Markets Data Volatility Heatmap Portfolio Calculator

WMT Deep Analytical Report

Walmart Inc. | Category: Equity Mega Cap | Ann. Div Yield: 0.75% ($0.94) | Last Updated: 2026-02-22 | Data Range: 1972-08-01 → 2026-02-01 (643 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% 1.73% 1.55% 1.65% 121.10 124.91 119.23 126.87
Weekly 4.20% 3.85% 4.00% 4.06% 3.42% 3.64% 118.86 127.26 114.87 131.68
Monthly 8.48% 8.35% 8.07% 8.91% 7.11% 7.58% 114.55 132.05 106.69 141.78
Quarterly 12.83% 15.11% 12.08% 15.53% 12.31% 13.13% 108.74 139.11 96.14 157.34
Annual — — — — 24.63% 26.26% 96.14 157.34 75.15 201.28
Option Time Horizon — — — — 9.47% 10.10% 111.87 135.21 101.76 148.65
Calculation Notes: Computed at 2026-02-22T14:17 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $122.99  |  Strike (K): $125.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $4.0250 (Bid $3.9500 / Ask $4.1000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.75%  |  Binomial IV (Annual): 24.63% (CRR binomial tree, American, n=20 steps)  |  BS IV: 24.90% (European Black-Scholes)  |  Yahoo IV (Annual): 26.26% → 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
2025-12-12 $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 6.29 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 -4.10%1170.89%1.57%
-4.10% to -2.70%4403.33%4.90%
-2.70% to -1.31%153911.65%16.54%
-1.31% to 0.09%476436.06%52.60%
0.09% to 1.48%411731.16%83.76%
1.48% to 2.88%142610.79%94.55%
2.88% to 4.27%4573.46%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%3.81% 94.97%95.45%
±3σ -5.49%5.66% 98.39%99.73%
Descriptive Statistics
Mean0.087%
Standard Error0.016%
Median0.000%
Mode0.000%
Standard Deviation1.859%
Sample Variance3.456%
Kurtosis6.29
Skewness0.23
Range34.579%
Minimum-16.825%
Maximum17.754%
Count13213
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.390% 6485 49.08% 0.682%
Negative -1.307% 6011 45.49% -0.595%
Zero 0.000% 717 5.43% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 3.41%
20 1 Month 2.72%
60 1 Quarter 2.22%
250 1 Year 2.14%
750 3 Years 1.68%
1,250 5 Years 1.73%
2,500 10 Years 1.72%
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 38.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.42%00.00%0.00%
-2.42% to -1.27%00.00%0.00%
-1.27% to -0.13%00.00%0.00%
-0.13% to 1.01%210815.95%15.95%
1.01% to 2.15%628647.57%63.52%
2.15% to 3.29%284221.51%85.03%
3.29% to 4.44%11238.50%93.53%
4.44% to 5.58%4463.38%96.90%
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% 86.33%68.27%
±2σ -0.89%5.20% 96.05%95.45%
±3σ -2.42%6.72% 98.29%99.73%
Descriptive Statistics
Mean2.152%
Standard Error0.013%
Median1.752%
Mode1.887%
Standard Deviation1.523%
Sample Variance2.319%
Kurtosis38.59
Skewness3.83
Range35.003%
Minimum0.224%
Maximum35.227%
Count13214
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.152% 13214 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%1130.86%0.86%
-4.75% to -3.57%1331.01%1.86%
-3.57% to -2.39%4513.41%5.27%
-2.39% to -1.21%141710.72%16.00%
-1.21% to -0.03%402230.44%46.44%
-0.03% to 1.15%497437.64%84.08%
1.15% to 2.33%143910.89%94.97%
2.33% to 3.50%4333.28%98.24%
3.50% to 4.68%1331.01%99.25%
Greater than 4.68%990.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.60%1.54% 78.10%68.27%
±2σ -3.18%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 Deviation1.572%
Sample Variance2.470%
Kurtosis8.24
Skewness0.03
Range34.134%
Minimum-17.371%
Maximum16.763%
Count13214
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.141% 5992 45.35% 0.517%
Negative -1.173% 6203 46.94% -0.551%
Zero 0.000% 1019 7.71% 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 5.38 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 -9.03%321.15%1.72%
-9.03% to -5.88%853.05%4.77%
-5.88% to -2.73%34012.19%16.95%
-2.73% to 0.42%96134.44%51.40%
0.42% to 3.57%89932.22%83.62%
3.57% to 6.72%29710.65%94.27%
6.72% to 9.87%1043.73%97.99%
9.87% to 13.02%351.25%99.25%
Greater than 13.02%210.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.78%4.62% 76.85%68.27%
±2σ -7.98%8.82% 94.80%95.45%
±3σ -12.17%13.02% 98.67%99.73%
Descriptive Statistics
Mean0.421%
Standard Error0.079%
Median0.334%
Mode0.000%
Standard Deviation4.198%
Sample Variance17.621%
Kurtosis5.38
Skewness0.27
Range55.700%
Minimum-23.566%
Maximum32.134%
Count2790
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.118% 1505 53.94% 1.682%
Negative -2.882% 1221 43.76% -1.261%
Zero 0.000% 64 2.29% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 7.66%
12 1 Quarter 5.28%
52 1 Year 5.20%
156 3 Years 3.95%
260 5 Years 4.06%
520 10 Years 4.01%
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 22.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.99%00.00%0.00%
-5.99% to -3.10%00.00%0.00%
-3.10% to -0.22%00.00%0.00%
-0.22% to 2.67%47416.98%16.98%
2.67% to 5.55%130246.65%63.63%
5.55% to 8.44%59821.43%85.06%
8.44% to 11.32%2217.92%92.98%
11.32% to 14.21%1083.87%96.85%
14.21% to 17.09%351.25%98.10%
Greater than 17.09%531.90%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.71%9.40% 85.09%68.27%
±2σ -2.14%13.24% 95.84%95.45%
±3σ -5.99%17.09% 98.10%99.73%
Descriptive Statistics
Mean5.552%
Standard Error0.073%
Median4.475%
Mode4.762%
Standard Deviation3.846%
Sample Variance14.792%
Kurtosis22.94
Skewness3.15
Range61.286%
Minimum0.646%
Maximum61.932%
Count2791
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.552% 2791 100.00% 5.552%
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 6.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.21%150.54%0.54%
-12.21% to -9.21%321.15%1.68%
-9.21% to -6.21%973.48%5.16%
-6.21% to -3.20%32411.61%16.77%
-3.20% to -0.20%95734.29%51.06%
-0.20% to 2.80%90732.50%83.55%
2.80% to 5.80%31711.36%94.91%
5.80% to 8.81%792.83%97.74%
8.81% to 11.81%381.36%99.10%
Greater than 11.81%250.90%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.20%3.80% 77.32%68.27%
±2σ -8.21%7.81% 94.95%95.45%
±3σ -12.21%11.81% 98.57%99.73%
Descriptive Statistics
Mean-0.201%
Standard Error0.076%
Median-0.275%
Mode0.000%
Standard Deviation4.004%
Sample Variance16.031%
Kurtosis6.50
Skewness0.63
Range54.687%
Minimum-22.293%
Maximum32.394%
Count2791
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.944% 1227 43.96% 1.294%
Negative -2.795% 1493 53.49% -1.495%
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 7.96 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%8012.46%17.45%
-4.56% to 1.80%22735.36%52.80%
1.80% to 8.16%19430.22%83.02%
8.16% to 14.52%7912.31%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% 78.19%68.27%
±2σ -15.16%18.76% 96.11%95.45%
±3σ -23.64%27.24% 98.60%99.73%
Descriptive Statistics
Mean1.804%
Standard Error0.335%
Median1.381%
Mode0.000%
Standard Deviation8.480%
Sample Variance71.902%
Kurtosis7.96
Skewness0.99
Range92.183%
Minimum-33.505%
Maximum58.678%
Count642
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.559% 385 59.97% 3.933%
Negative -5.404% 253 39.41% -2.130%
Zero 0.000% 4 0.62% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 10.03%
12 1 Year 10.67%
36 3 Years 8.83%
60 5 Years 8.91%
120 10 Years 8.73%
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 3.07. Further, an Excess Kurtosis of 16.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.36%00.00%0.00%
-12.36% to -6.10%00.00%0.00%
-6.10% to 0.17%00.00%0.00%
0.17% to 6.43%11417.73%17.73%
6.43% to 12.70%28644.48%62.21%
12.70% to 18.96%14522.55%84.76%
18.96% to 25.22%578.86%93.62%
25.22% to 31.49%223.42%97.05%
31.49% to 37.75%91.40%98.44%
Greater than 37.75%101.56%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.34%21.05% 86.00%68.27%
±2σ -4.01%29.40% 96.73%95.45%
±3σ -12.36%37.75% 98.44%99.73%
Descriptive Statistics
Mean12.695%
Standard Error0.329%
Median10.672%
Mode16.667%
Standard Deviation8.353%
Sample Variance69.769%
Kurtosis16.27
Skewness3.07
Range76.144%
Minimum2.665%
Maximum78.809%
Count643
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.695% 643 100.00% 12.695%
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 5.68 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 -19.11%30.47%1.09%
-19.11% to -13.05%152.33%3.42%
-13.05% to -7.00%9414.62%18.04%
-7.00% to -0.95%21833.90%51.94%
-0.95% to 5.10%19630.48%82.43%
5.10% to 11.15%7311.35%93.78%
11.15% to 17.21%294.51%98.29%
17.21% to 23.26%50.78%99.07%
Greater than 23.26%60.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -9.02%7.12% 78.07%68.27%
±2σ -17.09%15.19% 95.65%95.45%
±3σ -25.16%23.26% 98.44%99.73%
Descriptive Statistics
Mean-0.950%
Standard Error0.318%
Median-1.276%
Mode0.000%
Standard Deviation8.070%
Sample Variance65.117%
Kurtosis5.68
Skewness0.75
Range84.969%
Minimum-36.979%
Maximum47.990%
Count643
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.016% 259 40.28% 2.423%
Negative -5.723% 379 58.94% -3.373%
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 -33.26%10.47%0.47%
-33.26% to -23.64%20.93%1.40%
-23.64% to -14.02%104.67%6.07%
-14.02% to -4.40%2813.08%19.16%
-4.40% to 5.22%7032.71%51.87%
5.22% 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 -7.60%18.05% 71.96%68.27%
±2σ -20.43%30.88% 94.86%95.45%
±3σ -33.26%43.70% 99.07%99.73%
Descriptive Statistics
Mean5.223%
Standard Error0.877%
Median4.210%
Mode-36.985%
Standard Deviation12.826%
Sample Variance164.514%
Kurtosis0.51
Skewness0.21
Range81.234%
Minimum-36.985%
Maximum44.249%
Count214
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.282% 137 64.02% 7.863%
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 14.84%
12 3 Years 16.36%
20 5 Years 15.53%
40 10 Years 15.48%
80 20 Years 14.51%
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 7.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -21.24%00.00%0.00%
-21.24% to -9.91%00.00%0.00%
-9.91% to 1.42%00.00%0.00%
1.42% to 12.74%4621.40%21.40%
12.74% to 24.07%8539.53%60.93%
24.07% 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 69.39%10.47%97.67%
Greater than 69.39%52.33%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 8.97%39.18% 85.12%68.27%
±2σ -6.14%54.28% 95.81%95.45%
±3σ -21.24%69.39% 97.67%99.73%
Descriptive Statistics
Mean24.074%
Standard Error1.030%
Median20.706%
Mode13.475%
Standard Deviation15.105%
Sample Variance228.157%
Kurtosis7.89
Skewness2.31
Range101.643%
Minimum6.855%
Maximum108.498%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 24.074% 215 100.00% 24.074%
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 2.65 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -39.39%00.00%0.00%
-39.39% to -30.33%10.47%0.47%
-30.33% to -21.28%83.72%4.19%
-21.28% to -12.22%4119.07%23.26%
-12.22% to -3.16%6027.91%51.16%
-3.16% to 5.90%6731.16%82.33%
5.90% to 14.96%2310.70%93.02%
14.96% to 24.01%115.12%98.14%
24.01% to 33.07%20.93%99.07%
Greater than 33.07%20.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.24%8.92% 73.02%68.27%
±2σ -27.31%20.99% 95.81%95.45%
±3σ -39.39%33.07% 99.07%99.73%
Descriptive Statistics
Mean-3.160%
Standard Error0.824%
Median-3.603%
Mode0.000%
Standard Deviation12.077%
Sample Variance145.844%
Kurtosis2.65
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 -10.298% 133 61.86% -6.370%
Zero 0.000% 2 0.93% 0.000%