Markets Data Volatility Heatmap Portfolio Calculator

IBM Deep Analytical Report

International Business Machines Corporation | Category: Equity Mega Cap | Ann. Div Yield: 2.78% ($6.71) | Last Updated: 2026-03-24 | Data Range: 1962-01-01 → 2026-03-01 (771 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 1.59% 1.21% 1.34% 2.02% 2.69% 2.80% 240.26 253.55 233.88 260.47
Weekly 3.60% 3.14% 3.56% 4.95% 5.93% 6.15% 232.61 261.89 219.23 277.88
Monthly 7.01% 6.63% 7.05% 11.33% 12.34% 12.81% 218.17 279.23 192.84 315.89
Quarterly 11.46% 11.09% 11.41% 20.50% 21.37% 22.19% 199.33 305.62 160.97 378.43
Annual — — — — 42.74% 44.37% 160.97 378.43 104.99 580.24
Option Time Horizon — — — — 16.13% 16.75% 210.04 290.02 178.75 340.79
Calculation Notes: Computed at 2026-03-23T16:32 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $246.82  |  Strike (K): $250.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $14.5500 (Bid $13.7500 / Ask $15.3500)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 2.78%  |  Binomial IV (Annual): 42.74% (CRR binomial tree, American, n=20 steps)  |  BS IV: 42.82% (European Black-Scholes)  |  Yahoo IV (Annual): 44.37% → 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
2026-02-10 $1.6800
2025-11-10 $1.6800
2025-08-08 $1.6800
2025-05-09 $1.6800
2025-02-10 $1.6700
2024-11-12 $1.6700
2024-08-09 $1.6700
2024-05-09 $1.6700
2024-02-08 $1.6600
2023-11-09 $1.6600
2023-08-09 $1.6600
2023-05-09 $1.6600
2023-02-09 $1.6500
2022-11-09 $1.6500
2022-08-09 $1.6500
2022-05-09 $1.6500
2022-02-10 $1.6400
2021-11-09 $1.6400
2021-08-09 $1.5679
2021-05-07 $1.5679
2021-02-09 $1.5583
2020-11-09 $1.5583
2020-08-07 $1.5583
2020-05-07 $1.5583
2020-02-07 $1.5488
2019-11-07 $1.5488
2019-08-08 $1.5488
2019-05-09 $1.5488
2019-02-07 $1.5010
2018-11-08 $1.5010
2018-08-09 $1.5010
2018-05-09 $1.5010
2018-02-08 $1.4340
2017-11-09 $1.4340
2017-08-08 $1.4340
2017-05-08 $1.4340
2017-02-08 $1.3384
2016-11-08 $1.3384
2016-08-08 $1.3384
2016-05-06 $1.3384
2016-02-08 $1.2428
2015-11-06 $1.2428
2015-08-06 $1.2428
2015-05-06 $1.2428
2015-02-06 $1.0516
2014-11-06 $1.0516
2014-08-06 $1.0516
2014-05-07 $1.0516
2014-02-06 $0.9082
2013-11-06 $0.9082
2013-08-07 $0.9082
2013-05-08 $0.9082
2013-02-06 $0.8126
2012-11-07 $0.8126
2012-08-08 $0.8126
2012-05-08 $0.8126
2012-02-08 $0.7170
2011-11-08 $0.7170
2011-08-08 $0.7170
2011-05-06 $0.7170
2011-02-08 $0.6214
2010-11-08 $0.6214
2010-08-06 $0.6214
2010-05-06 $0.6214
2010-02-08 $0.5258
2009-11-06 $0.5258
2009-08-06 $0.5258
2009-05-06 $0.5258
2009-02-06 $0.4780
2008-11-06 $0.4780
2008-08-06 $0.4780
2008-05-07 $0.4780
2008-02-06 $0.3824
2007-11-07 $0.3824
2007-08-08 $0.3824
2007-05-08 $0.3824
2007-02-07 $0.2868
2006-11-08 $0.2868
2006-08-08 $0.2868
2006-05-08 $0.2868
2006-02-08 $0.1912
2005-11-08 $0.1912
2005-08-08 $0.1912
2005-05-06 $0.1912
2005-02-08 $0.1721
2004-11-08 $0.1721
2004-08-06 $0.1721
2004-05-06 $0.1721
2004-02-06 $0.1530
2003-11-06 $0.1530
2003-08-06 $0.1530
2003-05-07 $0.1530
2003-02-06 $0.1434
2002-11-06 $0.1434
2002-08-07 $0.1434
2002-05-08 $0.1434
2002-02-06 $0.1338
2001-11-07 $0.1338
2001-08-08 $0.1338
2001-05-08 $0.1338
2001-02-07 $0.1243
2000-11-08 $0.1243
2000-08-08 $0.1243
2000-05-08 $0.1243
2000-02-08 $0.1147
1999-11-08 $0.1147
1999-08-06 $0.1147
1999-05-06 $0.1147
1999-02-08 $0.1052
1998-11-06 $0.1052
1998-08-06 $0.1052
1998-05-06 $0.1052
1998-02-06 $0.0956
1997-11-06 $0.0956
1997-08-07 $0.0956
1997-05-07 $0.0956
1997-02-06 $0.0837
1996-11-06 $0.0837
1996-08-07 $0.0837
1996-05-08 $0.0837
1996-02-07 $0.0598
1995-11-08 $0.0598
1995-08-08 $0.0598
1995-05-04 $0.0598
1995-02-06 $0.0598
1994-11-04 $0.0598
1994-08-04 $0.0598
1994-05-05 $0.0598
1994-02-04 $0.0598
1993-11-04 $0.0598
1993-08-05 $0.0598
1993-05-06 $0.1291
1993-02-04 $0.1291
1992-11-05 $0.2892
1992-08-06 $0.2892
1992-05-07 $0.2892
1992-02-06 $0.2892
1991-11-04 $0.2892
1991-08-06 $0.2892
1991-05-06 $0.2892
1991-02-04 $0.2892
1990-11-05 $0.2892
1990-08-06 $0.2892
1990-05-04 $0.2892
1990-02-05 $0.2892
1989-11-02 $0.2892
1989-08-03 $0.2892
1989-05-04 $0.2892
1989-02-02 $0.2629
1988-11-04 $0.2629
1988-08-04 $0.2629
1988-05-05 $0.2629
1988-02-04 $0.2629
1987-11-05 $0.2629
1987-08-06 $0.2629
1987-05-07 $0.2629
1987-02-05 $0.2629
1986-11-05 $0.2629
1986-08-07 $0.2629
1986-05-08 $0.2629
1986-02-07 $0.2629
1985-11-06 $0.2629
1985-08-08 $0.2629
1985-05-03 $0.2629
1985-02-06 $0.2629
1984-10-31 $0.2629
1984-08-08 $0.2629
1984-05-04 $0.2271
1984-02-03 $0.2271
1983-11-02 $0.2271
1983-08-04 $0.2271
1983-05-05 $0.2271
1983-02-03 $0.2055
1982-11-04 $0.2055
1982-08-05 $0.2055
1982-05-06 $0.2055
1982-02-04 $0.2055
1981-11-04 $0.2055
1981-08-06 $0.2055
1981-05-07 $0.2055
1981-02-05 $0.2055
1980-11-05 $0.2055
1980-08-07 $0.2055
1980-05-08 $0.2055
1980-02-06 $0.2055
1979-11-07 $0.2055
1979-08-08 $0.2055
1979-05-04 $0.2055
1979-02-07 $0.2055
1978-11-01 $0.1721
1978-08-03 $0.1721
1978-05-04 $0.1721
1978-02-03 $0.1721
1977-11-02 $0.1494
1977-08-04 $0.1494
1977-05-05 $0.1494
1977-02-03 $0.1494
1976-11-04 $0.1344
1976-08-05 $0.1344
1976-05-06 $0.1046
1976-02-05 $0.1046
1975-11-05 $0.1046
1975-08-07 $0.1046
1975-05-08 $0.0896
1975-02-06 $0.0896
1974-11-06 $0.0896
1974-08-08 $0.0896
1974-05-08 $0.0765
1974-02-06 $0.0765
1973-11-08 $0.0669
1973-08-08 $0.0669
1973-05-04 $0.0669
1973-02-07 $0.0669
1972-11-08 $0.0645
1972-08-03 $0.0645
1972-05-04 $0.0645
1972-02-03 $0.0645
1971-11-05 $0.0621
1971-08-06 $0.0621
1971-05-07 $0.0621
1971-02-05 $0.0621
1970-10-30 $0.0574
1970-07-31 $0.0574
1970-05-01 $0.0574
1969-11-06 $0.0478
1969-08-01 $0.0478
1969-05-02 $0.0382
1969-02-06 $0.0382
1968-08-02 $0.0311
1968-05-03 $0.0311
1968-02-05 $0.0311
1967-11-03 $0.0263
1967-08-07 $0.0026
1967-05-01 $0.0026
1967-02-06 $0.0026
1966-11-03 $0.0026
1966-08-09 $0.0026
1966-05-24 $0.0026
1966-02-08 $0.0024
1965-11-01 $0.0024
1965-08-03 $0.0024
1965-05-04 $0.0024
1965-02-02 $0.0024
1964-11-02 $0.0020
1964-08-04 $0.0020
1964-05-25 $0.0020
1964-02-04 $0.0016
1963-11-04 $0.0016
1963-08-06 $0.0013
1963-05-07 $0.0013
1963-02-05 $0.0013
1962-11-05 $0.0010
1962-08-07 $0.0010
1962-05-08 $0.0010
1962-02-06 $0.0010
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.05. Further, an Excess Kurtosis of 10.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.74%1100.68%0.68%
-4.74% to -3.54%1621.00%1.68%
-3.54% to -2.35%4983.08%4.77%
-2.35% to -1.15%189111.70%16.47%
-1.15% to 0.04%557134.48%50.94%
0.04% to 1.24%524432.45%83.40%
1.24% to 2.44%185411.47%94.87%
2.44% to 3.63%5473.39%98.25%
3.63% to 4.83%1580.98%99.23%
Greater than 4.83%1240.77%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.55%1.64% 78.14%68.27%
±2σ -3.14%3.23% 95.20%95.45%
±3σ -4.74%4.83% 98.55%99.73%
Descriptive Statistics
Mean0.045%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.594%
Sample Variance2.541%
Kurtosis10.25
Skewness-0.05
Range36.683%
Minimum-23.519%
Maximum13.164%
Count16159
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.155% 8027 49.67% 0.574%
Negative -1.102% 7759 48.02% -0.529%
Zero 0.000% 373 2.31% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.99%
20 1 Month 3.23%
60 1 Quarter 3.37%
250 1 Year 2.72%
750 3 Years 2.09%
1,250 5 Years 2.02%
2,500 10 Years 1.93%
5,000 20 Years 1.88%
12,500 50 Years 2.05%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.09. Further, an Excess Kurtosis of 60.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.78%00.00%0.00%
-1.78% to -0.88%00.00%0.00%
-0.88% to 0.03%00.00%0.00%
0.03% to 0.94%261716.19%16.19%
0.94% to 1.85%759847.02%63.21%
1.85% to 2.75%355522.00%85.21%
2.75% to 3.66%12917.99%93.20%
3.66% to 4.57%5883.64%96.84%
4.57% to 5.48%2391.48%98.32%
Greater than 5.48%2721.68%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.64%3.06% 84.76%68.27%
±2σ -0.57%4.27% 95.90%95.45%
±3σ -1.78%5.48% 98.32%99.73%
Descriptive Statistics
Mean1.846%
Standard Error0.010%
Median1.542%
Mode1.205%
Standard Deviation1.210%
Sample Variance1.464%
Kurtosis60.71
Skewness4.09
Range37.832%
Minimum0.168%
Maximum38.000%
Count16160
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.846% 16160 100.00% 1.846%
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 0.85. Further, an Excess Kurtosis of 21.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.03%1050.65%0.65%
-4.03% to -3.02%1681.04%1.69%
-3.02% to -2.02%5713.53%5.22%
-2.02% to -1.01%195112.07%17.30%
-1.01% to -0.01%504431.21%48.51%
-0.01% to 1.00%551334.12%82.62%
1.00% to 2.01%197712.23%94.86%
2.01% to 3.01%5543.43%98.29%
3.01% to 4.02%1631.01%99.29%
Greater than 4.02%1140.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.35%1.34% 76.82%68.27%
±2σ -2.69%2.68% 95.11%95.45%
±3σ -4.03%4.02% 98.64%99.73%
Descriptive Statistics
Mean-0.005%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.341%
Sample Variance1.799%
Kurtosis21.72
Skewness0.85
Range42.244%
Minimum-11.493%
Maximum30.751%
Count16160
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.971% 7798 48.26% 0.469%
Negative -0.976% 7842 48.53% -0.474%
Zero 0.000% 520 3.22% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.01. Further, an Excess Kurtosis of 5.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.60%230.69%0.69%
-10.60% to -7.89%411.22%1.91%
-7.89% to -5.19%1073.19%5.10%
-5.19% to -2.48%40212.00%17.10%
-2.48% to 0.22%112633.61%50.72%
0.22% to 2.92%109432.66%83.37%
2.92% to 5.63%38411.46%94.84%
5.63% to 8.33%1073.19%98.03%
8.33% to 11.04%401.19%99.22%
Greater than 11.04%260.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.38%3.83% 78.00%68.27%
±2σ -6.99%7.43% 94.42%95.45%
±3σ -10.59%11.04% 98.54%99.73%
Descriptive Statistics
Mean0.220%
Standard Error0.062%
Median0.156%
Mode0.000%
Standard Deviation3.605%
Sample Variance12.996%
Kurtosis5.89
Skewness0.01
Range56.798%
Minimum-30.936%
Maximum25.862%
Count3350
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.662% 1745 52.09% 1.387%
Negative -2.479% 1577 47.08% -1.167%
Zero 0.000% 28 0.84% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 7.95%
12 1 Quarter 8.74%
52 1 Year 6.73%
156 3 Years 5.14%
260 5 Years 4.95%
520 10 Years 4.69%
1,040 20 Years 4.45%
2,600 50 Years 4.85%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.23. Further, an Excess Kurtosis of 23.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.61%00.00%0.00%
-4.61% to -2.25%00.00%0.00%
-2.25% to 0.10%00.00%0.00%
0.10% to 2.46%51415.34%15.34%
2.46% to 4.82%165249.30%64.64%
4.82% to 7.17%68720.50%85.14%
7.17% to 9.53%2718.09%93.23%
9.53% to 11.89%1153.43%96.66%
11.89% to 14.25%511.52%98.18%
Greater than 14.25%611.82%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.67%7.96% 85.59%68.27%
±2σ -1.47%11.10% 95.64%95.45%
±3σ -4.61%14.25% 98.18%99.73%
Descriptive Statistics
Mean4.817%
Standard Error0.054%
Median3.999%
Mode1.805%
Standard Deviation3.143%
Sample Variance9.881%
Kurtosis23.07
Skewness3.23
Range50.773%
Minimum0.727%
Maximum51.500%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.817% 3351 100.00% 4.817%
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 1.17. Further, an Excess Kurtosis of 12.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.67%150.45%0.45%
-10.67% to -8.00%330.98%1.43%
-8.00% to -5.34%1023.04%4.48%
-5.34% to -2.67%42412.65%17.13%
-2.67% to -0.00%114634.20%51.33%
-0.00% to 2.67%106931.90%83.23%
2.67% to 5.33%38711.55%94.78%
5.33% to 8.00%992.95%97.73%
8.00% to 10.67%491.46%99.19%
Greater than 10.67%270.81%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.56%3.55% 79.05%68.27%
±2σ -7.11%7.11% 94.81%95.45%
±3σ -10.67%10.67% 98.75%99.73%
Descriptive Statistics
Mean-0.002%
Standard Error0.061%
Median-0.126%
Mode0.000%
Standard Deviation3.556%
Sample Variance12.642%
Kurtosis12.74
Skewness1.17
Range66.918%
Minimum-20.429%
Maximum46.489%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.593% 1602 47.81% 1.240%
Negative -2.420% 1720 51.33% -1.242%
Zero 0.000% 29 0.86% 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 1.73 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -20.10%50.65%0.65%
-20.10% to -14.85%70.91%1.56%
-14.85% to -9.59%253.25%4.81%
-9.59% to -4.34%11715.19%20.00%
-4.34% to 0.92%23931.04%51.04%
0.92% to 6.18%22228.83%79.87%
6.18% to 11.43%10713.90%93.77%
11.43% to 16.69%354.55%98.31%
16.69% to 21.94%101.30%99.61%
Greater than 21.94%30.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.09%7.93% 73.25%68.27%
±2σ -13.10%14.94% 94.16%95.45%
±3σ -20.10%21.94% 98.96%99.73%
Descriptive Statistics
Mean0.920%
Standard Error0.253%
Median0.752%
Mode0.000%
Standard Deviation7.008%
Sample Variance49.107%
Kurtosis1.73
Skewness0.13
Range61.570%
Minimum-26.190%
Maximum35.380%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.882% 409 53.12% 3.124%
Negative -4.741% 358 46.49% -2.204%
Zero 0.000% 3 0.39% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 17.62%
12 1 Year 14.92%
36 3 Years 11.93%
60 5 Years 11.33%
120 10 Years 10.77%
240 20 Years 9.80%
600 50 Years 10.69%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.47. Further, an Excess Kurtosis of 9.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.79%00.00%0.00%
-8.79% to -3.81%00.00%0.00%
-3.81% to 1.16%00.00%0.00%
1.16% to 6.13%13517.51%17.51%
6.13% to 11.11%34945.27%62.78%
11.11% to 16.08%17722.96%85.73%
16.08% to 21.05%577.39%93.13%
21.05% to 26.03%253.24%96.37%
26.03% to 31.00%121.56%97.92%
Greater than 31.00%162.08%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.47%17.74% 85.08%68.27%
±2σ -2.16%24.37% 95.59%95.45%
±3σ -8.79%31.00% 97.92%99.73%
Descriptive Statistics
Mean11.107%
Standard Error0.239%
Median9.299%
Mode4.498%
Standard Deviation6.632%
Sample Variance43.987%
Kurtosis9.36
Skewness2.47
Range54.547%
Minimum2.703%
Maximum57.250%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.107% 771 100.00% 11.107%
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 0.59. 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 -21.31%20.26%0.26%
-21.31% to -16.02%20.26%0.52%
-16.02% to -10.73%395.06%5.58%
-10.73% to -5.45%11514.92%20.49%
-5.45% to -0.16%22429.05%49.55%
-0.16% to 5.13%24331.52%81.06%
5.13% to 10.42%10313.36%94.42%
10.42% to 15.71%263.37%97.80%
15.71% to 21.00%81.04%98.83%
Greater than 21.00%91.17%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.21%6.90% 73.15%68.27%
±2σ -14.26%13.95% 94.94%95.45%
±3σ -21.31%21.00% 98.57%99.73%
Descriptive Statistics
Mean-0.156%
Standard Error0.254%
Median-0.093%
Mode0.000%
Standard Deviation7.052%
Sample Variance49.736%
Kurtosis2.31
Skewness0.59
Range60.738%
Minimum-25.006%
Maximum35.732%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.237% 376 48.77% 2.554%
Negative -5.330% 392 50.84% -2.710%
Zero 0.000% 3 0.39% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.04. Further, an Excess Kurtosis of -0.19 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.70%00.00%0.00%
-31.70% to -23.10%31.17%1.17%
-23.10% to -14.51%145.45%6.61%
-14.51% to -5.91%4417.12%23.74%
-5.91% to 2.68%7428.79%52.53%
2.68% to 11.28%5922.96%75.49%
11.28% to 19.87%4015.56%91.05%
19.87% to 28.47%218.17%99.22%
28.47% to 37.06%20.78%100.00%
Greater than 37.06%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.78%14.14% 68.48%68.27%
±2σ -20.24%25.60% 96.50%95.45%
±3σ -31.70%37.06% 100.00%99.73%
Descriptive Statistics
Mean2.684%
Standard Error0.715%
Median1.971%
Mode1.297%
Standard Deviation11.460%
Sample Variance131.329%
Kurtosis-0.19
Skewness0.04
Range60.570%
Minimum-28.475%
Maximum32.095%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.087% 152 59.14% 5.966%
Negative -8.033% 105 40.86% -3.282%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 25.37%
12 3 Years 23.65%
20 5 Years 20.50%
40 10 Years 19.36%
80 20 Years 17.50%
200 50 Years 18.70%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.03. Further, an Excess Kurtosis of 5.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.57%00.00%0.00%
-12.57% to -4.25%00.00%0.00%
-4.25% to 4.07%00.00%0.00%
4.07% to 12.39%5119.77%19.77%
12.39% to 20.70%10942.25%62.02%
20.70% to 29.02%5822.48%84.50%
29.02% to 37.34%259.69%94.19%
37.34% to 45.66%51.94%96.12%
45.66% to 53.98%41.55%97.67%
Greater than 53.98%62.33%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 9.61%31.80% 81.78%68.27%
±2σ -1.48%42.89% 95.74%95.45%
±3σ -12.57%53.98% 97.67%99.73%
Descriptive Statistics
Mean20.704%
Standard Error0.691%
Median17.953%
Mode12.343%
Standard Deviation11.091%
Sample Variance123.020%
Kurtosis5.80
Skewness2.03
Range68.841%
Minimum7.034%
Maximum75.875%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 20.704% 258 100.00% 20.704%
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 0.62. Further, an Excess Kurtosis of 0.65 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -34.92%00.00%0.00%
-34.92% to -26.36%00.00%0.00%
-26.36% to -17.80%145.43%5.43%
-17.80% to -9.24%5220.16%25.58%
-9.24% to -0.68%6826.36%51.94%
-0.68% to 7.88%7328.29%80.23%
7.88% to 16.45%3413.18%93.41%
16.45% to 25.01%93.49%96.90%
25.01% to 33.57%62.33%99.22%
Greater than 33.57%20.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -12.09%10.74% 70.16%68.27%
±2σ -23.50%22.15% 94.96%95.45%
±3σ -34.92%33.57% 99.22%99.73%
Descriptive Statistics
Mean-0.676%
Standard Error0.711%
Median-1.199%
Mode-18.584%
Standard Deviation11.414%
Sample Variance130.272%
Kurtosis0.65
Skewness0.62
Range65.421%
Minimum-24.113%
Maximum41.308%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 9.035% 118 45.74% 4.132%
Negative -8.860% 140 54.26% -4.808%
Zero 0.000% 0 0.00% 0.000%