702
1985-02-08 $0.2702
1984-11-02 $0.2702
1984-08-13 $0.2702
1984-05-14 $0.2571
1984-02-10 $0.2571
1983-11-03 $0.2571
1983-08-15 $0.2571
1983-05-16 $0.2484
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.05. Further, an Excess Kurtosis of 13.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.98%1020.88%0.88%
-3.98% to -2.97%1080.93%1.81%
-2.97% to -1.96%3392.92%4.73%
-1.96% to -0.95%130211.23%15.96%
-0.95% to 0.05%419636.18%52.14%
0.05% to 1.06%364931.47%83.61%
1.06% to 2.07%136611.78%95.39%
2.07% to 3.08%3733.22%98.60%
3.08% to 4.08%890.77%99.37%
Greater than 4.08%730.63%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.29%1.40% 78.78%68.27%
±2σ -2.63%2.74% 95.58%95.45%
±3σ -3.98%4.08% 98.50%99.73%
Descriptive Statistics
Mean0.053%
Standard Error0.012%
Median0.000%
Mode0.000%
Standard Deviation1.343%
Sample Variance1.805%
Kurtosis13.88
Skewness-0.05
Range32.653%
Minimum-16.495%
Maximum16.158%
Count11597
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.986% 5644 48.67% 0.480%
Negative -0.986% 5015 43.24% -0.426%
Zero 0.000% 938 8.09% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.76%
20 1 Month 1.73%
60 1 Quarter 1.62%
250 1 Year 1.61%
750 3 Years 1.63%
1,250 5 Years 1.71%
2,500 10 Years 1.71%
5,000 20 Years 1.72%
12,500 50 Years 1.76%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.91. Further, an Excess Kurtosis of 57.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.89%00.00%0.00%
-1.89% to -0.99%00.00%0.00%
-0.99% to -0.10%00.00%0.00%
-0.10% to 0.80%140412.11%12.11%
0.80% to 1.69%606752.31%64.42%
1.69% to 2.58%259722.39%86.81%
2.58% to 3.48%8937.70%94.51%
3.48% to 4.37%2972.56%97.07%
4.37% to 5.27%1421.22%98.29%
Greater than 5.27%1981.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.50%2.88% 88.68%68.27%
±2σ -0.70%4.08% 96.53%95.45%
±3σ -1.89%5.27% 98.29%99.73%
Descriptive Statistics
Mean1.690%
Standard Error0.011%
Median1.399%
Mode1.093%
Standard Deviation1.193%
Sample Variance1.424%
Kurtosis57.27
Skewness4.91
Range29.902%
Minimum0.239%
Maximum30.141%
Count11598
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.690% 11598 100.00% 1.690%
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 0.34. Further, an Excess Kurtosis of 12.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.58%610.53%0.53%
-3.58% to -2.69%1000.86%1.39%
-2.69% to -1.80%3813.29%4.67%
-1.80% to -0.91%139712.05%16.72%
-0.91% to -0.01%357230.80%47.52%
-0.01% to 0.88%415035.78%83.30%
0.88% to 1.77%132711.44%94.74%
1.77% to 2.66%4023.47%98.21%
2.66% to 3.55%1211.04%99.25%
Greater than 3.55%870.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.20%1.17% 77.40%68.27%
±2σ -2.39%2.36% 95.43%95.45%
±3σ -3.58%3.55% 98.73%99.73%
Descriptive Statistics
Mean-0.015%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.189%
Sample Variance1.413%
Kurtosis12.60
Skewness0.34
Range31.811%
Minimum-13.910%
Maximum17.901%
Count11598
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.921% 5078 43.78% 0.403%
Negative -0.877% 5532 47.70% -0.418%
Zero 0.000% 988 8.52% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.12. Further, an Excess Kurtosis of 10.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.62%130.54%0.54%
-8.62% to -6.40%241.00%1.54%
-6.40% to -4.18%813.37%4.91%
-4.18% to -1.96%27811.58%16.49%
-1.96% to 0.26%79232.99%49.48%
0.26% to 2.48%81433.90%83.38%
2.48% to 4.70%28211.75%95.13%
4.70% to 6.92%773.21%98.33%
6.92% to 9.14%210.87%99.21%
Greater than 9.14%190.79%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.70%3.22% 78.34%68.27%
±2σ -5.66%6.18% 95.34%95.45%
±3σ -8.62%9.14% 98.67%99.73%
Descriptive Statistics
Mean0.258%
Standard Error0.060%
Median0.284%
Mode0.000%
Standard Deviation2.960%
Sample Variance8.761%
Kurtosis10.17
Skewness0.12
Range51.909%
Minimum-21.808%
Maximum30.101%
Count2401
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.126% 1299 54.10% 1.150%
Negative -2.064% 1038 43.23% -0.892%
Zero 0.000% 64 2.67% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.50%
12 1 Quarter 3.87%
52 1 Year 3.62%
156 3 Years 3.69%
260 5 Years 3.87%
520 10 Years 3.88%
1,040 20 Years 3.79%
2,600 50 Years 4.05%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.67. Further, an Excess Kurtosis of 65.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.95%00.00%0.00%
-4.95% to -2.67%00.00%0.00%
-2.67% to -0.40%00.00%0.00%
-0.40% to 1.87%2309.58%9.58%
1.87% to 4.15%134355.91%65.49%
4.15% to 6.42%54222.56%88.05%
6.42% to 8.70%1526.33%94.38%
8.70% to 10.97%773.21%97.59%
10.97% to 13.24%291.21%98.79%
Greater than 13.24%291.21%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.12%7.18% 90.01%68.27%
±2σ -1.92%10.21% 96.92%95.45%
±3σ -4.95%13.24% 98.79%99.73%
Descriptive Statistics
Mean4.147%
Standard Error0.062%
Median3.448%
Mode3.226%
Standard Deviation3.032%
Sample Variance9.193%
Kurtosis65.01
Skewness5.67
Range57.951%
Minimum0.820%
Maximum58.771%
Count2402
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.147% 2402 100.00% 4.147%
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 1.18. Further, an Excess Kurtosis of 11.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.95%140.58%0.58%
-8.95% to -6.72%180.75%1.33%
-6.72% to -4.49%672.79%4.12%
-4.49% to -2.26%29412.24%16.36%
-2.26% to -0.03%83134.60%50.96%
-0.03% to 2.20%79333.01%83.97%
2.20% to 4.42%26010.82%94.80%
4.42% to 6.65%833.46%98.25%
6.65% to 8.88%261.08%99.33%
Greater than 8.88%160.67%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.00%2.94% 78.31%68.27%
±2σ -5.97%5.91% 95.34%95.45%
±3σ -8.95%8.88% 98.75%99.73%
Descriptive Statistics
Mean-0.032%
Standard Error0.061%
Median-0.130%
Mode0.000%
Standard Deviation2.971%
Sample Variance8.825%
Kurtosis11.34
Skewness1.18
Range47.600%
Minimum-19.710%
Maximum27.890%
Count2402
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.183% 1094 45.55% 0.994%
Negative -2.009% 1228 51.12% -1.027%
Zero 0.000% 80 3.33% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.36. Further, an Excess Kurtosis of 2.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.07%50.91%0.91%
-15.07% to -11.04%71.27%2.17%
-11.04% to -7.00%152.72%4.89%
-7.00% to -2.97%7914.31%19.20%
-2.97% to 1.07%16129.17%48.37%
1.07% to 5.10%17631.88%80.25%
5.10% to 9.14%8114.67%94.93%
9.14% to 13.17%193.44%98.37%
13.17% to 17.21%61.09%99.46%
Greater than 17.21%30.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.31%6.45% 74.28%68.27%
±2σ -9.69%11.83% 94.38%95.45%
±3σ -15.07%17.21% 98.55%99.73%
Descriptive Statistics
Mean1.068%
Standard Error0.229%
Median1.279%
Mode0.000%
Standard Deviation5.380%
Sample Variance28.944%
Kurtosis2.55
Skewness-0.36
Range49.397%
Minimum-27.134%
Maximum22.263%
Count552
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.140% 345 62.50% 2.588%
Negative -4.154% 202 36.59% -1.520%
Zero 0.000% 5 0.91% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 7.29%
12 1 Year 6.76%
36 3 Years 7.40%
60 5 Years 7.93%
120 10 Years 8.06%
240 20 Years 7.79%
600 50 Years 8.59%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.46. Further, an Excess Kurtosis of 32.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.52%00.00%0.00%
-9.52% to -4.85%00.00%0.00%
-4.85% to -0.18%00.00%0.00%
-0.18% to 4.49%6211.21%11.21%
4.49% to 9.16%29753.71%64.92%
9.16% to 13.84%12923.33%88.25%
13.84% to 18.51%335.97%94.21%
18.51% to 23.18%183.25%97.47%
23.18% to 27.85%40.72%98.19%
Greater than 27.85%101.81%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.93%15.39% 89.51%68.27%
±2σ -3.29%21.62% 96.56%95.45%
±3σ -9.52%27.85% 98.19%99.73%
Descriptive Statistics
Mean9.164%
Standard Error0.265%
Median7.637%
Mode10.366%
Standard Deviation6.229%
Sample Variance38.801%
Kurtosis32.97
Skewness4.46
Range69.373%
Minimum2.395%
Maximum71.768%
Count553
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 9.164% 553 100.00% 9.164%
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 1.05. Further, an Excess Kurtosis of 5.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.14%10.18%0.18%
-17.14% to -12.95%40.72%0.90%
-12.95% to -8.76%162.89%3.80%
-8.76% to -4.57%9417.00%20.80%
-4.57% to -0.38%18132.73%53.53%
-0.38% to 3.81%15628.21%81.74%
3.81% to 8.01%7213.02%94.76%
8.01% to 12.20%193.44%98.19%
12.20% to 16.39%50.90%99.10%
Greater than 16.39%50.90%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.96%5.21% 74.68%68.27%
±2σ -11.55%10.80% 95.30%95.45%
±3σ -17.14%16.39% 98.92%99.73%
Descriptive Statistics
Mean-0.376%
Standard Error0.238%
Median-0.704%
Mode0.000%
Standard Deviation5.588%
Sample Variance31.221%
Kurtosis5.18
Skewness1.05
Range56.795%
Minimum-19.557%
Maximum37.238%
Count553
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.467% 229 41.41% 1.850%
Negative -3.907% 315 56.96% -2.226%
Zero 0.000% 9 1.63% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.07. Further, an Excess Kurtosis of 3.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -22.60%10.54%0.54%
-22.60% to -16.18%21.09%1.63%
-16.18% to -9.77%105.43%7.07%
-9.77% to -3.35%1910.33%17.39%
-3.35% to 3.06%4926.63%44.02%
3.06% to 9.48%6836.96%80.98%
9.48% to 15.89%2815.22%96.20%
15.89% to 22.31%52.72%98.91%
22.31% to 28.72%00.00%98.91%
Greater than 28.72%21.09%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.49%11.62% 77.72%68.27%
±2σ -14.04%20.17% 94.02%95.45%
±3σ -22.60%28.72% 98.37%99.73%
Descriptive Statistics
Mean3.063%
Standard Error0.631%
Median3.729%
Mode-33.000%
Standard Deviation8.553%
Sample Variance73.158%
Kurtosis3.39
Skewness-0.07
Range74.232%
Minimum-33.000%
Maximum41.232%
Count184
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.342% 125 67.94% 4.988%
Negative -6.106% 58 31.52% -1.925%
Zero 0.000% 1 0.54% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 10.38%
12 3 Years 11.83%
20 5 Years 13.22%
40 10 Years 13.31%
80 20 Years 13.25%
200 50 Years 14.65%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.51. Further, an Excess Kurtosis of 28.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -18.38%00.00%0.00%
-18.38% to -9.65%00.00%0.00%
-9.65% to -0.91%00.00%0.00%
-0.91% to 7.83%126.49%6.49%
7.83% to 16.57%11562.16%68.65%
16.57% to 25.30%3820.54%89.19%
25.30% to 34.04%115.95%95.14%
34.04% to 42.78%42.16%97.30%
42.78% to 51.52%21.08%98.38%
Greater than 51.52%31.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.92%28.22% 91.89%68.27%
±2σ -6.73%39.87% 96.76%95.45%
±3σ -18.38%51.52% 98.38%99.73%
Descriptive Statistics
Mean16.566%
Standard Error0.857%
Median14.045%
Mode16.667%
Standard Deviation11.650%
Sample Variance135.729%
Kurtosis28.89
Skewness4.51
Range106.353%
Minimum5.415%
Maximum111.768%
Count185
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 16.566% 185 100.00% 16.566%
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 1.40. Further, an Excess Kurtosis of 6.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -27.52%10.54%0.54%
-27.52% to -20.95%10.54%1.08%
-20.95% to -14.39%31.62%2.70%
-14.39% to -7.82%2915.68%18.38%
-7.82% to -1.25%7440.00%58.38%
-1.25% to 5.32%4926.49%84.86%
5.32% to 11.89%158.11%92.97%
11.89% to 18.46%84.32%97.30%
18.46% to 25.02%42.16%99.46%
Greater than 25.02%10.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.01%7.51% 78.92%68.27%
±2σ -18.76%16.27% 94.59%95.45%
±3σ -27.52%25.02% 98.92%99.73%
Descriptive Statistics
Mean-1.249%
Standard Error0.644%
Median-2.381%
Mode-5.128%
Standard Deviation8.758%
Sample Variance76.694%
Kurtosis6.70
Skewness1.40
Range78.428%
Minimum-28.055%
Maximum50.373%
Count185
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.956% 69 37.30% 2.594%
Negative -6.183% 115 62.16% -3.843%
Zero 0.000% 1 0.54% 0.000%