Markets Data Volatility Heatmap Portfolio Calculator

CAT Deep Analytical Report

Caterpillar Inc. | Category: Equity Mega Cap | Ann. Div Yield: 0.78% ($5.94) | 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 1.86% 1.41% 1.57% 2.54% 2.44% 2.50% 741.43 778.50 723.57 797.72
Weekly 4.35% 3.58% 4.29% 6.14% 5.37% 5.51% 720.02 801.65 682.39 845.86
Monthly 8.47% 7.52% 8.54% 14.00% 11.18% 11.47% 679.40 849.58 607.56 950.04
Quarterly 14.02% 12.26% 14.03% 26.60% 19.36% 19.87% 626.03 922.01 515.85 1118.95
Annual — — — — 38.72% 39.75% 515.85 1118.95 350.25 1648.00
Option Time Horizon — — — — 14.89% 15.29% 654.62 881.74 564.05 1023.33
Calculation Notes: Computed at 2026-02-22T14:17 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $759.74  |  Strike (K): $760.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $45.9500 (Bid $45.3000 / Ask $46.6000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.78%  |  Binomial IV (Annual): 38.72% (CRR binomial tree, American, n=20 steps)  |  BS IV: 38.25% (European Black-Scholes)  |  Yahoo IV (Annual): 39.75% → 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
2026-01-20 $1.5100
2025-10-20 $1.5100
2025-07-21 $1.5100
2025-04-21 $1.4100
2025-01-21 $1.4100
2024-10-21 $1.4100
2024-07-22 $1.4100
2024-04-19 $1.3000
2024-01-19 $1.3000
2023-10-20 $1.3000
2023-07-19 $1.3000
2023-04-21 $1.2000
2023-01-19 $1.2000
2022-10-21 $1.2000
2022-07-19 $1.2000
2022-04-22 $1.1100
2022-01-19 $1.1100
2021-10-22 $1.1100
2021-07-19 $1.1100
2021-04-23 $1.0300
2021-01-19 $1.0300
2020-10-23 $1.0300
2020-07-17 $1.0300
2020-04-17 $1.0300
2020-01-17 $1.0300
2019-10-18 $1.0300
2019-07-19 $1.0300
2019-04-18 $0.8600
2019-01-18 $0.8600
2018-10-19 $0.8600
2018-07-19 $0.8600
2018-04-20 $0.7800
2018-01-19 $0.7800
2017-10-20 $0.7800
2017-07-18 $0.7800
2017-04-20 $0.7700
2017-01-18 $0.7700
2016-10-20 $0.7700
2016-07-18 $0.7700
2016-04-21 $0.7700
2016-01-15 $0.7700
2015-10-22 $0.7700
2015-07-16 $0.7700
2015-04-16 $0.7000
2015-01-15 $0.7000
2014-10-16 $0.7000
2014-07-17 $0.7000
2014-04-16 $0.6000
2014-01-16 $0.6000
2013-10-17 $0.6000
2013-07-18 $0.6000
2013-04-18 $0.5200
2012-12-20 $0.5200
2012-10-18 $0.5200
2012-07-18 $0.5200
2012-04-19 $0.4600
2012-01-18 $0.4600
2011-10-20 $0.4600
2011-07-18 $0.4600
2011-04-20 $0.4400
2011-01-18 $0.4400
2010-10-21 $0.4400
2010-07-16 $0.4400
2010-04-22 $0.4200
2010-01-15 $0.4200
2009-10-22 $0.4200
2009-07-16 $0.4200
2009-04-16 $0.4200
2009-01-15 $0.4200
2008-10-16 $0.4200
2008-07-17 $0.4200
2008-04-17 $0.3600
2008-01-17 $0.3600
2007-10-18 $0.3600
2007-07-18 $0.3600
2007-04-19 $0.3000
2007-01-18 $0.3000
2006-10-19 $0.3000
2006-07-18 $0.3000
2006-04-20 $0.2500
2006-01-18 $0.2500
2005-10-20 $0.2500
2005-07-20 $0.2500
2005-04-21 $0.2050
2005-01-18 $0.2050
2004-10-21 $0.2050
2004-07-16 $0.2050
2004-04-22 $0.1850
2004-01-15 $0.1850
2003-10-16 $0.1850
2003-07-17 $0.1750
2003-04-16 $0.1750
2003-01-16 $0.1750
2002-10-17 $0.1750
2002-07-18 $0.1750
2002-04-18 $0.1750
2002-01-17 $0.1750
2001-10-18 $0.1750
2001-07-18 $0.1750
2001-04-19 $0.1700
2001-01-18 $0.1700
2000-10-18 $0.1700
2000-07-18 $0.1700
2000-04-19 $0.1625
2000-01-18 $0.1625
1999-10-21 $0.1625
1999-07-16 $0.1625
1999-04-22 $0.1500
1999-01-15 $0.1500
1998-10-22 $0.1500
1998-07-16 $0.1500
1998-04-16 $0.1250
1998-01-15 $0.1250
1997-10-16 $0.1250
1997-07-17 $0.1250
1997-04-17 $0.1000
1997-01-16 $0.1000
1996-10-17 $0.1000
1996-07-18 $0.1000
1996-04-18 $0.0875
1996-01-18 $0.0875
1995-10-19 $0.0875
1995-07-18 $0.0875
1995-04-18 $0.0625
1995-01-13 $0.0625
1994-10-18 $0.0375
1994-07-14 $0.0375
1994-04-19 $0.0187
1994-01-13 $0.0187
1993-10-19 $0.0187
1993-07-14 $0.0187
1993-04-20 $0.0187
1993-01-13 $0.0187
1992-10-20 $0.0187
1992-07-14 $0.0187
1992-04-13 $0.0187
1992-01-14 $0.0187
1991-10-15 $0.0375
1991-07-16 $0.0375
1991-04-16 $0.0375
1991-01-15 $0.0375
1990-10-16 $0.0375
1990-07-16 $0.0375
1990-04-17 $0.0375
1990-01-16 $0.0375
1989-10-17 $0.0375
1989-07-14 $0.0375
1989-04-18 $0.0375
1989-01-13 $0.0375
1988-10-18 $0.0238
1988-07-14 $0.0238
1988-04-19 $0.0234
1988-01-13 $0.0234
1987-10-20 $0.0156
1987-07-14 $0.0156
1987-04-13 $0.0156
1987-01-13 $0.0156
1986-10-14 $0.0156
1986-07-15 $0.0156
1986-04-15 $0.0156
1986-01-13 $0.0156
1985-10-15 $0.0156
1985-07-16 $0.0156
1985-04-16 $0.0156
1985-01-14 $0.0156
1984-10-16 $0.0156
1984-07-16 $0.0469
1984-04-16 $0.0469
1984-01-16 $0.0469
1983-10-18 $0.0469
1983-07-14 $0.0469
1983-04-19 $0.0469
1983-01-14 $0.0469
1982-10-19 $0.0469
1982-07-14 $0.0844
1982-04-20 $0.0844
1982-01-14 $0.0844
1969-10-14 $0.0250
1969-07-08 $0.0250
1969-04-08 $0.0250
1969-01-09 $0.0250
1968-10-08 $0.0250
1968-07-09 $0.0250
1968-01-10 $0.0250
1967-10-10 $0.0250
1967-07-11 $0.0250
1967-04-11 $0.0250
1967-01-11 $0.0250
1966-10-10 $0.0250
1966-07-12 $0.0250
1966-04-11 $0.0250
1966-01-11 $0.0250
1965-10-08 $0.0208
1965-07-09 $0.0208
1965-04-14 $0.0208
1965-01-15 $0.0208
1964-10-15 $0.0167
1964-07-15 $0.0167
1964-04-15 $0.0167
1964-01-15 $0.0125
1963-10-15 $0.0125
1963-07-16 $0.0125
1963-04-16 $0.0125
1963-01-15 $0.0104
1962-10-16 $0.0104
1962-07-17 $0.0104
1962-04-16 $0.0104
1962-01-16 $0.0104
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.03. Further, an Excess Kurtosis of 5.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.53%1030.64%0.64%
-5.53% to -4.13%1671.03%1.67%
-4.13% to -2.73%5643.49%5.17%
-2.73% to -1.33%195512.11%17.28%
-1.33% to 0.06%562834.87%52.15%
0.06% to 1.46%489530.33%82.47%
1.46% to 2.86%194512.05%94.52%
2.86% to 4.25%5573.45%97.97%
4.25% to 5.65%2091.29%99.27%
Greater than 5.65%1180.73%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.80%1.93% 76.31%68.27%
±2σ -3.66%3.79% 94.73%95.45%
±3σ -5.53%5.65% 98.63%99.73%
Descriptive Statistics
Mean0.063%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.863%
Sample Variance3.470%
Kurtosis5.59
Skewness-0.03
Range36.345%
Minimum-21.622%
Maximum14.723%
Count16141
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.428% 7828 48.50% 0.693%
Negative -1.352% 7514 46.55% -0.629%
Zero 0.000% 799 4.95% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 3.18%
20 1 Month 3.84%
60 1 Quarter 3.02%
250 1 Year 2.76%
750 3 Years 2.48%
1,250 5 Years 2.54%
2,500 10 Years 2.50%
5,000 20 Years 2.63%
12,500 50 Years 2.46%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.34. Further, an Excess Kurtosis of 31.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.00%00.00%0.00%
-2.00% to -0.94%00.00%0.00%
-0.94% to 0.12%00.00%0.00%
0.12% to 1.18%293418.18%18.18%
1.18% to 2.24%709743.97%62.14%
2.24% to 3.30%364122.56%84.70%
3.30% to 4.36%13718.49%93.19%
4.36% to 5.41%5773.57%96.77%
5.41% to 6.47%2541.57%98.34%
Greater than 6.47%2681.66%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.83%3.65% 82.80%68.27%
±2σ -0.59%5.06% 95.85%95.45%
±3σ -2.00%6.47% 98.34%99.73%
Descriptive Statistics
Mean2.237%
Standard Error0.011%
Median1.917%
Mode1.266%
Standard Deviation1.412%
Sample Variance1.995%
Kurtosis31.04
Skewness3.34
Range32.312%
Minimum0.188%
Maximum32.500%
Count16142
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.237% 16142 100.00% 2.237%
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 0.37. Further, an Excess Kurtosis of 6.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.72%1020.63%0.63%
-4.72% to -3.54%1941.20%1.83%
-3.54% to -2.36%5883.64%5.48%
-2.36% to -1.18%201712.50%17.97%
-1.18% to -0.00%473629.34%47.31%
-0.00% to 1.18%562134.82%82.13%
1.18% to 2.36%201012.45%94.59%
2.36% to 3.54%5623.48%98.07%
3.54% to 4.72%2041.26%99.33%
Greater than 4.72%1080.67%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.57%1.57% 75.85%68.27%
±2σ -3.15%3.15% 94.72%95.45%
±3σ -4.72%4.72% 98.70%99.73%
Descriptive Statistics
Mean-0.001%
Standard Error0.012%
Median0.000%
Mode0.000%
Standard Deviation1.573%
Sample Variance2.475%
Kurtosis6.64
Skewness0.37
Range33.694%
Minimum-10.049%
Maximum23.645%
Count16142
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.207% 7523 46.60% 0.563%
Negative -1.190% 7637 47.31% -0.563%
Zero 0.000% 982 6.08% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. 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 -12.72%140.42%0.42%
-12.72% to -9.46%361.08%1.49%
-9.46% to -6.21%1404.18%5.68%
-6.21% to -2.95%44513.30%18.98%
-2.95% to 0.31%105531.53%50.51%
0.31% to 3.57%100430.01%80.51%
3.57% to 6.83%45813.69%94.20%
6.83% to 10.09%1414.21%98.42%
10.09% to 13.35%300.90%99.31%
Greater than 13.35%230.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.03%4.66% 73.07%68.27%
±2σ -8.38%9.01% 95.07%95.45%
±3σ -12.72%13.35% 98.89%99.73%
Descriptive Statistics
Mean0.314%
Standard Error0.075%
Median0.278%
Mode0.000%
Standard Deviation4.346%
Sample Variance18.889%
Kurtosis2.31
Skewness0.08
Range47.127%
Minimum-25.505%
Maximum21.622%
Count3346
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.417% 1739 51.97% 1.776%
Negative -3.156% 1550 46.32% -1.462%
Zero 0.000% 57 1.70% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 8.01%
12 1 Quarter 6.78%
52 1 Year 6.62%
156 3 Years 5.95%
260 5 Years 6.14%
520 10 Years 6.05%
1,040 20 Years 6.32%
2,600 50 Years 6.02%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.78. Further, an Excess Kurtosis of 16.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.72%00.00%0.00%
-4.72% to -2.03%00.00%0.00%
-2.03% to 0.66%00.00%0.00%
0.66% to 3.35%62718.73%18.73%
3.35% to 6.03%142442.55%61.28%
6.03% to 8.72%78023.30%84.58%
8.72% to 11.41%2798.34%92.92%
11.41% to 14.09%1293.85%96.77%
14.09% to 16.78%571.70%98.48%
Greater than 16.78%511.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.45%9.62% 81.21%68.27%
±2σ -1.13%13.20% 95.82%95.45%
±3σ -4.72%16.78% 98.48%99.73%
Descriptive Statistics
Mean6.032%
Standard Error0.062%
Median5.205%
Mode4.167%
Standard Deviation3.583%
Sample Variance12.837%
Kurtosis16.39
Skewness2.78
Range42.779%
Minimum0.971%
Maximum43.750%
Count3347
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.032% 3347 100.00% 6.032%
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 4.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.93%160.48%0.48%
-12.93% to -9.71%210.63%1.11%
-9.71% to -6.49%1394.15%5.26%
-6.49% to -3.27%49414.76%20.02%
-3.27% to -0.06%105531.52%51.54%
-0.06% to 3.16%100830.12%81.66%
3.16% to 6.38%41812.49%94.14%
6.38% to 9.60%1344.00%98.15%
9.60% to 12.81%401.20%99.34%
Greater than 12.81%220.66%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.35%4.23% 74.04%68.27%
±2σ -8.64%8.52% 95.49%95.45%
±3σ -12.93%12.81% 98.86%99.73%
Descriptive Statistics
Mean-0.057%
Standard Error0.074%
Median-0.225%
Mode0.000%
Standard Deviation4.290%
Sample Variance18.403%
Kurtosis4.02
Skewness0.61
Range53.437%
Minimum-17.230%
Maximum36.207%
Count3347
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.322% 1561 46.64% 1.549%
Negative -3.107% 1730 51.69% -1.606%
Zero 0.000% 56 1.67% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.12. Further, an Excess Kurtosis of 1.71 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -24.09%30.39%0.39%
-24.09% to -17.74%60.78%1.17%
-17.74% to -11.39%273.51%4.68%
-11.39% to -5.04%13517.56%22.24%
-5.04% to 1.31%22228.87%51.11%
1.31% to 7.67%21227.57%78.67%
7.67% to 14.02%12416.12%94.80%
14.02% to 20.37%273.51%98.31%
20.37% to 26.72%70.91%99.22%
Greater than 26.72%60.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.15%9.78% 71.39%68.27%
±2σ -15.62%18.25% 95.58%95.45%
±3σ -24.09%26.72% 98.83%99.73%
Descriptive Statistics
Mean1.315%
Standard Error0.305%
Median1.173%
Mode0.000%
Standard Deviation8.469%
Sample Variance71.732%
Kurtosis1.71
Skewness0.12
Range76.081%
Minimum-35.260%
Maximum40.821%
Count769
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.003% 435 56.57% 3.961%
Negative -6.149% 331 43.04% -2.647%
Zero 0.000% 3 0.39% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 16.97%
12 1 Year 15.52%
36 3 Years 13.88%
60 5 Years 14.00%
120 10 Years 13.50%
240 20 Years 13.78%
600 50 Years 13.29%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.17. Further, an Excess Kurtosis of 19.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.60%00.00%0.00%
-8.60% to -2.96%00.00%0.00%
-2.96% to 2.69%00.00%0.00%
2.69% to 8.33%13517.53%17.53%
8.33% to 13.97%34044.16%61.69%
13.97% to 19.61%17322.47%84.16%
19.61% to 25.25%749.61%93.77%
25.25% to 30.89%303.90%97.66%
30.89% to 36.53%60.78%98.44%
Greater than 36.53%121.56%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 6.45%21.49% 82.73%68.27%
±2σ -1.07%29.01% 96.75%95.45%
±3σ -8.60%36.53% 98.44%99.73%
Descriptive Statistics
Mean13.967%
Standard Error0.271%
Median12.397%
Mode15.615%
Standard Deviation7.521%
Sample Variance56.572%
Kurtosis19.68
Skewness3.17
Range81.704%
Minimum3.053%
Maximum84.757%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.967% 770 100.00% 13.967%
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 4.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -26.00%10.13%0.13%
-26.00% to -19.59%50.65%0.78%
-19.59% to -13.19%232.99%3.77%
-13.19% to -6.78%14418.70%22.47%
-6.78% to -0.37%24431.69%54.16%
-0.37% to 6.04%20426.49%80.65%
6.04% to 12.45%10814.03%94.68%
12.45% to 18.86%263.38%98.05%
18.86% to 25.26%91.17%99.22%
Greater than 25.26%60.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.91%8.18% 73.51%68.27%
±2σ -17.46%16.72% 95.84%95.45%
±3σ -26.00%25.26% 99.09%99.73%
Descriptive Statistics
Mean-0.369%
Standard Error0.308%
Median-1.092%
Mode0.000%
Standard Deviation8.544%
Sample Variance73.000%
Kurtosis4.29
Skewness0.96
Range81.749%
Minimum-28.058%
Maximum53.691%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.891% 342 44.42% 3.061%
Negative -6.228% 424 55.06% -3.429%
Zero 0.000% 4 0.52% 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 0.10 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -38.20%10.39%0.39%
-38.20% to -27.69%00.00%0.39%
-27.69% to -17.18%145.45%5.84%
-17.18% to -6.67%4316.73%22.57%
-6.67% to 3.85%7027.24%49.81%
3.85% to 14.36%7228.02%77.82%
14.36% to 24.87%3814.79%92.61%
24.87% to 35.38%166.23%98.83%
35.38% to 45.90%20.78%99.61%
Greater than 45.90%10.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.17%17.86% 68.09%68.27%
±2σ -24.19%31.88% 96.89%95.45%
±3σ -38.20%45.90% 99.22%99.73%
Descriptive Statistics
Mean3.847%
Standard Error0.874%
Median3.898%
Mode-8.878%
Standard Deviation14.017%
Sample Variance196.477%
Kurtosis0.10
Skewness0.15
Range93.853%
Minimum-44.498%
Maximum49.355%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 14.044% 142 55.25% 7.760%
Negative -8.744% 115 44.75% -3.913%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 32.98%
12 3 Years 28.24%
20 5 Years 26.60%
40 10 Years 24.91%
80 20 Years 24.73%
200 50 Years 23.07%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.49. Further, an Excess Kurtosis of 24.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.39%00.00%0.00%
-11.39% to -2.19%00.00%0.00%
-2.19% to 7.00%00.00%0.00%
7.00% to 16.20%4316.67%16.67%
16.20% to 25.39%11243.41%60.08%
25.39% to 34.58%6224.03%84.11%
34.58% to 43.78%2810.85%94.96%
43.78% to 52.97%72.71%97.67%
52.97% to 62.17%31.16%98.84%
Greater than 62.17%31.16%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 13.13%37.65% 83.33%68.27%
±2σ 0.87%49.91% 97.29%95.45%
±3σ -11.39%62.17% 98.84%99.73%
Descriptive Statistics
Mean25.390%
Standard Error0.763%
Median23.044%
Mode20.000%
Standard Deviation12.259%
Sample Variance150.294%
Kurtosis24.22
Skewness3.49
Range125.158%
Minimum8.019%
Maximum133.177%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 25.390% 258 100.00% 25.390%
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 1.02. Further, an Excess Kurtosis of 3.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -43.41%00.00%0.00%
-43.41% to -32.89%00.00%0.00%
-32.89% to -22.36%114.26%4.26%
-22.36% to -11.84%5119.77%24.03%
-11.84% to -1.32%7227.91%51.94%
-1.32% to 9.21%6926.74%78.68%
9.21% to 19.73%3814.73%93.41%
19.73% to 30.25%135.04%98.45%
30.25% to 40.78%31.16%99.61%
Greater than 40.78%10.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.35%12.71% 70.16%68.27%
±2σ -29.38%26.75% 97.67%95.45%
±3σ -43.41%40.78% 99.61%99.73%
Descriptive Statistics
Mean-1.317%
Standard Error0.874%
Median-2.665%
Mode-32.524%
Standard Deviation14.032%
Sample Variance196.885%
Kurtosis3.94
Skewness1.02
Range114.906%
Minimum-32.524%
Maximum82.382%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.725% 119 46.12% 4.947%
Negative -11.627% 139 53.88% -6.264%
Zero 0.000% 0 0.00% 0.000%