Markets Data Volatility Heatmap Portfolio Calculator

IBM Deep Analytical Report

International Business Machines Corporation | Category: Equity Mega Cap | Ann. Div Yield: 2.62% ($6.71) | Last Updated: 2026-02-22 | Data Range: 1962-01-01 → 2026-02-01 (770 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% 1.99% 2.16% 2.29% 251.65 262.79 246.26 268.54
Weekly 3.59% 3.13% 3.54% 4.86% 4.77% 5.05% 245.19 269.71 233.78 282.88
Monthly 6.99% 6.55% 7.02% 11.22% 9.92% 10.52% 232.87 283.98 210.88 313.59
Quarterly 11.44% 11.00% 11.38% 19.97% 17.18% 18.21% 216.56 305.37 182.37 362.61
Annual — — — — 34.36% 36.43% 182.37 362.61 129.34 511.31
Option Time Horizon — — — — 13.22% 14.01% 225.32 293.50 197.42 334.97
Calculation Notes: Computed at 2026-02-22T14:17 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $257.16  |  Strike (K): $260.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $12.4250 (Bid $11.6500 / Ask $13.2000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 2.62%  |  Binomial IV (Annual): 34.36% (CRR binomial tree, American, n=20 steps)  |  BS IV: 34.45% (European Black-Scholes)  |  Yahoo IV (Annual): 36.43% → 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 -0.02. Further, an Excess Kurtosis of 10.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.72%1110.69%0.69%
-4.72% to -3.53%1651.02%1.71%
-3.53% to -2.34%4973.08%4.79%
-2.34% to -1.15%188911.71%16.50%
-1.15% to 0.04%555934.45%50.94%
0.04% to 1.24%523832.46%83.40%
1.24% to 2.43%185111.47%94.87%
2.43% to 3.62%5453.38%98.25%
3.62% to 4.82%1580.98%99.23%
Greater than 4.82%1250.77%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.55%1.64% 78.06%68.27%
±2σ -3.14%3.23% 95.18%95.45%
±3σ -4.73%4.82% 98.54%99.73%
Descriptive Statistics
Mean0.045%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.590%
Sample Variance2.529%
Kurtosis10.10
Skewness-0.02
Range36.683%
Minimum-23.519%
Maximum13.164%
Count16138
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.153% 8017 49.68% 0.573%
Negative -1.100% 7748 48.01% -0.528%
Zero 0.000% 373 2.31% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.57%
20 1 Month 3.62%
60 1 Quarter 2.80%
250 1 Year 2.66%
750 3 Years 2.03%
1,250 5 Years 1.99%
2,500 10 Years 1.91%
5,000 20 Years 1.87%
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 4.06. Further, an Excess Kurtosis of 60.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.77%00.00%0.00%
-1.77% to -0.87%00.00%0.00%
-0.87% to 0.04%00.00%0.00%
0.04% to 0.94%262716.28%16.28%
0.94% to 1.84%757546.94%63.21%
1.84% to 2.75%354621.97%85.18%
2.75% to 3.65%12877.97%93.16%
3.65% to 4.55%5903.66%96.82%
4.55% to 5.46%2421.50%98.31%
Greater than 5.46%2721.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.64%3.05% 84.70%68.27%
±2σ -0.57%4.25% 95.89%95.45%
±3σ -1.77%5.46% 98.31%99.73%
Descriptive Statistics
Mean1.844%
Standard Error0.009%
Median1.540%
Mode1.205%
Standard Deviation1.205%
Sample Variance1.451%
Kurtosis60.91
Skewness4.06
Range37.832%
Minimum0.168%
Maximum38.000%
Count16139
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.844% 16139 100.00% 1.844%
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 0.80. Further, an Excess Kurtosis of 21.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.02%1050.65%0.65%
-4.02% to -3.01%1721.07%1.72%
-3.01% to -2.01%5693.53%5.24%
-2.01% to -1.01%195412.11%17.35%
-1.01% to -0.01%502531.14%48.49%
-0.01% to 1.00%549634.05%82.54%
1.00% to 2.00%198712.31%94.85%
2.00% to 3.00%5533.43%98.28%
3.00% to 4.01%1621.00%99.28%
Greater than 4.01%1160.72%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.34%1.33% 76.71%68.27%
±2σ -2.68%2.67% 95.09%95.45%
±3σ -4.02%4.01% 98.63%99.73%
Descriptive Statistics
Mean-0.005%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.337%
Sample Variance1.787%
Kurtosis21.38
Skewness0.80
Range42.244%
Minimum-11.493%
Maximum30.751%
Count16139
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.970% 7791 48.27% 0.468%
Negative -0.975% 7828 48.50% -0.473%
Zero 0.000% 520 3.22% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.03. Further, an Excess Kurtosis of 5.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.56%220.66%0.66%
-10.56% to -7.87%431.29%1.94%
-7.87% to -5.17%1063.17%5.11%
-5.17% to -2.47%40612.13%17.24%
-2.47% to 0.22%112233.53%50.78%
0.22% to 2.92%108632.46%83.23%
2.92% to 5.61%38911.63%94.86%
5.61% to 8.31%1063.17%98.03%
8.31% to 11.00%391.17%99.19%
Greater than 11.00%270.81%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.37%3.81% 77.97%68.27%
±2σ -6.97%7.41% 94.38%95.45%
±3σ -10.56%11.00% 98.54%99.73%
Descriptive Statistics
Mean0.221%
Standard Error0.062%
Median0.156%
Mode0.000%
Standard Deviation3.594%
Sample Variance12.920%
Kurtosis5.91
Skewness0.03
Range56.798%
Minimum-30.936%
Maximum25.862%
Count3346
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.658% 1743 52.09% 1.385%
Negative -2.472% 1575 47.07% -1.164%
Zero 0.000% 28 0.84% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 9.60%
12 1 Quarter 6.40%
52 1 Year 6.40%
156 3 Years 4.96%
260 5 Years 4.86%
520 10 Years 4.64%
1,040 20 Years 4.42%
2,600 50 Years 4.84%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.25. Further, an Excess Kurtosis of 23.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.59%00.00%0.00%
-4.59% to -2.24%00.00%0.00%
-2.24% to 0.11%00.00%0.00%
0.11% to 2.46%51215.30%15.30%
2.46% to 4.81%165149.33%64.63%
4.81% to 7.16%68620.50%85.12%
7.16% to 9.51%2728.13%93.25%
9.51% to 11.86%1133.38%96.62%
11.86% to 14.21%531.58%98.21%
Greater than 14.21%601.79%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.67%7.94% 85.66%68.27%
±2σ -1.46%11.07% 95.64%95.45%
±3σ -4.59%14.21% 98.21%99.73%
Descriptive Statistics
Mean4.808%
Standard Error0.054%
Median3.995%
Mode1.805%
Standard Deviation3.133%
Sample Variance9.816%
Kurtosis23.37
Skewness3.25
Range50.773%
Minimum0.727%
Maximum51.500%
Count3347
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.808% 3347 100.00% 4.808%
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 1.16. Further, an Excess Kurtosis of 12.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.64%160.48%0.48%
-10.64% to -7.98%320.96%1.43%
-7.98% to -5.32%1043.11%4.54%
-5.32% to -2.66%42312.64%17.18%
-2.66% to -0.00%114334.15%51.33%
-0.00% to 2.65%106631.85%83.18%
2.65% to 5.31%38411.47%94.65%
5.31% to 7.97%1033.08%97.73%
7.97% to 10.63%501.49%99.22%
Greater than 10.63%260.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.55%3.54% 78.94%68.27%
±2σ -7.09%7.08% 94.83%95.45%
±3σ -10.64%10.63% 98.75%99.73%
Descriptive Statistics
Mean-0.004%
Standard Error0.061%
Median-0.126%
Mode0.000%
Standard Deviation3.544%
Sample Variance12.558%
Kurtosis12.84
Skewness1.16
Range66.918%
Minimum-20.429%
Maximum46.489%
Count3347
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.585% 1600 47.80% 1.236%
Negative -2.416% 1718 51.33% -1.240%
Zero 0.000% 29 0.87% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.16. Further, an Excess Kurtosis of 1.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -20.05%40.52%0.52%
-20.05% to -14.81%81.04%1.56%
-14.81% to -9.56%253.25%4.81%
-9.56% to -4.32%11815.34%20.16%
-4.32% to 0.93%23931.08%51.24%
0.93% to 6.17%21928.48%79.71%
6.17% to 11.41%10713.91%93.63%
11.41% to 16.66%364.68%98.31%
16.66% to 21.90%101.30%99.61%
Greater than 21.90%30.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.07%7.92% 72.95%68.27%
±2σ -13.06%14.91% 94.15%95.45%
±3σ -20.05%21.90% 99.09%99.73%
Descriptive Statistics
Mean0.925%
Standard Error0.252%
Median0.735%
Mode0.000%
Standard Deviation6.992%
Sample Variance48.885%
Kurtosis1.68
Skewness0.16
Range61.570%
Minimum-26.190%
Maximum35.380%
Count769
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.889% 408 53.06% 3.124%
Negative -4.725% 358 46.55% -2.200%
Zero 0.000% 3 0.39% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 12.44%
12 1 Year 14.04%
36 3 Years 11.53%
60 5 Years 11.22%
120 10 Years 10.73%
240 20 Years 9.74%
600 50 Years 10.66%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.44. Further, an Excess Kurtosis of 9.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.57%00.00%0.00%
-8.57% to -3.66%00.00%0.00%
-3.66% to 1.25%00.00%0.00%
1.25% to 6.17%13717.79%17.79%
6.17% to 11.08%34745.06%62.86%
11.08% to 16.00%17322.47%85.32%
16.00% to 20.91%587.53%92.86%
20.91% to 25.82%283.64%96.49%
25.82% to 30.74%111.43%97.92%
Greater than 30.74%162.08%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.53%17.63% 84.42%68.27%
±2σ -2.02%24.19% 95.58%95.45%
±3σ -8.57%30.74% 97.92%99.73%
Descriptive Statistics
Mean11.083%
Standard Error0.236%
Median9.298%
Mode4.498%
Standard Deviation6.552%
Sample Variance42.930%
Kurtosis9.28
Skewness2.44
Range54.547%
Minimum2.703%
Maximum57.250%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.083% 770 100.00% 11.083%
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 0.54. Further, an Excess Kurtosis of 2.17 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -21.21%20.26%0.26%
-21.21% to -15.95%20.26%0.52%
-15.95% to -10.69%395.06%5.58%
-10.69% to -5.42%11514.94%20.52%
-5.42% to -0.16%22228.83%49.35%
-0.16% to 5.10%24331.56%80.91%
5.10% to 10.37%10413.51%94.42%
10.37% to 15.63%253.25%97.66%
15.63% to 20.89%101.30%98.96%
Greater than 20.89%81.04%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.18%6.86% 72.99%68.27%
±2σ -14.20%13.88% 94.81%95.45%
±3σ -21.21%20.89% 98.70%99.73%
Descriptive Statistics
Mean-0.161%
Standard Error0.253%
Median-0.084%
Mode0.000%
Standard Deviation7.018%
Sample Variance49.249%
Kurtosis2.17
Skewness0.54
Range60.738%
Minimum-25.006%
Maximum35.732%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.215% 376 48.83% 2.547%
Negative -5.332% 391 50.78% -2.708%
Zero 0.000% 3 0.39% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.05. Further, an Excess Kurtosis of -0.19 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.61%00.00%0.00%
-31.61% to -23.04%31.17%1.17%
-23.04% to -14.46%145.45%6.61%
-14.46% to -5.88%4517.51%24.12%
-5.88% to 2.70%7328.40%52.53%
2.70% to 11.28%5922.96%75.49%
11.28% to 19.85%4015.56%91.05%
19.85% to 28.43%218.17%99.22%
28.43% to 37.01%20.78%100.00%
Greater than 37.01%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.74%14.13% 68.48%68.27%
±2σ -20.18%25.57% 96.11%95.45%
±3σ -31.61%37.01% 100.00%99.73%
Descriptive Statistics
Mean2.697%
Standard Error0.713%
Median1.971%
Mode1.297%
Standard Deviation11.437%
Sample Variance130.815%
Kurtosis-0.19
Skewness0.05
Range60.570%
Minimum-28.475%
Maximum32.095%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.087% 152 59.14% 5.966%
Negative -8.002% 105 40.86% -3.269%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 22.70%
12 3 Years 22.76%
20 5 Years 19.97%
40 10 Years 19.09%
80 20 Years 17.37%
200 50 Years 18.65%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.07. Further, an Excess Kurtosis of 6.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.38%00.00%0.00%
-12.38% to -4.12%00.00%0.00%
-4.12% to 4.13%00.00%0.00%
4.13% to 12.38%5119.77%19.77%
12.38% to 20.63%10841.86%61.63%
20.63% to 28.89%5822.48%84.11%
28.89% to 37.14%2710.47%94.57%
37.14% to 45.39%41.55%96.12%
45.39% to 53.64%41.55%97.67%
Greater than 53.64%62.33%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 9.63%31.64% 81.78%68.27%
±2σ -1.37%42.64% 95.74%95.45%
±3σ -12.38%53.64% 97.67%99.73%
Descriptive Statistics
Mean20.633%
Standard Error0.685%
Median17.952%
Mode12.343%
Standard Deviation11.003%
Sample Variance121.069%
Kurtosis6.07
Skewness2.07
Range68.841%
Minimum7.034%
Maximum75.875%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 20.633% 258 100.00% 20.633%
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 0.61. Further, an Excess Kurtosis of 0.65 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -34.82%00.00%0.00%
-34.82% to -26.29%00.00%0.00%
-26.29% to -17.76%145.43%5.43%
-17.76% to -9.23%5220.16%25.58%
-9.23% to -0.69%6826.36%51.94%
-0.69% to 7.84%7328.29%80.23%
7.84% to 16.37%3413.18%93.41%
16.37% to 24.90%93.49%96.90%
24.90% to 33.43%62.33%99.22%
Greater than 33.43%20.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -12.07%10.68% 70.16%68.27%
±2σ -23.45%22.06% 95.35%95.45%
±3σ -34.82%33.43% 99.22%99.73%
Descriptive Statistics
Mean-0.695%
Standard Error0.708%
Median-1.199%
Mode-18.584%
Standard Deviation11.376%
Sample Variance129.416%
Kurtosis0.65
Skewness0.61
Range65.421%
Minimum-24.113%
Maximum41.308%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.993% 118 45.74% 4.113%
Negative -8.860% 140 54.26% -4.808%
Zero 0.000% 0 0.00% 0.000%