Markets Data Volatility Heatmap Portfolio Calculator

WMT Deep Analytical Report

Walmart Inc. | Category: Equity Mega Cap | Ann. Div Yield: 0.79% ($0.94) | Last Updated: 2026-03-24 | Data Range: 1972-08-01 → 2026-03-01 (644 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 1.86% 1.52% 1.57% 1.74% 1.72% 1.79% 118.45 122.59 116.43 124.71
Weekly 4.20% 3.84% 4.00% 4.07% 3.78% 3.95% 116.03 125.14 111.72 129.97
Monthly 8.48% 8.35% 8.07% 8.91% 7.87% 8.22% 111.37 130.37 102.94 141.05
Quarterly 12.83% 15.10% 12.08% 15.58% 13.64% 14.23% 105.14 138.11 91.73 158.28
Annual — — — — 27.28% 28.47% 91.73 158.28 69.83 207.92
Option Time Horizon — — — — 10.30% 10.74% 108.71 133.57 98.08 148.05
Calculation Notes: Computed at 2026-03-23T16:31 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $120.50  |  Strike (K): $125.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.3000 (Bid $3.2000 / Ask $3.4000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.79%  |  Binomial IV (Annual): 27.28% (CRR binomial tree, American, n=20 steps)  |  BS IV: 27.37% (European Black-Scholes)  |  Yahoo IV (Annual): 28.47% → 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
2026-03-20 $0.2480
2025-12-12 $0.2350
2025-08-15 $0.2350
2025-05-09 $0.2350
2025-03-21 $0.2350
2024-12-13 $0.2080
2024-08-16 $0.2080
2024-05-09 $0.2080
2024-03-14 $0.2080
2023-12-07 $0.1900
2023-08-10 $0.1900
2023-05-04 $0.1900
2023-03-16 $0.1900
2022-12-08 $0.1867
2022-08-11 $0.1867
2022-05-05 $0.1867
2022-03-17 $0.1867
2021-12-09 $0.1833
2021-08-12 $0.1833
2021-05-06 $0.1833
2021-03-18 $0.1833
2020-12-10 $0.1800
2020-08-13 $0.1800
2020-05-07 $0.1800
2020-03-19 $0.1800
2019-12-05 $0.1767
2019-08-08 $0.1767
2019-05-09 $0.1767
2019-03-14 $0.1767
2018-12-06 $0.1733
2018-08-09 $0.1733
2018-05-10 $0.1733
2018-03-08 $0.1733
2017-12-07 $0.1700
2017-08-09 $0.1700
2017-05-10 $0.1700
2017-03-08 $0.1700
2016-12-07 $0.1667
2016-08-10 $0.1667
2016-05-11 $0.1667
2016-03-09 $0.1667
2015-12-02 $0.1633
2015-08-05 $0.1633
2015-05-06 $0.1633
2015-03-11 $0.1633
2014-12-03 $0.1600
2014-08-06 $0.1600
2014-05-07 $0.1600
2014-03-07 $0.1600
2013-12-04 $0.1567
2013-08-07 $0.1567
2013-05-08 $0.1567
2013-03-08 $0.1567
2012-12-05 $0.1327
2012-08-08 $0.1327
2012-05-09 $0.1327
2012-03-08 $0.1327
2011-12-07 $0.1217
2011-08-10 $0.1217
2011-05-11 $0.1217
2011-03-09 $0.1217
2010-12-08 $0.1010
2010-08-11 $0.1010
2010-05-12 $0.1010
2010-03-10 $0.1010
2009-12-09 $0.0910
2009-08-12 $0.0910
2009-05-13 $0.0910
2009-03-11 $0.0910
2008-12-11 $0.0793
2008-08-13 $0.0793
2008-05-14 $0.0793
2008-03-12 $0.0793
2007-12-12 $0.0733
2007-08-15 $0.0733
2007-05-16 $0.0733
2007-03-14 $0.0733
2006-12-13 $0.0560
2006-08-16 $0.0560
2006-05-17 $0.0560
2006-03-15 $0.0560
2005-12-14 $0.0500
2005-08-17 $0.0500
2005-05-18 $0.0500
2005-03-16 $0.0500
2004-12-15 $0.0433
2004-08-18 $0.0433
2004-05-19 $0.0433
2004-03-17 $0.0433
2003-12-17 $0.0300
2003-10-02 $0.0300
2003-06-18 $0.0300
2003-03-19 $0.0300
2002-12-18 $0.0250
2002-09-18 $0.0250
2002-06-19 $0.0250
2002-03-20 $0.0250
2001-12-19 $0.0233
2001-09-19 $0.0233
2001-06-20 $0.0233
2001-03-21 $0.0233
2000-12-20 $0.0200
2000-09-13 $0.0200
2000-06-14 $0.0200
2000-03-15 $0.0200
1999-12-15 $0.0167
1999-09-15 $0.0167
1999-06-16 $0.0167
1999-03-17 $0.0167
1998-12-09 $0.0130
1998-09-16 $0.0130
1998-06-17 $0.0130
1998-03-18 $0.0130
1997-12-17 $0.0113
1997-09-17 $0.0113
1997-06-18 $0.0113
1997-03-17 $0.0113
1996-12-11 $0.0087
1996-08-29 $0.0087
1996-06-13 $0.0087
1996-03-15 $0.0087
1995-11-29 $0.0083
1995-08-31 $0.0083
1995-06-08 $0.0083
1995-03-15 $0.0083
1994-11-29 $0.0070
1994-08-30 $0.0070
1994-06-07 $0.0070
1994-03-15 $0.0070
1993-11-26 $0.0053
1993-08-31 $0.0053
1993-06-08 $0.0053
1993-03-17 $0.0053
1992-12-04 $0.0043
1992-09-01 $0.0043
1992-06-09 $0.0043
1992-03-17 $0.0043
1991-12-05 $0.0035
1991-08-26 $0.0035
1991-06-11 $0.0035
1991-03-18 $0.0035
1990-12-04 $0.0029
1990-08-27 $0.0029
1990-06-11 $0.0029
1990-03-19 $0.0029
1989-12-05 $0.0023
1989-08-28 $0.0023
1989-06-12 $0.0023
1989-03-17 $0.0023
1988-12-05 $0.0017
1988-08-29 $0.0017
1988-06-13 $0.0017
1988-03-17 $0.0017
1987-12-07 $0.0013
1987-08-27 $0.0013
1987-06-15 $0.0013
1987-03-17 $0.0013
1986-12-05 $0.0009
1986-08-26 $0.0009
1986-06-16 $0.0009
1986-03-18 $0.0009
1985-12-06 $0.0007
1985-08-27 $0.0007
1985-06-17 $0.0007
1985-03-18 $0.0007
1984-12-07 $0.0005
1984-08-28 $0.0005
1984-06-15 $0.0005
1984-03-19 $0.0005
1983-12-06 $0.0004
1983-08-29 $0.0004
1983-06-14 $0.0004
1983-03-18 $0.0004
1982-12-07 $0.0002
1982-08-30 $0.0002
1982-06-15 $0.0002
1982-03-23 $0.0002
1981-10-05 $0.0011
1981-08-31 $0.0002
1981-06-16 $0.0002
1981-03-24 $0.0002
1980-12-23 $0.0003
1980-08-29 $0.0001
1980-06-16 $0.0001
1980-03-28 $0.0001
1979-12-10 $0.0001
1979-08-31 $0.0001
1979-06-25 $0.0001
1979-03-19 $0.0001
1978-12-08 $0.0001
1978-09-01 $0.0001
1978-06-19 $0.0001
1978-03-17 $0.0001
1977-11-23 $0.0001
1977-09-02 $0.0001
1977-06-20 $0.0001
1977-03-21 $0.0000
1976-12-08 $0.0000
1976-09-03 $0.0000
1976-06-21 $0.0000
1976-03-16 $0.0000
1975-12-05 $0.0000
1975-09-08 $0.0000
1975-06-23 $0.0000
1975-03-11 $0.0000
1974-09-10 $0.0000
1974-03-13 $0.0000
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.23. Further, an Excess Kurtosis of 6.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.49%900.68%0.68%
-5.49% to -4.09%1170.88%1.56%
-4.09% to -2.70%4433.35%4.91%
-2.70% to -1.31%154211.65%16.56%
-1.31% to 0.09%476936.04%52.60%
0.09% to 1.48%412331.15%83.75%
1.48% to 2.87%142710.78%94.54%
2.87% to 4.27%4603.48%98.01%
4.27% to 5.66%1401.06%99.07%
Greater than 5.66%1230.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.77%1.95% 78.04%68.27%
±2σ -3.63%3.80% 94.98%95.45%
±3σ -5.49%5.66% 98.39%99.73%
Descriptive Statistics
Mean0.087%
Standard Error0.016%
Median0.000%
Mode0.000%
Standard Deviation1.858%
Sample Variance3.454%
Kurtosis6.28
Skewness0.23
Range34.579%
Minimum-16.825%
Maximum17.754%
Count13234
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.389% 6495 49.08% 0.682%
Negative -1.307% 6022 45.50% -0.595%
Zero 0.000% 717 5.42% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.35%
20 1 Month 2.26%
60 1 Quarter 2.35%
250 1 Year 2.10%
750 3 Years 1.70%
1,250 5 Years 1.74%
2,500 10 Years 1.73%
5,000 20 Years 1.71%
12,500 50 Years 2.24%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.83. Further, an Excess Kurtosis of 38.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.41%00.00%0.00%
-2.41% to -1.27%00.00%0.00%
-1.27% to -0.13%00.00%0.00%
-0.13% to 1.01%212116.03%16.03%
1.01% to 2.15%628447.48%63.51%
2.15% to 3.29%285121.54%85.05%
3.29% to 4.43%11238.49%93.53%
4.43% to 5.58%4473.38%96.91%
5.58% to 6.72%1831.38%98.29%
Greater than 6.72%2261.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.63%3.67% 86.32%68.27%
±2σ -0.89%5.20% 96.06%95.45%
±3σ -2.41%6.72% 98.29%99.73%
Descriptive Statistics
Mean2.152%
Standard Error0.013%
Median1.752%
Mode1.887%
Standard Deviation1.522%
Sample Variance2.315%
Kurtosis38.63
Skewness3.83
Range35.003%
Minimum0.224%
Maximum35.227%
Count13235
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.152% 13235 100.00% 2.152%
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 0.03. Further, an Excess Kurtosis of 8.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.75%1130.85%0.85%
-4.75% to -3.57%1331.00%1.86%
-3.57% to -2.39%4533.42%5.28%
-2.39% to -1.21%142110.74%16.02%
-1.21% to -0.03%402730.43%46.45%
-0.03% to 1.15%497737.60%84.05%
1.15% to 2.32%144510.92%94.97%
2.32% to 3.50%4333.27%98.24%
3.50% to 4.68%1341.01%99.25%
Greater than 4.68%990.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.60%1.54% 78.07%68.27%
±2σ -3.17%3.11% 95.07%95.45%
±3σ -4.75%4.68% 98.40%99.73%
Descriptive Statistics
Mean-0.033%
Standard Error0.014%
Median0.000%
Mode0.000%
Standard Deviation1.571%
Sample Variance2.469%
Kurtosis8.24
Skewness0.03
Range34.134%
Minimum-17.371%
Maximum16.763%
Count13235
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.141% 6002 45.35% 0.517%
Negative -1.173% 6214 46.95% -0.551%
Zero 0.000% 1019 7.70% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.27. Further, an Excess Kurtosis of 5.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.17%160.57%0.57%
-12.17% to -9.02%321.15%1.72%
-9.02% to -5.87%863.08%4.80%
-5.87% to -2.73%34012.17%16.96%
-2.73% to 0.42%96234.43%51.40%
0.42% to 3.56%90132.25%83.64%
3.56% to 6.71%29710.63%94.27%
6.71% to 9.86%1043.72%98.00%
9.86% to 13.00%351.25%99.25%
Greater than 13.00%210.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.78%4.61% 76.81%68.27%
±2σ -7.97%8.81% 94.81%95.45%
±3σ -12.17%13.00% 98.68%99.73%
Descriptive Statistics
Mean0.419%
Standard Error0.079%
Median0.334%
Mode0.000%
Standard Deviation4.195%
Sample Variance17.595%
Kurtosis5.39
Skewness0.27
Range55.700%
Minimum-23.566%
Maximum32.134%
Count2794
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.115% 1507 53.94% 1.680%
Negative -2.881% 1223 43.77% -1.261%
Zero 0.000% 64 2.29% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 5.04%
12 1 Quarter 5.72%
52 1 Year 5.06%
156 3 Years 3.99%
260 5 Years 4.07%
520 10 Years 4.02%
1,040 20 Years 3.87%
2,600 50 Years 5.26%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.15. Further, an Excess Kurtosis of 22.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.98%00.00%0.00%
-5.98% to -3.10%00.00%0.00%
-3.10% to -0.21%00.00%0.00%
-0.21% to 2.67%47416.96%16.96%
2.67% to 5.55%130546.69%63.65%
5.55% to 8.43%59921.43%85.08%
8.43% to 11.32%2217.91%92.99%
11.32% to 14.20%1083.86%96.85%
14.20% to 17.08%341.22%98.07%
Greater than 17.08%541.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.71%9.39% 85.12%68.27%
±2σ -2.14%13.24% 95.85%95.45%
±3σ -5.98%17.08% 98.07%99.73%
Descriptive Statistics
Mean5.551%
Standard Error0.073%
Median4.475%
Mode4.762%
Standard Deviation3.844%
Sample Variance14.775%
Kurtosis22.96
Skewness3.15
Range61.286%
Minimum0.646%
Maximum61.932%
Count2795
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.551% 2795 100.00% 5.551%
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 0.63. Further, an Excess Kurtosis of 6.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.20%150.54%0.54%
-12.20% to -9.20%321.14%1.68%
-9.20% to -6.20%983.51%5.19%
-6.20% to -3.20%32311.56%16.74%
-3.20% to -0.20%95934.31%51.06%
-0.20% to 2.80%90832.49%83.54%
2.80% to 5.80%31711.34%94.88%
5.80% to 8.80%802.86%97.75%
8.80% to 11.80%381.36%99.11%
Greater than 11.80%250.89%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.20%3.80% 77.25%68.27%
±2σ -8.20%7.80% 94.99%95.45%
±3σ -12.20%11.80% 98.57%99.73%
Descriptive Statistics
Mean-0.200%
Standard Error0.076%
Median-0.275%
Mode0.000%
Standard Deviation4.001%
Sample Variance16.007%
Kurtosis6.51
Skewness0.63
Range54.687%
Minimum-22.293%
Maximum32.394%
Count2795
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.943% 1229 43.97% 1.294%
Negative -2.793% 1495 53.49% -1.494%
Zero 0.000% 71 2.54% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.99. Further, an Excess Kurtosis of 7.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -23.64%40.62%0.62%
-23.64% to -17.28%30.47%1.09%
-17.28% to -10.92%253.89%4.98%
-10.92% to -4.56%8112.60%17.57%
-4.56% to 1.80%22635.15%52.72%
1.80% to 8.16%19530.33%83.05%
8.16% to 14.52%7912.29%95.33%
14.52% to 20.88%213.27%98.60%
20.88% to 27.24%40.62%99.22%
Greater than 27.24%50.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.68%10.28% 78.23%68.27%
±2σ -15.16%18.76% 96.11%95.45%
±3σ -23.64%27.24% 98.60%99.73%
Descriptive Statistics
Mean1.798%
Standard Error0.334%
Median1.374%
Mode0.000%
Standard Deviation8.480%
Sample Variance71.917%
Kurtosis7.94
Skewness0.99
Range92.183%
Minimum-33.505%
Maximum58.678%
Count643
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.569% 385 59.88% 3.933%
Negative -5.405% 254 39.50% -2.135%
Zero 0.000% 4 0.62% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 10.70%
12 1 Year 10.04%
36 3 Years 8.82%
60 5 Years 8.91%
120 10 Years 8.75%
240 20 Years 8.23%
600 50 Years 11.21%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.08. Further, an Excess Kurtosis of 16.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.35%00.00%0.00%
-12.35% to -6.09%00.00%0.00%
-6.09% to 0.17%00.00%0.00%
0.17% to 6.43%11417.70%17.70%
6.43% to 12.69%28744.57%62.27%
12.69% to 18.95%14522.52%84.78%
18.95% to 25.21%578.85%93.63%
25.21% to 31.47%223.42%97.05%
31.47% to 37.73%91.40%98.45%
Greater than 37.73%101.55%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.34%21.04% 86.02%68.27%
±2σ -4.00%29.38% 96.74%95.45%
±3σ -12.35%37.73% 98.45%99.73%
Descriptive Statistics
Mean12.690%
Standard Error0.329%
Median10.671%
Mode16.667%
Standard Deviation8.347%
Sample Variance69.680%
Kurtosis16.29
Skewness3.08
Range76.144%
Minimum2.665%
Maximum78.809%
Count644
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.690% 644 100.00% 12.690%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.75. Further, an Excess Kurtosis of 5.66 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.16%40.62%0.62%
-25.16% to -19.10%30.47%1.09%
-19.10% to -13.05%152.33%3.42%
-13.05% to -7.00%9414.60%18.01%
-7.00% to -0.94%21934.01%52.02%
-0.94% to 5.11%19530.28%82.30%
5.11% to 11.16%7411.49%93.79%
11.16% to 17.21%294.50%98.29%
17.21% to 23.27%50.78%99.07%
Greater than 23.27%60.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -9.02%7.12% 77.95%68.27%
±2σ -17.09%15.20% 95.65%95.45%
±3σ -25.16%23.27% 98.45%99.73%
Descriptive Statistics
Mean-0.945%
Standard Error0.318%
Median-1.267%
Mode0.000%
Standard Deviation8.070%
Sample Variance65.129%
Kurtosis5.66
Skewness0.75
Range84.969%
Minimum-36.979%
Maximum47.990%
Count644
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.015% 260 40.37% 2.428%
Negative -5.733% 379 58.85% -3.374%
Zero 0.000% 5 0.78% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.21. Further, an Excess Kurtosis of 0.51 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -33.27%10.47%0.47%
-33.27% to -23.65%20.93%1.40%
-23.65% to -14.03%104.67%6.07%
-14.03% to -4.41%2813.08%19.16%
-4.41% to 5.21%7032.71%51.87%
5.21% to 14.84%5425.23%77.10%
14.84% to 24.46%3315.42%92.52%
24.46% to 34.08%136.07%98.60%
34.08% to 43.70%20.93%99.53%
Greater than 43.70%10.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.62%18.04% 71.96%68.27%
±2σ -20.44%30.87% 94.86%95.45%
±3σ -33.27%43.70% 99.07%99.73%
Descriptive Statistics
Mean5.214%
Standard Error0.877%
Median4.210%
Mode-36.985%
Standard Deviation12.829%
Sample Variance164.572%
Kurtosis0.51
Skewness0.21
Range81.234%
Minimum-36.985%
Maximum44.249%
Count214
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.267% 137 64.02% 7.853%
Negative -7.336% 77 35.98% -2.640%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 15.06%
12 3 Years 16.43%
20 5 Years 15.58%
40 10 Years 15.51%
80 20 Years 14.52%
200 50 Years 20.35%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.31. Further, an Excess Kurtosis of 7.90 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -21.23%00.00%0.00%
-21.23% to -9.90%00.00%0.00%
-9.90% to 1.43%00.00%0.00%
1.43% to 12.75%4621.40%21.40%
12.75% to 24.08%8539.53%60.93%
24.08% to 35.40%5626.05%86.98%
35.40% to 46.73%136.05%93.02%
46.73% to 58.06%94.19%97.21%
58.06% to 69.38%10.47%97.67%
Greater than 69.38%52.33%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 8.98%39.18% 85.12%68.27%
±2σ -6.13%54.28% 95.81%95.45%
±3σ -21.23%69.38% 97.67%99.73%
Descriptive Statistics
Mean24.078%
Standard Error1.030%
Median20.706%
Mode13.475%
Standard Deviation15.102%
Sample Variance228.061%
Kurtosis7.90
Skewness2.31
Range101.643%
Minimum6.855%
Maximum108.498%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 24.078% 215 100.00% 24.078%
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 0.82. Further, an Excess Kurtosis of 2.64 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -39.38%00.00%0.00%
-39.38% to -30.33%10.47%0.47%
-30.33% to -21.27%83.72%4.19%
-21.27% to -12.21%4219.53%23.72%
-12.21% to -3.15%5927.44%51.16%
-3.15% to 5.91%6731.16%82.33%
5.91% to 14.97%2310.70%93.02%
14.97% to 24.02%115.12%98.14%
24.02% to 33.08%20.93%99.07%
Greater than 33.08%20.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.23%8.93% 73.02%68.27%
±2σ -27.31%21.00% 95.81%95.45%
±3σ -39.38%33.08% 99.07%99.73%
Descriptive Statistics
Mean-3.151%
Standard Error0.824%
Median-3.603%
Mode0.000%
Standard Deviation12.078%
Sample Variance145.868%
Kurtosis2.64
Skewness0.82
Range87.727%
Minimum-30.573%
Maximum57.154%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.627% 80 37.21% 3.210%
Negative -10.283% 133 61.86% -6.361%
Zero 0.000% 2 0.93% 0.000%