Markets Data Volatility Heatmap Portfolio Calculator

SO Deep Analytical Report

The Southern Company | Category: Equity Mega Cap | Ann. Div Yield: 3.15% ($2.94) | Last Updated: 2026-03-24 | Data Range: 1981-12-01 → 2026-03-01 (532 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 1.26% 1.06% 1.16% 1.74% 1.55% 1.70% 92.68 95.60 91.25 97.10
Weekly 2.65% 2.46% 2.61% 3.89% 3.42% 3.75% 90.97 97.40 87.91 100.78
Monthly 4.87% 4.83% 4.86% 8.34% 7.11% 7.80% 87.67 101.07 81.65 108.51
Quarterly 7.36% 7.59% 7.11% 14.23% 12.32% 13.51% 83.22 106.47 73.58 120.42
Annual — — — — 24.63% 27.01% 73.58 120.42 57.52 154.05
Option Time Horizon — — — — 9.30% 10.20% 85.77 103.30 78.16 113.36
Calculation Notes: Computed at 2026-03-23T16:33 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $94.13  |  Strike (K): $95.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.1250 (Bid $2.7500 / Ask $3.5000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.15%  |  Binomial IV (Annual): 24.63% (CRR binomial tree, American, n=20 steps)  |  BS IV: 24.74% (European Black-Scholes)  |  Yahoo IV (Annual): 27.01% → 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
2026-02-17 $0.7400
2025-11-17 $0.7400
2025-08-18 $0.7400
2025-05-19 $0.7400
2025-02-18 $0.7200
2024-11-18 $0.7200
2024-08-19 $0.7200
2024-05-17 $0.7200
2024-02-16 $0.7000
2023-11-17 $0.7000
2023-08-18 $0.7000
2023-05-12 $0.7000
2023-02-17 $0.6800
2022-11-18 $0.6800
2022-08-12 $0.6800
2022-05-13 $0.6800
2022-02-18 $0.6600
2021-11-12 $0.6600
2021-08-13 $0.6600
2021-05-14 $0.6600
2021-02-12 $0.6400
2020-11-13 $0.6400
2020-08-14 $0.6400
2020-05-15 $0.6400
2020-02-14 $0.6200
2019-11-15 $0.6200
2019-08-16 $0.6200
2019-05-17 $0.6200
2019-02-15 $0.6000
2018-11-16 $0.6000
2018-08-17 $0.6000
2018-05-18 $0.6000
2018-02-16 $0.5800
2017-11-17 $0.5800
2017-08-17 $0.5800
2017-05-11 $0.5800
2017-02-16 $0.5600
2016-11-17 $0.5600
2016-08-11 $0.5600
2016-05-12 $0.5600
2016-02-11 $0.5430
2015-11-12 $0.5430
2015-08-13 $0.5430
2015-05-14 $0.5430
2015-02-12 $0.5250
2014-10-30 $0.5250
2014-07-31 $0.5250
2014-05-01 $0.5250
2014-01-30 $0.5070
2013-10-31 $0.5070
2013-08-01 $0.5070
2013-05-02 $0.5070
2013-01-31 $0.4900
2012-11-01 $0.4900
2012-08-02 $0.4900
2012-05-03 $0.4900
2012-02-02 $0.4730
2011-11-03 $0.4730
2011-07-28 $0.4730
2011-04-28 $0.4730
2011-02-03 $0.4550
2010-10-28 $0.4550
2010-07-29 $0.4550
2010-04-29 $0.4550
2010-01-28 $0.4380
2009-10-29 $0.4380
2009-07-30 $0.4380
2009-04-30 $0.4380
2009-01-29 $0.4200
2008-10-30 $0.4200
2008-07-31 $0.4200
2008-05-01 $0.4200
2008-01-31 $0.4030
2007-11-01 $0.4030
2007-08-02 $0.4030
2007-05-03 $0.4030
2007-02-01 $0.3880
2006-11-02 $0.3880
2006-08-03 $0.3880
2006-04-27 $0.3880
2006-02-02 $0.3730
2005-11-03 $0.3730
2005-07-28 $0.3730
2005-04-28 $0.3730
2005-02-03 $0.3580
2004-10-28 $0.3580
2004-07-29 $0.3580
2004-04-29 $0.3500
2004-01-29 $0.3500
2003-10-30 $0.3500
2003-07-31 $0.3500
2003-05-01 $0.3420
2003-01-30 $0.3430
2002-10-31 $0.3430
2002-08-01 $0.3430
2002-05-02 $0.3350
2002-01-31 $0.3350
2001-11-01 $0.3350
2001-08-02 $0.3350
2001-05-03 $0.3350
2001-02-01 $0.2047
2000-11-02 $0.2047
2000-08-03 $0.2047
2000-04-27 $0.2047
2000-02-03 $0.2047
1999-10-28 $0.2047
1999-07-29 $0.2047
1999-04-29 $0.2047
1999-01-28 $0.2047
1998-10-29 $0.2047
1998-07-30 $0.2047
1998-04-30 $0.2047
1998-01-29 $0.2047
1997-10-30 $0.1985
1997-07-31 $0.1985
1997-05-01 $0.1985
1997-01-30 $0.1985
1996-10-31 $0.1924
1996-08-01 $0.1924
1996-05-02 $0.1924
1996-02-01 $0.1924
1995-11-02 $0.1863
1995-08-03 $0.1863
1995-04-25 $0.1863
1995-01-31 $0.1863
1994-11-01 $0.1802
1994-07-26 $0.1802
1994-04-26 $0.1802
1994-02-01 $0.1802
1993-10-26 $0.1741
1993-07-27 $0.1741
1993-04-27 $0.1741
1993-01-26 $0.1741
1992-10-27 $0.1680
1992-07-28 $0.1680
1992-04-28 $0.1680
1992-01-28 $0.1680
1991-10-29 $0.1634
1991-07-30 $0.1634
1991-04-30 $0.1634
1991-01-29 $0.1634
1990-10-30 $0.1634
1990-07-31 $0.1634
1990-05-01 $0.1634
1990-01-30 $0.1634
1989-10-31 $0.1634
1989-08-01 $0.1634
1989-04-25 $0.1634
1989-01-31 $0.1634
1988-11-01 $0.1634
1988-07-26 $0.1634
1988-04-26 $0.1634
1988-01-26 $0.1634
1987-10-27 $0.1634
1987-07-28 $0.1634
1987-04-28 $0.1634
1987-01-27 $0.1634
1986-10-28 $0.1634
1986-07-29 $0.1558
1986-04-29 $0.1558
1986-01-28 $0.1558
1985-10-29 $0.1558
1985-07-30 $0.1466
1985-04-30 $0.1466
1985-01-29 $0.1466
1984-10-30 $0.1466
1984-07-31 $0.1375
1984-05-01 $0.1375
1984-01-31 $0.1375
1983-11-01 $0.1375
1983-07-26 $0.1298
1983-04-26 $0.1298
1983-02-01 $0.1298
1982-10-26 $0.1298
1982-07-27 $0.1298
1982-04-27 $0.1237
1982-01-26 $0.1237
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.25. Further, an Excess Kurtosis of 16.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.73%730.66%0.66%
-3.73% to -2.78%1030.92%1.58%
-2.78% to -1.83%3423.07%4.65%
-1.83% to -0.89%140412.60%17.25%
-0.89% to 0.06%405836.41%53.66%
0.06% to 1.01%324429.11%82.77%
1.01% to 1.95%139012.47%95.24%
1.95% to 2.90%3683.30%98.55%
2.90% to 3.85%990.89%99.43%
Greater than 3.85%630.57%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.20%1.32% 77.73%68.27%
±2σ -2.46%2.58% 95.76%95.45%
±3σ -3.73%3.85% 98.78%99.73%
Descriptive Statistics
Mean0.060%
Standard Error0.012%
Median0.000%
Mode0.000%
Standard Deviation1.262%
Sample Variance1.592%
Kurtosis16.36
Skewness0.25
Range36.956%
Minimum-18.182%
Maximum18.774%
Count11144
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.979% 5308 47.63% 0.466%
Negative -0.948% 4771 42.81% -0.406%
Zero 0.000% 1065 9.56% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.86%
20 1 Month 1.67%
60 1 Quarter 1.75%
250 1 Year 1.63%
750 3 Years 1.66%
1,250 5 Years 1.74%
2,500 10 Years 1.75%
5,000 20 Years 1.64%
12,500 50 Years 1.77%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.97. Further, an Excess Kurtosis of 36.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.47%00.00%0.00%
-1.47% to -0.67%00.00%0.00%
-0.67% to 0.13%00.00%0.00%
0.13% to 0.92%171915.42%15.42%
0.92% to 1.72%530947.64%63.06%
1.72% to 2.52%250822.50%85.56%
2.52% to 3.31%9668.67%94.23%
3.31% to 4.11%3032.72%96.95%
4.11% to 4.91%1621.45%98.40%
Greater than 4.91%1781.60%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.66%2.78% 85.75%68.27%
±2σ -0.41%3.84% 96.26%95.45%
±3σ -1.47%4.91% 98.40%99.73%
Descriptive Statistics
Mean1.719%
Standard Error0.010%
Median1.486%
Mode1.613%
Standard Deviation1.062%
Sample Variance1.127%
Kurtosis36.44
Skewness3.97
Range21.397%
Minimum0.281%
Maximum21.678%
Count11145
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.719% 11145 100.00% 1.719%
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 0.45. Further, an Excess Kurtosis of 15.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.51%660.59%0.59%
-3.51% to -2.64%1171.05%1.64%
-2.64% to -1.77%3503.14%4.78%
-1.77% to -0.91%143512.88%17.66%
-0.91% to -0.04%320628.77%46.42%
-0.04% to 0.83%401035.98%82.40%
0.83% to 1.70%141612.71%95.11%
1.70% to 2.56%3623.25%98.36%
2.56% to 3.43%1181.06%99.42%
Greater than 3.43%650.58%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.20%1.12% 77.11%68.27%
±2σ -2.35%2.27% 95.38%95.45%
±3σ -3.51%3.43% 98.82%99.73%
Descriptive Statistics
Mean-0.039%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.157%
Sample Variance1.339%
Kurtosis15.87
Skewness0.45
Range34.182%
Minimum-13.349%
Maximum20.833%
Count11145
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.901% 4762 42.73% 0.385%
Negative -0.898% 5255 47.15% -0.423%
Zero 0.000% 1128 10.12% 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 18.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.68%120.52%0.52%
-7.68% to -5.69%251.08%1.60%
-5.69% to -3.69%753.25%4.85%
-3.69% to -1.70%27511.92%16.78%
-1.70% to 0.29%75932.90%49.67%
0.29% to 2.28%76933.33%83.01%
2.28% to 4.27%28412.31%95.32%
4.27% to 6.26%753.25%98.57%
6.26% to 8.25%220.95%99.52%
Greater than 8.25%110.48%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.37%2.94% 77.85%68.27%
±2σ -5.02%5.60% 95.62%95.45%
±3σ -7.68%8.25% 99.00%99.73%
Descriptive Statistics
Mean0.288%
Standard Error0.055%
Median0.304%
Mode0.000%
Standard Deviation2.655%
Sample Variance7.047%
Kurtosis18.23
Skewness0.51
Range57.534%
Minimum-23.391%
Maximum34.143%
Count2307
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.957% 1259 54.57% 1.068%
Negative -1.881% 957 41.48% -0.780%
Zero 0.000% 91 3.94% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.33%
12 1 Quarter 4.05%
52 1 Year 3.62%
156 3 Years 3.70%
260 5 Years 3.89%
520 10 Years 3.94%
1,040 20 Years 3.61%
2,600 50 Years 3.89%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.41. Further, an Excess Kurtosis of 38.55 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.44%00.00%0.00%
-3.44% to -1.59%00.00%0.00%
-1.59% to 0.26%00.00%0.00%
0.26% to 2.10%32013.86%13.86%
2.10% to 3.95%113649.22%63.08%
3.95% to 5.80%53623.22%86.31%
5.80% to 7.65%1837.93%94.24%
7.65% to 9.50%733.16%97.40%
9.50% to 11.35%251.08%98.48%
Greater than 11.35%351.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.49%6.42% 87.13%68.27%
±2σ -0.98%8.88% 96.66%95.45%
±3σ -3.44%11.35% 98.48%99.73%
Descriptive Statistics
Mean3.953%
Standard Error0.051%
Median3.383%
Mode2.273%
Standard Deviation2.465%
Sample Variance6.078%
Kurtosis38.55
Skewness4.41
Range34.174%
Minimum0.669%
Maximum34.843%
Count2308
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.953% 2308 100.00% 3.953%
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 1.41. Further, an Excess Kurtosis of 19.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.96%70.30%0.30%
-7.96% to -6.01%180.78%1.08%
-6.01% to -4.05%723.12%4.20%
-4.05% to -2.10%30613.26%17.46%
-2.10% to -0.14%78033.80%51.26%
-0.14% to 1.81%75532.71%83.97%
1.81% to 3.77%25310.96%94.93%
3.77% to 5.73%793.42%98.35%
5.73% to 7.68%220.95%99.31%
Greater than 7.68%160.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.75%2.47% 77.99%68.27%
±2σ -5.35%5.07% 95.41%95.45%
±3σ -7.96%7.68% 99.00%99.73%
Descriptive Statistics
Mean-0.140%
Standard Error0.054%
Median-0.245%
Mode0.000%
Standard Deviation2.607%
Sample Variance6.798%
Kurtosis19.24
Skewness1.41
Range53.903%
Minimum-21.417%
Maximum32.486%
Count2308
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.941% 994 43.07% 0.836%
Negative -1.845% 1221 52.90% -0.976%
Zero 0.000% 93 4.03% 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 1.08 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -13.38%10.19%0.19%
-13.38% to -9.73%81.51%1.69%
-9.73% to -6.08%264.90%6.59%
-6.08% to -2.43%7614.31%20.90%
-2.43% to 1.22%14928.06%48.96%
1.22% to 4.87%16731.45%80.41%
4.87% to 8.52%7313.75%94.16%
8.52% to 12.17%244.52%98.68%
12.17% to 15.82%40.75%99.44%
Greater than 15.82%30.56%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.64%6.09% 71.37%68.27%
±2σ -8.51%10.96% 95.10%95.45%
±3σ -13.38%15.82% 99.25%99.73%
Descriptive Statistics
Mean1.223%
Standard Error0.211%
Median1.441%
Mode0.000%
Standard Deviation4.867%
Sample Variance23.685%
Kurtosis1.08
Skewness0.07
Range37.652%
Minimum-13.490%
Maximum24.162%
Count531
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.203% 324 61.02% 2.565%
Negative -3.562% 200 37.66% -1.342%
Zero 0.000% 7 1.32% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 7.63%
12 1 Year 7.31%
36 3 Years 7.54%
60 5 Years 8.34%
120 10 Years 8.38%
240 20 Years 7.53%
600 50 Years 8.10%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.95. Further, an Excess Kurtosis of 33.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.00%00.00%0.00%
-6.00% to -2.38%00.00%0.00%
-2.38% to 1.24%00.00%0.00%
1.24% to 4.87%8215.41%15.41%
4.87% to 8.49%25046.99%62.41%
8.49% to 12.11%12222.93%85.34%
12.11% to 15.73%448.27%93.61%
15.73% to 19.36%173.20%96.80%
19.36% to 22.98%81.50%98.31%
Greater than 22.98%91.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 3.66%13.32% 84.02%68.27%
±2σ -1.17%18.15% 96.43%95.45%
±3σ -6.01%22.98% 98.31%99.73%
Descriptive Statistics
Mean8.488%
Standard Error0.209%
Median7.364%
Mode6.087%
Standard Deviation4.831%
Sample Variance23.334%
Kurtosis33.30
Skewness3.95
Range61.311%
Minimum2.083%
Maximum63.394%
Count532
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.488% 532 100.00% 8.488%
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 0.72 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.14%10.19%0.19%
-15.14% to -11.50%40.75%0.94%
-11.50% to -7.86%264.89%5.83%
-7.86% to -4.21%7413.91%19.74%
-4.21% to -0.57%17633.08%52.82%
-0.57% to 3.07%14427.07%79.89%
3.07% to 6.72%6712.59%92.48%
6.72% to 10.36%285.26%97.74%
10.36% to 14.00%101.88%99.62%
Greater than 14.00%20.38%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.43%4.29% 70.68%68.27%
±2σ -10.28%9.14% 95.11%95.45%
±3σ -15.14%14.00% 99.44%99.73%
Descriptive Statistics
Mean-0.570%
Standard Error0.211%
Median-1.058%
Mode0.000%
Standard Deviation4.857%
Sample Variance23.595%
Kurtosis0.72
Skewness0.34
Range35.495%
Minimum-18.414%
Maximum17.081%
Count532
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.935% 220 41.35% 1.627%
Negative -3.883% 301 56.58% -2.197%
Zero 0.000% 11 2.07% 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 1.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -18.50%10.56%0.56%
-18.50% to -12.97%10.56%1.13%
-12.97% to -7.45%84.52%5.65%
-7.45% to -1.93%2916.38%22.03%
-1.93% to 3.59%5229.38%51.41%
3.59% to 9.11%4424.86%76.27%
9.11% to 14.63%3218.08%94.35%
14.63% to 20.15%63.39%97.74%
20.15% to 25.68%31.69%99.44%
Greater than 25.68%10.56%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.77%10.95% 77.40%68.27%
±2σ -11.13%18.31% 93.79%95.45%
±3σ -18.50%25.68% 98.87%99.73%
Descriptive Statistics
Mean3.590%
Standard Error0.553%
Median3.515%
Mode2.487%
Standard Deviation7.362%
Sample Variance54.194%
Kurtosis1.24
Skewness0.13
Range51.429%
Minimum-18.693%
Maximum32.736%
Count177
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.141% 124 70.06% 5.003%
Negative -4.807% 52 29.38% -1.412%
Zero 0.000% 1 0.56% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 12.66%
12 3 Years 12.52%
20 5 Years 14.23%
40 10 Years 14.39%
80 20 Years 13.09%
200 50 Years 13.97%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.92. Further, an Excess Kurtosis of 14.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.67%00.00%0.00%
-7.67% to -1.97%00.00%0.00%
-1.97% to 3.72%00.00%0.00%
3.72% to 9.42%2614.61%14.61%
9.42% to 15.11%8547.75%62.36%
15.11% to 20.80%4525.28%87.64%
20.80% to 26.50%116.18%93.82%
26.50% to 32.19%42.25%96.07%
32.19% to 37.89%42.25%98.31%
Greater than 37.89%31.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 7.52%22.70% 83.15%68.27%
±2σ -0.07%30.29% 96.07%95.45%
±3σ -7.67%37.89% 98.31%99.73%
Descriptive Statistics
Mean15.110%
Standard Error0.569%
Median13.589%
Mode12.069%
Standard Deviation7.592%
Sample Variance57.635%
Kurtosis14.81
Skewness2.92
Range64.745%
Minimum3.939%
Maximum68.684%
Count178
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 15.110% 178 100.00% 15.110%
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 0.44. Further, an Excess Kurtosis of 1.22 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -23.09%10.56%0.56%
-23.09% to -17.75%00.00%0.56%
-17.75% to -12.42%73.93%4.49%
-12.42% to -7.09%3519.66%24.16%
-7.09% to -1.76%4927.53%51.69%
-1.76% to 3.58%5329.78%81.46%
3.58% to 8.91%2212.36%93.82%
8.91% to 14.24%42.25%96.07%
14.24% to 19.57%63.37%99.44%
Greater than 19.57%10.56%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.87%5.35% 76.40%68.27%
±2σ -15.98%12.46% 93.26%95.45%
±3σ -23.09%19.57% 98.88%99.73%
Descriptive Statistics
Mean-1.757%
Standard Error0.533%
Median-2.042%
Mode0.000%
Standard Deviation7.110%
Sample Variance50.556%
Kurtosis1.22
Skewness0.44
Range49.249%
Minimum-24.676%
Maximum24.573%
Count178
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.459% 64 35.95% 1.963%
Negative -6.130% 108 60.67% -3.719%
Zero 0.000% 6 3.37% 0.000%