Markets Data Volatility Heatmap Portfolio Calculator

LUV Deep Analytical Report

Southwest Airlines Co. | Category: Equity Large Cap | Ann. Div Yield: 1.38% ($0.72) | Last Updated: 2026-02-22 | Data Range: 1980-01-01 → 2026-02-01 (554 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 2.35% 1.81% 2.08% 3.17% 2.68% 2.99% 50.71 53.50 49.38 54.95
Weekly 5.08% 4.37% 5.01% 7.65% 5.89% 6.57% 49.11 55.25 46.30 58.60
Monthly 9.96% 8.77% 9.93% 16.54% 12.26% 13.69% 46.08 58.89 40.76 66.57
Quarterly 19.13% 15.98% 18.29% 30.61% 21.24% 23.71% 42.12 64.42 34.06 79.66
Annual — — — — 42.48% 47.41% 34.06 79.66 22.27 121.83
Option Time Horizon — — — — 13.89% 15.50% 45.34 59.85 39.46 68.77
Calculation Notes: Computed at 2026-02-22T14:24 UTC  |  Reference Contract: Call option expiring 2026-04-02 (39 days)  |  Spot Price (S): $52.09  |  Strike (K): $54.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $2.1600 (Bid $1.8700 / Ask $2.4500)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 1.38%  |  Binomial IV (Annual): 42.48% (CRR binomial tree, American, n=20 steps)  |  BS IV: 42.98% (European Black-Scholes)  |  Yahoo IV (Annual): 47.41% → 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
2025-12-26 $0.1800
2025-09-03 $0.1800
2025-06-18 $0.1800
2025-03-12 $0.1800
2024-12-26 $0.1800
2024-09-04 $0.1800
2024-06-18 $0.1800
2024-03-05 $0.1800
2023-12-20 $0.1800
2023-09-05 $0.1800
2023-06-20 $0.1800
2023-03-07 $0.1800
2023-01-09 $0.1800
2020-03-03 $0.1800
2019-12-10 $0.1800
2019-08-20 $0.1800
2019-06-04 $0.1800
2019-03-05 $0.1600
2018-12-04 $0.1600
2018-08-21 $0.1600
2018-06-05 $0.1600
2018-03-06 $0.1250
2017-12-06 $0.1250
2017-08-22 $0.1250
2017-06-05 $0.1250
2017-03-07 $0.1000
2016-12-06 $0.1000
2016-08-16 $0.1000
2016-06-06 $0.1000
2016-03-01 $0.0750
2015-12-08 $0.0750
2015-08-18 $0.0750
2015-06-01 $0.0750
2015-03-03 $0.0600
2014-12-09 $0.0600
2014-08-19 $0.0600
2014-06-02 $0.0600
2014-03-04 $0.0400
2013-12-10 $0.0400
2013-08-06 $0.0400
2013-06-03 $0.0400
2013-03-05 $0.0100
2012-12-04 $0.0100
2012-08-14 $0.0100
2012-06-04 $0.0100
2012-02-28 $0.0050
2011-12-06 $0.0050
2011-08-23 $0.0050
2011-06-06 $0.0050
2011-03-01 $0.0050
2010-12-07 $0.0050
2010-08-24 $0.0050
2010-06-07 $0.0050
2010-03-02 $0.0050
2009-12-08 $0.0050
2009-09-01 $0.0050
2009-06-08 $0.0050
2009-02-24 $0.0050
2008-12-09 $0.0050
2008-08-26 $0.0050
2008-06-10 $0.0050
2008-02-26 $0.0050
2007-12-04 $0.0050
2007-08-28 $0.0050
2007-06-05 $0.0050
2007-02-27 $0.0050
2006-12-05 $0.0050
2006-08-29 $0.0050
2006-06-06 $0.0050
2006-02-28 $0.0050
2005-12-06 $0.0050
2005-08-30 $0.0050
2005-06-07 $0.0050
2005-03-01 $0.0050
2004-12-07 $0.0050
2004-08-31 $0.0050
2004-06-08 $0.0050
2004-03-02 $0.0050
2003-12-03 $0.0050
2003-08-29 $0.0050
2003-06-02 $0.0050
2003-03-04 $0.0050
2002-12-09 $0.0050
2002-08-30 $0.0050
2002-06-03 $0.0050
2002-02-27 $0.0050
2001-12-03 $0.0050
2001-08-31 $0.0050
2001-06-04 $0.0030
2001-02-28 $0.0050
2000-12-04 $0.0040
2000-09-01 $0.0040
2000-05-31 $0.0040
2000-03-01 $0.0040
1999-12-06 $0.0040
1999-08-30 $0.0033
1999-06-02 $0.0036
1999-03-03 $0.0036
1998-12-07 $0.0036
1998-08-31 $0.0036
1998-06-03 $0.0030
1998-03-04 $0.0030
1997-12-08 $0.0030
1997-08-29 $0.0024
1997-05-28 $0.0024
1997-02-26 $0.0024
1996-12-09 $0.0020
1996-08-30 $0.0020
1996-05-29 $0.0020
1996-02-28 $0.0020
1995-12-04 $0.0020
1995-09-01 $0.0020
1995-05-26 $0.0020
1995-02-27 $0.0020
1994-11-30 $0.0020
1994-08-30 $0.0020
1994-05-27 $0.0020
1994-02-28 $0.0020
1993-11-30 $0.0020
1993-08-30 $0.0020
1993-05-28 $0.0020
1993-02-26 $0.0020
1992-12-01 $0.0020
1992-08-31 $0.0020
1992-06-01 $0.0018
1992-02-28 $0.0016
1991-11-29 $0.0016
1991-08-29 $0.0016
1991-05-31 $0.0016
1991-03-01 $0.0016
1990-11-29 $0.0016
1990-09-06 $0.0016
1990-06-07 $0.0015
1990-03-05 $0.0015
1989-11-29 $0.0015
1989-09-01 $0.0015
1989-06-07 $0.0015
1989-03-06 $0.0015
1988-11-29 $0.0015
1988-09-02 $0.0014
1988-06-07 $0.0014
1988-03-04 $0.0014
1987-11-27 $0.0014
1987-09-02 $0.0014
1987-06-08 $0.0014
1987-03-04 $0.0014
1986-11-26 $0.0014
1986-09-03 $0.0014
1986-06-06 $0.0014
1986-03-05 $0.0014
1985-11-26 $0.0014
1985-09-04 $0.0014
1985-06-06 $0.0014
1985-03-06 $0.0014
1984-11-28 $0.0014
1984-09-05 $0.0014
1984-06-04 $0.0014
1984-03-07 $0.0014
1983-11-30 $0.0014
1983-09-02 $0.0014
1983-05-31 $0.0014
1983-03-09 $0.0014
1982-11-26 $0.0014
1982-09-03 $0.0014
1982-06-04 $0.0014
1982-03-09 $0.0014
1981-11-25 $0.0014
1981-09-02 $0.0011
1981-06-09 $0.0011
1981-03-10 $0.0011
1980-11-28 $0.0011
1980-09-30 $0.0011
1980-06-06 $0.0007
1980-03-03 $0.0007
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.00. Further, an Excess Kurtosis of 5.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.97%660.57%0.57%
-6.97% to -5.21%1020.88%1.45%
-5.21% to -3.45%4083.51%4.96%
-3.45% to -1.69%150512.95%17.90%
-1.69% to 0.08%406734.99%52.90%
0.08% to 1.84%342029.42%82.32%
1.84% to 3.60%135211.63%93.95%
3.60% to 5.37%4714.05%98.00%
5.37% to 7.13%1451.25%99.25%
Greater than 7.13%870.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.27%2.43% 75.88%68.27%
±2σ -4.62%4.78% 95.04%95.45%
±3σ -6.97%7.13% 98.68%99.73%
Descriptive Statistics
Mean0.078%
Standard Error0.022%
Median0.000%
Mode0.000%
Standard Deviation2.351%
Sample Variance5.526%
Kurtosis5.53
Skewness0.00
Range42.763%
Minimum-24.065%
Maximum18.698%
Count11623
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.833% 5571 47.93% 0.879%
Negative -1.713% 5434 46.75% -0.801%
Zero 0.000% 618 5.32% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 4.21%
20 1 Month 4.47%
60 1 Quarter 3.45%
250 1 Year 3.60%
750 3 Years 3.14%
1,250 5 Years 3.17%
2,500 10 Years 3.04%
5,000 20 Years 3.06%
12,500 50 Years 3.10%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.66. Further, an Excess Kurtosis of 14.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.47%00.00%0.00%
-2.47% to -1.11%00.00%0.00%
-1.11% to 0.24%20.02%0.02%
0.24% to 1.60%212018.24%18.26%
1.60% to 2.95%511544.00%62.26%
2.95% to 4.31%254521.89%84.15%
4.31% to 5.67%10579.09%93.25%
5.67% to 7.02%4063.49%96.74%
7.02% to 8.38%1901.63%98.37%
Greater than 8.38%1891.63%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.15%4.76% 82.25%68.27%
±2σ -0.66%6.57% 95.76%95.45%
±3σ -2.47%8.38% 98.37%99.73%
Descriptive Statistics
Mean2.954%
Standard Error0.017%
Median2.510%
Mode2.632%
Standard Deviation1.808%
Sample Variance3.270%
Kurtosis14.27
Skewness2.66
Range24.708%
Minimum0.232%
Maximum24.940%
Count11624
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.954% 11624 100.00% 2.954%
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 0.26. Further, an Excess Kurtosis of 5.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.24%720.62%0.62%
-6.24% to -4.68%1421.22%1.84%
-4.68% to -3.12%4533.90%5.74%
-3.12% to -1.56%144612.44%18.18%
-1.56% to 0.00%406935.01%53.18%
0.00% to 1.56%333828.72%81.90%
1.56% to 3.12%145612.53%94.43%
3.12% to 4.68%4473.85%98.27%
4.68% to 6.24%1191.02%99.29%
Greater than 6.24%820.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.08%2.08% 75.54%68.27%
±2σ -4.16%4.16% 94.84%95.45%
±3σ -6.24%6.24% 98.68%99.73%
Descriptive Statistics
Mean0.004%
Standard Error0.019%
Median0.000%
Mode0.000%
Standard Deviation2.080%
Sample Variance4.328%
Kurtosis5.08
Skewness0.26
Range37.541%
Minimum-13.905%
Maximum23.636%
Count11624
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.600% 5442 46.82% 0.749%
Negative -1.584% 5465 47.02% -0.745%
Zero 0.000% 717 6.17% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.02. 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 -14.86%150.62%0.62%
-14.86% to -11.05%311.29%1.91%
-11.05% to -7.24%843.49%5.40%
-7.24% to -3.44%32513.50%18.90%
-3.44% to 0.37%76331.70%50.60%
0.37% to 4.18%74030.74%81.35%
4.18% to 7.99%30412.63%93.98%
7.99% to 11.79%963.99%97.96%
11.79% to 15.60%361.50%99.46%
Greater than 15.60%130.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.71%5.45% 73.91%68.27%
±2σ -9.78%10.53% 94.39%95.45%
±3σ -14.86%15.60% 98.84%99.73%
Descriptive Statistics
Mean0.371%
Standard Error0.103%
Median0.332%
Mode0.000%
Standard Deviation5.077%
Sample Variance25.776%
Kurtosis2.32
Skewness-0.02
Range55.982%
Minimum-29.032%
Maximum26.950%
Count2407
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.948% 1250 51.93% 2.050%
Negative -3.691% 1095 45.49% -1.679%
Zero 0.000% 62 2.58% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 12.18%
12 1 Quarter 8.83%
52 1 Year 9.20%
156 3 Years 7.69%
260 5 Years 7.65%
520 10 Years 7.21%
1,040 20 Years 6.99%
2,600 50 Years 7.35%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.40. Further, an Excess Kurtosis of 10.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.51%00.00%0.00%
-5.51% to -2.23%00.00%0.00%
-2.23% to 1.04%00.00%0.00%
1.04% to 4.32%47119.56%19.56%
4.32% to 7.60%99941.49%61.05%
7.60% to 10.88%55322.97%84.01%
10.88% to 14.15%2229.22%93.23%
14.15% to 17.43%783.24%96.47%
17.43% to 20.70%411.70%98.17%
Greater than 20.70%441.83%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 3.23%11.97% 81.85%68.27%
±2σ -1.14%16.34% 95.85%95.45%
±3σ -5.51%20.70% 98.17%99.73%
Descriptive Statistics
Mean7.598%
Standard Error0.089%
Median6.621%
Mode5.882%
Standard Deviation4.369%
Sample Variance19.088%
Kurtosis10.50
Skewness2.40
Range47.264%
Minimum1.360%
Maximum48.624%
Count2408
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.598% 2408 100.00% 7.598%
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 0.69. Further, an Excess Kurtosis of 3.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.06%90.37%0.37%
-15.06% to -11.31%200.83%1.20%
-11.31% to -7.55%963.99%5.19%
-7.55% to -3.80%33814.04%19.23%
-3.80% to -0.05%77732.27%51.50%
-0.05% to 3.71%72830.23%81.73%
3.71% to 7.46%29712.33%94.06%
7.46% to 11.22%873.61%97.67%
11.22% to 14.97%301.25%98.92%
Greater than 14.97%261.08%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.05%4.96% 73.96%68.27%
±2σ -10.06%9.97% 95.35%95.45%
±3σ -15.06%14.97% 98.55%99.73%
Descriptive Statistics
Mean-0.046%
Standard Error0.102%
Median-0.264%
Mode0.000%
Standard Deviation5.006%
Sample Variance25.055%
Kurtosis3.85
Skewness0.69
Range62.138%
Minimum-21.229%
Maximum40.909%
Count2408
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.879% 1115 46.30% 1.796%
Negative -3.577% 1240 51.49% -1.842%
Zero 0.000% 53 2.20% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.15. Further, an Excess Kurtosis of 0.20 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -28.32%00.00%0.00%
-28.32% to -20.85%61.08%1.08%
-20.85% to -13.39%325.79%6.87%
-13.39% to -5.92%8815.91%22.78%
-5.92% to 1.55%15127.31%50.09%
1.55% to 9.02%15427.85%77.94%
9.02% to 16.48%8214.83%92.77%
16.48% to 23.95%305.42%98.19%
23.95% to 31.42%71.27%99.46%
Greater than 31.42%30.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.41%11.51% 70.34%68.27%
±2σ -18.37%21.46% 95.12%95.45%
±3σ -28.32%31.42% 99.46%99.73%
Descriptive Statistics
Mean1.549%
Standard Error0.423%
Median1.477%
Mode0.000%
Standard Deviation9.957%
Sample Variance99.148%
Kurtosis0.20
Skewness0.15
Range61.761%
Minimum-26.761%
Maximum35.000%
Count553
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.758% 300 54.25% 4.751%
Negative -7.140% 248 44.85% -3.202%
Zero 0.000% 5 0.90% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 21.49%
12 1 Year 19.90%
36 3 Years 16.74%
60 5 Years 16.54%
120 10 Years 15.95%
240 20 Years 15.22%
600 50 Years 15.97%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.95. Further, an Excess Kurtosis of 6.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.78%00.00%0.00%
-8.78% to -2.21%00.00%0.00%
-2.21% to 4.37%00.00%0.00%
4.37% to 10.94%11821.30%21.30%
10.94% to 17.51%21438.63%59.93%
17.51% to 24.09%12923.29%83.21%
24.09% to 30.66%5710.29%93.50%
30.66% to 37.24%183.25%96.75%
37.24% to 43.81%91.62%98.38%
Greater than 43.81%91.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 8.75%26.28% 78.88%68.27%
±2σ -0.02%35.05% 95.85%95.45%
±3σ -8.78%43.81% 98.38%99.73%
Descriptive Statistics
Mean17.514%
Standard Error0.372%
Median15.702%
Mode20.000%
Standard Deviation8.766%
Sample Variance76.835%
Kurtosis6.13
Skewness1.95
Range62.455%
Minimum4.745%
Maximum67.200%
Count554
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 17.514% 554 100.00% 17.514%
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 0.51. Further, an Excess Kurtosis of 0.64 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -30.25%00.00%0.00%
-30.25% to -22.80%30.54%0.54%
-22.80% to -15.36%254.51%5.05%
-15.36% to -7.91%9316.79%21.84%
-7.91% to -0.46%17331.23%53.07%
-0.46% to 6.99%14325.81%78.88%
6.99% to 14.44%7513.54%92.42%
14.44% to 21.89%295.23%97.65%
21.89% to 29.34%101.81%99.46%
Greater than 29.34%30.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.39%9.47% 72.02%68.27%
±2σ -20.32%19.41% 95.49%95.45%
±3σ -30.25%29.34% 99.46%99.73%
Descriptive Statistics
Mean-0.457%
Standard Error0.422%
Median-1.160%
Mode0.000%
Standard Deviation9.932%
Sample Variance98.641%
Kurtosis0.64
Skewness0.51
Range65.597%
Minimum-26.984%
Maximum38.613%
Count554
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.325% 245 44.22% 3.682%
Negative -7.593% 302 54.51% -4.139%
Zero 0.000% 7 1.26% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.94. Further, an Excess Kurtosis of 4.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -52.50%00.00%0.00%
-52.50% to -38.15%21.08%1.08%
-38.15% to -23.81%73.78%4.86%
-23.81% to -9.46%3619.46%24.32%
-9.46% to 4.88%4825.95%50.27%
4.88% to 19.23%5529.73%80.00%
19.23% to 33.57%2815.14%95.14%
33.57% to 47.92%73.78%98.92%
47.92% to 62.26%10.54%99.46%
Greater than 62.26%10.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -14.24%24.01% 71.35%68.27%
±2σ -33.37%43.14% 97.30%95.45%
±3σ -52.50%62.26% 99.46%99.73%
Descriptive Statistics
Mean4.883%
Standard Error1.406%
Median4.735%
Mode-42.942%
Standard Deviation19.127%
Sample Variance365.848%
Kurtosis4.97
Skewness0.94
Range157.567%
Minimum-42.942%
Maximum114.625%
Count185
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 17.756% 105 56.76% 10.078%
Negative -12.012% 80 43.24% -5.194%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 34.78%
12 3 Years 33.69%
20 5 Years 30.61%
40 10 Years 29.08%
80 20 Years 27.59%
200 50 Years 28.59%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.17. Further, an Excess Kurtosis of 7.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -14.74%00.00%0.00%
-14.74% to -2.75%00.00%0.00%
-2.75% to 9.23%00.00%0.00%
9.23% to 21.22%3418.28%18.28%
21.22% to 33.20%7841.94%60.22%
33.20% to 45.19%4725.27%85.48%
45.19% to 57.18%158.06%93.55%
57.18% to 69.16%31.61%95.16%
69.16% to 81.15%63.23%98.39%
Greater than 81.15%31.61%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 17.22%49.19% 82.80%68.27%
±2σ 1.24%65.17% 94.62%95.45%
±3σ -14.74%81.15% 98.39%99.73%
Descriptive Statistics
Mean33.204%
Standard Error1.172%
Median30.051%
Mode22.353%
Standard Deviation15.981%
Sample Variance255.379%
Kurtosis7.17
Skewness2.17
Range109.255%
Minimum9.793%
Maximum119.048%
Count186
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 33.204% 186 100.00% 33.204%
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 0.98. Further, an Excess Kurtosis of 2.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -56.17%00.00%0.00%
-56.17% to -42.45%10.54%0.54%
-42.45% to -28.73%31.61%2.15%
-28.73% to -15.01%3719.89%22.04%
-15.01% to -1.29%6032.26%54.30%
-1.29% to 12.43%4323.12%77.42%
12.43% to 26.15%3217.20%94.62%
26.15% to 39.88%63.23%97.85%
39.88% to 53.59%21.08%98.92%
Greater than 53.59%21.08%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -19.58%17.01% 72.04%68.27%
±2σ -37.88%35.30% 96.24%95.45%
±3σ -56.17%53.60% 98.92%99.73%
Descriptive Statistics
Mean-1.287%
Standard Error1.341%
Median-3.841%
Mode-20.000%
Standard Deviation18.294%
Sample Variance334.675%
Kurtosis2.35
Skewness0.98
Range130.583%
Minimum-53.271%
Maximum77.312%
Count186
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 15.275% 80 43.01% 6.570%
Negative -13.787% 106 56.99% -7.857%
Zero 0.000% 0 0.00% 0.000%