Markets Data Volatility Heatmap Portfolio Calculator

DUK Deep Analytical Report

Duke Energy Corporation | Category: Equity Mega Cap | Ann. Div Yield: 3.34% ($4.22) | Last Updated: 2026-02-22 | Data Range: 1980-03-01 → 2026-02-01 (552 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% 1.72% 1.11% 1.19% 125.38 128.20 123.99 129.63
Weekly 2.96% 3.03% 2.97% 3.87% 2.45% 2.61% 123.71 129.92 120.72 133.15
Monthly 5.38% 6.23% 5.59% 8.04% 5.10% 5.43% 120.48 133.41 114.49 140.39
Quarterly 8.55% 11.66% 8.76% 13.00% 8.83% 9.41% 116.06 138.49 106.25 151.28
Annual — — — — 17.67% 18.82% 106.25 151.28 89.04 180.51
Option Time Horizon — — — — 6.80% 7.24% 118.45 135.69 110.67 145.24
Calculation Notes: Computed at 2026-02-22T14:18 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $126.78  |  Strike (K): $130.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $2.1250 (Bid $1.9000 / Ask $2.3500)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.34%  |  Binomial IV (Annual): 17.67% (CRR binomial tree, American, n=20 steps)  |  BS IV: 17.70% (European Black-Scholes)  |  Yahoo IV (Annual): 18.82% → 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%3372.91%4.73%
-1.96% to -0.95%129911.22%15.95%
-0.95% to 0.05%419336.22%52.17%
0.05% to 1.06%364531.49%83.66%
1.06% to 2.07%135711.72%95.38%
2.07% to 3.08%3733.22%98.60%
3.08% to 4.08%900.78%99.38%
Greater than 4.08%720.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.29%1.40% 78.80%68.27%
±2σ -2.64%2.74% 95.57%95.45%
±3σ -3.98%4.08% 98.51%99.73%
Descriptive Statistics
Mean0.053%
Standard Error0.012%
Median0.000%
Mode0.000%
Standard Deviation1.344%
Sample Variance1.806%
Kurtosis13.88
Skewness-0.05
Range32.653%
Minimum-16.495%
Maximum16.158%
Count11576
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.987% 5631 48.64% 0.480%
Negative -0.986% 5007 43.25% -0.426%
Zero 0.000% 938 8.10% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.89%
20 1 Month 1.82%
60 1 Quarter 1.53%
250 1 Year 1.61%
750 3 Years 1.65%
1,250 5 Years 1.72%
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 57.21 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 -1.00%00.00%0.00%
-1.00% to -0.10%00.00%0.00%
-0.10% to 0.79%139312.03%12.03%
0.79% to 1.69%606552.39%64.42%
1.69% to 2.58%259122.38%86.80%
2.58% to 3.48%8927.70%94.51%
3.48% to 4.38%2972.57%97.07%
4.38% to 5.27%1411.22%98.29%
Greater than 5.27%1981.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.50%2.88% 88.70%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 Deviation1.194%
Sample Variance1.426%
Kurtosis57.21
Skewness4.91
Range29.902%
Minimum0.239%
Maximum30.141%
Count11577
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.690% 11577 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%4.68%
-1.80% to -0.91%139612.06%16.74%
-0.91% to -0.01%356030.75%47.49%
-0.01% to 0.88%414535.80%83.29%
0.88% to 1.77%132511.45%94.74%
1.77% to 2.66%4023.47%98.21%
2.66% to 3.55%1201.04%99.25%
Greater than 3.55%870.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.20%1.17% 77.39%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 Variance1.414%
Kurtosis12.60
Skewness0.34
Range31.811%
Minimum-13.910%
Maximum17.901%
Count11577
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.921% 5070 43.79% 0.403%
Negative -0.878% 5519 47.67% -0.419%
Zero 0.000% 988 8.53% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.13. Further, an Excess Kurtosis of 10.19 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%803.34%4.88%
-4.18% to -1.96%27811.60%16.48%
-1.96% to 0.26%79133.00%49.48%
0.26% to 2.48%81333.92%83.40%
2.48% to 4.70%28111.72%95.12%
4.70% to 6.92%773.21%98.33%
6.92% to 9.14%210.88%99.21%
Greater than 9.14%190.79%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.70%3.22% 78.35%68.27%
±2σ -5.66%6.18% 95.33%95.45%
±3σ -8.62%9.14% 98.66%99.73%
Descriptive Statistics
Mean0.258%
Standard Error0.060%
Median0.284%
Mode0.000%
Standard Deviation2.960%
Sample Variance8.762%
Kurtosis10.19
Skewness0.13
Range51.909%
Minimum-21.808%
Maximum30.101%
Count2397
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.126% 1297 54.11% 1.150%
Negative -2.064% 1036 43.22% -0.892%
Zero 0.000% 64 2.67% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.22%
12 1 Quarter 3.42%
52 1 Year 3.57%
156 3 Years 3.70%
260 5 Years 3.87%
520 10 Years 3.87%
1,040 20 Years 3.78%
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 5.66. Further, an Excess Kurtosis of 64.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.96%00.00%0.00%
-4.96% to -2.68%00.00%0.00%
-2.68% to -0.41%00.00%0.00%
-0.41% to 1.87%2309.59%9.59%
1.87% to 4.15%134255.96%65.55%
4.15% to 6.42%53922.48%88.03%
6.42% to 8.70%1536.38%94.41%
8.70% to 10.97%763.17%97.58%
10.97% to 13.25%291.21%98.79%
Greater than 13.25%291.21%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.11%7.18% 90.03%68.27%
±2σ -1.92%10.21% 96.96%95.45%
±3σ -4.96%13.25% 98.79%99.73%
Descriptive Statistics
Mean4.146%
Standard Error0.062%
Median3.448%
Mode3.226%
Standard Deviation3.034%
Sample Variance9.206%
Kurtosis64.94
Skewness5.66
Range57.951%
Minimum0.820%
Maximum58.771%
Count2398
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.146% 2398 100.00% 4.146%
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 11.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.94%140.58%0.58%
-8.94% to -6.71%180.75%1.33%
-6.71% to -4.49%672.79%4.13%
-4.49% to -2.26%29212.18%16.31%
-2.26% to -0.03%83034.61%50.92%
-0.03% to 2.20%79333.07%83.99%
2.20% to 4.42%26010.84%94.83%
4.42% to 6.65%823.42%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% 78.32%68.27%
±2σ -5.97%5.91% 95.33%95.45%
±3σ -8.94%8.88% 98.75%99.73%
Descriptive Statistics
Mean-0.032%
Standard Error0.061%
Median-0.129%
Mode0.000%
Standard Deviation2.970%
Sample Variance8.820%
Kurtosis11.37
Skewness1.18
Range47.600%
Minimum-19.710%
Maximum27.890%
Count2398
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.181% 1093 45.58% 0.994%
Negative -2.009% 1225 51.08% -1.026%
Zero 0.000% 80 3.34% 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 2.57 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.06%50.91%0.91%
-15.06% to -11.03%71.27%2.18%
-11.03% to -6.99%152.72%4.90%
-6.99% to -2.96%7914.34%19.24%
-2.96% to 1.07%16029.04%48.28%
1.07% to 5.10%17631.94%80.22%
5.10% to 9.13%8114.70%94.92%
9.13% to 13.16%193.45%98.37%
13.16% to 17.19%61.09%99.46%
Greater than 17.19%30.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.31%6.44% 74.41%68.27%
±2σ -9.68%11.82% 94.37%95.45%
±3σ -15.06%17.19% 98.55%99.73%
Descriptive Statistics
Mean1.068%
Standard Error0.229%
Median1.286%
Mode0.000%
Standard Deviation5.375%
Sample Variance28.896%
Kurtosis2.57
Skewness-0.36
Range49.397%
Minimum-27.134%
Maximum22.263%
Count551
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.131% 345 62.61% 2.587%
Negative -4.161% 201 36.48% -1.518%
Zero 0.000% 5 0.91% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 7.34%
12 1 Year 6.71%
36 3 Years 7.39%
60 5 Years 8.04%
120 10 Years 8.09%
240 20 Years 7.79%
600 50 Years 8.60%
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 32.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.53%00.00%0.00%
-9.53% to -4.86%00.00%0.00%
-4.86% to -0.18%00.00%0.00%
-0.18% to 4.49%6211.23%11.23%
4.49% to 9.17%29753.80%65.04%
9.17% to 13.84%12823.19%88.22%
13.84% to 18.52%335.98%94.20%
18.52% to 23.19%183.26%97.46%
23.19% to 27.86%40.72%98.19%
Greater than 27.86%101.81%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.93%15.40% 89.49%68.27%
±2σ -3.30%21.63% 96.56%95.45%
±3σ -9.53%27.86% 98.19%99.73%
Descriptive Statistics
Mean9.166%
Standard Error0.265%
Median7.650%
Mode10.366%
Standard Deviation6.233%
Sample Variance38.852%
Kurtosis32.93
Skewness4.46
Range69.373%
Minimum2.395%
Maximum71.768%
Count552
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 9.166% 552 100.00% 9.166%
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 1.06. Further, an Excess Kurtosis of 5.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.13%10.18%0.18%
-17.13% to -12.94%40.72%0.91%
-12.94% to -8.76%162.90%3.80%
-8.76% to -4.57%9316.85%20.65%
-4.57% to -0.38%18232.97%53.62%
-0.38% to 3.81%15528.08%81.70%
3.81% to 8.00%7213.04%94.75%
8.00% to 12.19%193.44%98.19%
12.19% to 16.38%50.91%99.09%
Greater than 16.38%50.91%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.96%5.21% 74.82%68.27%
±2σ -11.55%10.80% 95.29%95.45%
±3σ -17.13%16.38% 98.91%99.73%
Descriptive Statistics
Mean-0.376%
Standard Error0.238%
Median-0.716%
Mode0.000%
Standard Deviation5.586%
Sample Variance31.200%
Kurtosis5.20
Skewness1.06
Range56.795%
Minimum-19.557%
Maximum37.238%
Count552
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.474% 228 41.30% 1.848%
Negative -3.898% 315 57.06% -2.224%
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 22.30%52.72%98.91%
22.30% 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%11.61% 77.72%68.27%
±2σ -14.05%20.17% 94.02%95.45%
±3σ -22.60%28.72% 98.37%99.73%
Descriptive Statistics
Mean3.061%
Standard Error0.631%
Median3.729%
Mode-33.000%
Standard Deviation8.553%
Sample Variance73.147%
Kurtosis3.39
Skewness-0.07
Range74.232%
Minimum-33.000%
Maximum41.232%
Count184
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.339% 125 67.94% 4.986%
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 9.25%
12 3 Years 11.46%
20 5 Years 13.00%
40 10 Years 13.19%
80 20 Years 13.20%
200 50 Years 14.62%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.50. Further, an Excess Kurtosis of 28.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -18.45%00.00%0.00%
-18.45% to -9.70%00.00%0.00%
-9.70% to -0.95%00.00%0.00%
-0.95% to 7.79%126.49%6.49%
7.79% to 16.54%11562.16%68.65%
16.54% to 25.29%3820.54%89.19%
25.29% to 34.04%115.95%95.14%
34.04% to 42.78%42.16%97.30%
42.78% to 51.53%21.08%98.38%
Greater than 51.53%31.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.88%28.20% 91.89%68.27%
±2σ -6.79%39.87% 96.76%95.45%
±3σ -18.45%51.53% 98.38%99.73%
Descriptive Statistics
Mean16.541%
Standard Error0.857%
Median14.045%
Mode16.667%
Standard Deviation11.663%
Sample Variance136.024%
Kurtosis28.79
Skewness4.50
Range106.353%
Minimum5.415%
Maximum111.768%
Count185
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 16.541% 185 100.00% 16.541%
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 -14.38%31.62%2.70%
-14.38% 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 -10.00%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-1.247%
Standard Error0.644%
Median-2.381%
Mode-5.128%
Standard Deviation8.757%
Sample Variance76.682%
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 -6.180% 115 62.16% -3.842%
Zero 0.000% 1 0.54% 0.000%