Markets Data Volatility Heatmap Portfolio Calculator

LUV Deep Analytical Report

Southwest Airlines Co. | Category: Equity Large Cap | Ann. Div Yield: 1.83% ($0.72) | Last Updated: 2026-03-24 | Data Range: 1980-01-01 → 2026-03-01 (555 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% 3.19% 3.74% 3.75% 39.19 42.23 37.75 43.84
Weekly 5.08% 4.38% 5.01% 7.71% 8.23% 8.25% 37.47 44.17 34.51 47.96
Monthly 9.97% 8.77% 9.95% 16.64% 17.13% 17.18% 34.28 48.29 28.88 57.31
Quarterly 19.18% 15.94% 18.36% 31.58% 29.67% 29.75% 30.24 54.74 22.48 73.64
Annual — — — — 59.34% 59.50% 22.48 73.64 12.42 133.30
Option Time Horizon — — — — 22.40% 22.46% 32.52 50.90 26.00 63.67
Calculation Notes: Computed at 2026-03-23T16:42 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $40.69  |  Strike (K): $42.50 (first OTM call ≥ spot)  |  Observed Mid-Price: $2.9500 (Bid $2.6000 / Ask $3.3000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 1.83%  |  Binomial IV (Annual): 59.34% (CRR binomial tree, American, n=20 steps)  |  BS IV: 60.04% (European Black-Scholes)  |  Yahoo IV (Annual): 59.50% → 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
2026-03-12 $0.1800
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 5.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.98%660.57%0.57%
-6.98% to -5.22%1040.89%1.46%
-5.22% to -3.46%4093.51%4.97%
-3.46% to -1.69%150812.95%17.92%
-1.69% to 0.07%406934.95%52.87%
0.07% to 1.84%342529.41%82.28%
1.84% to 3.60%136111.69%93.97%
3.60% to 5.37%4704.04%98.01%
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 -2.28%2.43% 75.84%68.27%
±2σ -4.63%4.78% 95.03%95.45%
±3σ -6.98%7.13% 98.69%99.73%
Descriptive Statistics
Mean0.075%
Standard Error0.022%
Median0.000%
Mode0.000%
Standard Deviation2.353%
Sample Variance5.536%
Kurtosis5.50
Skewness0.00
Range42.763%
Minimum-24.065%
Maximum18.698%
Count11644
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.834% 5578 47.91% 0.879%
Negative -1.716% 5448 46.79% -0.803%
Zero 0.000% 618 5.31% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 4.52%
20 1 Month 5.01%
60 1 Quarter 4.03%
250 1 Year 3.70%
750 3 Years 3.19%
1,250 5 Years 3.19%
2,500 10 Years 3.07%
5,000 20 Years 3.07%
12,500 50 Years 3.11%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.65. Further, an Excess Kurtosis of 14.21 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 -1.12%00.00%0.00%
-1.12% to 0.24%20.02%0.02%
0.24% to 1.60%212618.26%18.27%
1.60% to 2.96%512544.01%62.28%
2.96% to 4.31%253921.80%84.09%
4.31% to 5.67%10659.15%93.23%
5.67% to 7.03%4113.53%96.76%
7.03% to 8.39%1881.61%98.38%
Greater than 8.39%1891.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.15%4.77% 82.23%68.27%
±2σ -0.66%6.58% 95.77%95.45%
±3σ -2.47%8.39% 98.38%99.73%
Descriptive Statistics
Mean2.957%
Standard Error0.017%
Median2.513%
Mode2.632%
Standard Deviation1.810%
Sample Variance3.276%
Kurtosis14.21
Skewness2.65
Range24.708%
Minimum0.232%
Maximum24.940%
Count11645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.957% 11645 100.00% 2.957%
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 5.06 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%4543.90%5.74%
-3.12% to -1.56%144912.44%18.18%
-1.56% to 0.01%407334.98%53.16%
0.01% to 1.57%334228.70%81.85%
1.57% to 3.13%146312.56%94.42%
3.13% to 4.69%4493.86%98.27%
4.69% to 6.25%1221.05%99.32%
Greater than 6.25%790.68%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.08%2.09% 75.53%68.27%
±2σ -4.16%4.17% 94.86%95.45%
±3σ -6.24%6.25% 98.70%99.73%
Descriptive Statistics
Mean0.005%
Standard Error0.019%
Median0.000%
Mode0.000%
Standard Deviation2.082%
Sample Variance4.333%
Kurtosis5.06
Skewness0.26
Range37.541%
Minimum-13.905%
Maximum23.636%
Count11645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.602% 5455 46.84% 0.750%
Negative -1.585% 5473 47.00% -0.745%
Zero 0.000% 717 6.16% 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 2.31 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -14.88%150.62%0.62%
-14.88% to -11.07%311.29%1.91%
-11.07% to -7.26%823.40%5.31%
-7.26% to -3.45%32913.65%18.95%
-3.45% to 0.36%76031.52%50.48%
0.36% to 4.17%74530.90%81.38%
4.17% to 7.98%30412.61%93.99%
7.98% to 11.79%963.98%97.97%
11.79% to 15.60%361.49%99.46%
Greater than 15.60%130.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.72%5.44% 73.83%68.27%
±2σ -9.80%10.52% 94.40%95.45%
±3σ -14.88%15.60% 98.84%99.73%
Descriptive Statistics
Mean0.360%
Standard Error0.103%
Median0.329%
Mode0.000%
Standard Deviation5.081%
Sample Variance25.817%
Kurtosis2.31
Skewness-0.02
Range55.982%
Minimum-29.032%
Maximum26.950%
Count2411
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.947% 1250 51.85% 2.046%
Negative -3.699% 1099 45.58% -1.686%
Zero 0.000% 62 2.57% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 13.11%
12 1 Quarter 10.47%
52 1 Year 9.52%
156 3 Years 7.85%
260 5 Years 7.71%
520 10 Years 7.27%
1,040 20 Years 7.02%
2,600 50 Years 7.36%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.39. Further, an Excess Kurtosis of 10.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.54%00.00%0.00%
-5.54% to -2.25%00.00%0.00%
-2.25% to 1.03%00.00%0.00%
1.03% to 4.32%47119.53%19.53%
4.32% to 7.61%100141.50%61.03%
7.61% to 10.90%55623.05%84.08%
10.90% to 14.19%2209.12%93.20%
14.19% to 17.48%783.23%96.43%
17.48% to 20.76%411.70%98.13%
Greater than 20.76%451.87%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 3.23%12.00% 81.88%68.27%
±2σ -1.16%16.38% 95.77%95.45%
±3σ -5.54%20.76% 98.13%99.73%
Descriptive Statistics
Mean7.611%
Standard Error0.089%
Median6.632%
Mode5.882%
Standard Deviation4.384%
Sample Variance19.219%
Kurtosis10.37
Skewness2.39
Range47.264%
Minimum1.360%
Maximum48.624%
Count2412
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.611% 2412 100.00% 7.611%
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 3.83 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 -11.30%200.83%1.20%
-11.30% to -7.55%963.98%5.18%
-7.55% to -3.79%33914.05%19.24%
-3.79% to -0.04%77632.17%51.41%
-0.04% to 3.72%73230.35%81.76%
3.72% to 7.47%29612.27%94.03%
7.47% to 11.23%883.65%97.68%
11.23% to 14.98%301.24%98.92%
Greater than 14.98%261.08%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.04%4.97% 73.96%68.27%
±2σ -10.05%9.98% 95.36%95.45%
±3σ -15.06%14.98% 98.55%99.73%
Descriptive Statistics
Mean-0.037%
Standard Error0.102%
Median-0.260%
Mode0.000%
Standard Deviation5.007%
Sample Variance25.068%
Kurtosis3.83
Skewness0.69
Range62.138%
Minimum-21.229%
Maximum40.909%
Count2412
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.884% 1119 46.39% 1.802%
Negative -3.577% 1240 51.41% -1.839%
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 0.19 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -28.42%00.00%0.00%
-28.42% to -20.94%61.08%1.08%
-20.94% to -13.46%325.78%6.86%
-13.46% to -5.98%8916.06%22.92%
-5.98% to 1.50%15127.26%50.18%
1.50% to 8.98%15527.98%78.16%
8.98% to 16.46%8114.62%92.78%
16.46% to 23.95%305.42%98.19%
23.95% to 31.43%71.26%99.46%
Greater than 31.43%30.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.47%11.48% 70.04%68.27%
±2σ -18.44%21.45% 95.13%95.45%
±3σ -28.42%31.43% 99.46%99.73%
Descriptive Statistics
Mean1.504%
Standard Error0.424%
Median1.470%
Mode0.000%
Standard Deviation9.974%
Sample Variance99.487%
Kurtosis0.19
Skewness0.15
Range61.761%
Minimum-26.761%
Maximum35.000%
Count554
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.737% 300 54.15% 4.731%
Negative -7.181% 249 44.95% -3.228%
Zero 0.000% 5 0.90% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 20.31%
12 1 Year 19.77%
36 3 Years 16.93%
60 5 Years 16.64%
120 10 Years 16.04%
240 20 Years 15.28%
600 50 Years 15.98%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.94. Further, an Excess Kurtosis of 6.08 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 -2.20%00.00%0.00%
-2.20% to 4.38%00.00%0.00%
4.38% to 10.96%11821.26%21.26%
10.96% to 17.53%21538.74%60.00%
17.53% to 24.11%12823.06%83.06%
24.11% to 30.69%5810.45%93.51%
30.69% to 37.27%183.24%96.76%
37.27% to 43.84%91.62%98.38%
Greater than 43.84%91.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 8.76%26.30% 78.56%68.27%
±2σ -0.01%35.07% 95.86%95.45%
±3σ -8.78%43.84% 98.38%99.73%
Descriptive Statistics
Mean17.534%
Standard Error0.372%
Median15.714%
Mode20.000%
Standard Deviation8.770%
Sample Variance76.921%
Kurtosis6.08
Skewness1.94
Range62.455%
Minimum4.745%
Maximum67.200%
Count555
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 17.534% 555 100.00% 17.534%
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 0.50. Further, an Excess Kurtosis of 0.62 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -30.27%00.00%0.00%
-30.27% to -22.80%30.54%0.54%
-22.80% to -15.34%254.50%5.05%
-15.34% to -7.88%9416.94%21.98%
-7.88% to -0.41%17431.35%53.33%
-0.41% to 7.05%14125.41%78.74%
7.05% to 14.51%7513.51%92.25%
14.51% to 21.98%315.59%97.84%
21.98% to 29.44%91.62%99.46%
Greater than 29.44%30.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.37%9.54% 72.07%68.27%
±2σ -20.32%19.49% 95.50%95.45%
±3σ -30.27%29.44% 99.46%99.73%
Descriptive Statistics
Mean-0.414%
Standard Error0.422%
Median-1.091%
Mode0.000%
Standard Deviation9.951%
Sample Variance99.022%
Kurtosis0.62
Skewness0.50
Range65.597%
Minimum-26.984%
Maximum38.613%
Count555
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.364% 246 44.32% 3.707%
Negative -7.575% 302 54.41% -4.122%
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 4.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -52.78%00.00%0.00%
-52.78% to -38.40%21.08%1.08%
-38.40% to -24.01%73.78%4.86%
-24.01% to -9.63%3720.00%24.86%
-9.63% to 4.75%4825.95%50.81%
4.75% to 19.14%5328.65%79.46%
19.14% to 33.52%2915.68%95.14%
33.52% to 47.90%73.78%98.92%
47.90% to 62.28%10.54%99.46%
Greater than 62.28%10.54%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -14.42%23.93% 71.35%68.27%
±2σ -33.60%43.11% 97.30%95.45%
±3σ -52.78%62.28% 99.46%99.73%
Descriptive Statistics
Mean4.753%
Standard Error1.410%
Median4.509%
Mode-42.942%
Standard Deviation19.177%
Sample Variance367.751%
Kurtosis4.92
Skewness0.94
Range157.567%
Minimum-42.942%
Maximum114.625%
Count185
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 17.834% 104 56.22% 10.026%
Negative -12.042% 81 43.78% -5.272%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 39.62%
12 3 Years 35.30%
20 5 Years 31.58%
40 10 Years 29.56%
80 20 Years 27.83%
200 50 Years 28.69%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.16. 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 -14.46%00.00%0.00%
-14.46% to -2.51%00.00%0.00%
-2.51% to 9.45%00.00%0.00%
9.45% to 21.41%3719.89%19.89%
21.41% to 33.37%7540.32%60.22%
33.37% to 45.32%4725.27%85.48%
45.32% to 57.28%158.06%93.55%
57.28% to 69.24%31.61%95.16%
69.24% to 81.19%63.23%98.39%
Greater than 81.19%31.61%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 17.42%49.31% 83.33%68.27%
±2σ 1.48%65.25% 94.62%95.45%
±3σ -14.46%81.19% 98.39%99.73%
Descriptive Statistics
Mean33.366%
Standard Error1.169%
Median30.168%
Mode22.353%
Standard Deviation15.943%
Sample Variance254.189%
Kurtosis7.17
Skewness2.16
Range109.255%
Minimum9.793%
Maximum119.048%
Count186
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 33.366% 186 100.00% 33.366%
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 0.96. Further, an Excess Kurtosis of 2.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -56.22%00.00%0.00%
-56.22% to -42.45%10.54%0.54%
-42.45% to -28.68%31.61%2.15%
-28.68% to -14.91%3719.89%22.04%
-14.91% to -1.15%6032.26%54.30%
-1.15% to 12.62%4222.58%76.88%
12.62% to 26.39%3317.74%94.62%
26.39% to 40.16%63.23%97.85%
40.16% to 53.93%21.08%98.92%
Greater than 53.93%21.08%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -19.50%17.21% 72.58%68.27%
±2σ -37.86%35.57% 96.24%95.45%
±3σ -56.22%53.93% 98.92%99.73%
Descriptive Statistics
Mean-1.145%
Standard Error1.346%
Median-3.604%
Mode-20.000%
Standard Deviation18.357%
Sample Variance336.972%
Kurtosis2.26
Skewness0.96
Range130.583%
Minimum-53.271%
Maximum77.312%
Count186
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 15.333% 81 43.55% 6.677%
Negative -13.858% 105 56.45% -7.823%
Zero 0.000% 0 0.00% 0.000%