Markets Data Volatility Heatmap Portfolio Calculator

CAT Deep Analytical Report

Caterpillar Inc. | Category: Equity Mega Cap | Ann. Div Yield: 0.87% ($5.94) | 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 1.86% 1.41% 1.57% 2.55% 2.97% 3.02% 675.31 716.70 655.51 738.34
Weekly 4.34% 3.58% 4.29% 6.16% 6.55% 6.64% 651.60 742.78 610.30 793.04
Monthly 8.46% 7.52% 8.54% 13.99% 13.63% 13.83% 607.04 797.30 529.68 913.73
Quarterly 14.00% 12.26% 14.02% 26.60% 23.61% 23.95% 549.39 880.96 433.85 1115.57
Annual — — — — 47.22% 47.90% 433.85 1115.57 270.56 1788.85
Option Time Horizon — — — — 17.82% 18.08% 582.12 831.43 487.09 993.64
Calculation Notes: Computed at 2026-03-23T16:32 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $695.70  |  Strike (K): $700.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $48.4000 (Bid $47.7000 / Ask $49.1000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.87%  |  Binomial IV (Annual): 47.22% (CRR binomial tree, American, n=20 steps)  |  BS IV: 46.97% (European Black-Scholes)  |  Yahoo IV (Annual): 47.90% → 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 5.58 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%5673.51%5.18%
-2.73% to -1.33%195712.11%17.29%
-1.33% to 0.06%563634.87%52.16%
0.06% to 1.46%489930.31%82.47%
1.46% to 2.86%194812.05%94.52%
2.86% to 4.25%5583.45%97.98%
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%
Kurtosis5.58
Skewness-0.03
Range36.345%
Minimum-21.622%
Maximum14.723%
Count16162
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.428% 7836 48.48% 0.692%
Negative -1.352% 7527 46.57% -0.630%
Zero 0.000% 799 4.94% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 3.25%
20 1 Month 3.79%
60 1 Quarter 3.36%
250 1 Year 2.85%
750 3 Years 2.50%
1,250 5 Years 2.55%
2,500 10 Years 2.52%
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 3.33. Further, an Excess Kurtosis of 30.96 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%293918.18%18.18%
1.18% to 2.24%710743.97%62.15%
2.24% to 3.30%364222.53%84.69%
3.30% to 4.36%13748.50%93.19%
4.36% to 5.42%5803.59%96.78%
5.42% to 6.48%2541.57%98.35%
Greater than 6.48%2671.65%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.83%3.65% 82.82%68.27%
±2σ -0.59%5.06% 95.85%95.45%
±3σ -2.00%6.48% 98.35%99.73%
Descriptive Statistics
Mean2.239%
Standard Error0.011%
Median1.918%
Mode1.266%
Standard Deviation1.413%
Sample Variance1.996%
Kurtosis30.96
Skewness3.33
Range32.312%
Minimum0.188%
Maximum32.500%
Count16163
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.239% 16163 100.00% 2.239%
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 0.36. Further, an Excess Kurtosis of 6.63 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%1951.21%1.84%
-3.54% to -2.36%5873.63%5.47%
-2.36% to -1.18%201612.47%17.94%
-1.18% to -0.00%474429.35%47.29%
-0.00% to 1.18%563334.85%82.14%
1.18% to 2.36%201212.45%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% 75.86%68.27%
±2σ -3.15%3.15% 94.75%95.45%
±3σ -4.72%4.72% 98.70%99.73%
Descriptive Statistics
Mean-0.001%
Standard Error0.012%
Median0.000%
Mode0.000%
Standard Deviation1.574%
Sample Variance2.476%
Kurtosis6.63
Skewness0.36
Range33.694%
Minimum-10.049%
Maximum23.645%
Count16163
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.206% 7537 46.63% 0.562%
Negative -1.191% 7644 47.29% -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%361.07%1.49%
-9.46% to -6.21%1414.21%5.70%
-6.21% to -2.95%44513.28%18.99%
-2.95% to 0.31%105731.55%50.54%
0.31% to 3.57%100229.91%80.45%
3.57% to 6.83%46013.73%94.18%
6.83% to 10.09%1424.24%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%9.00% 95.07%95.45%
±3σ -12.72%13.35% 98.90%99.73%
Descriptive Statistics
Mean0.312%
Standard Error0.075%
Median0.278%
Mode0.000%
Standard Deviation4.345%
Sample Variance18.881%
Kurtosis2.31
Skewness0.08
Range47.127%
Minimum-25.505%
Maximum21.622%
Count3350
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.416% 1740 51.94% 1.774%
Negative -3.155% 1553 46.36% -1.463%
Zero 0.000% 57 1.70% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 8.12%
12 1 Quarter 7.49%
52 1 Year 6.78%
156 3 Years 5.94%
260 5 Years 6.16%
520 10 Years 6.07%
1,040 20 Years 6.33%
2,600 50 Years 6.03%
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 16.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.71%00.00%0.00%
-4.71% to -2.03%00.00%0.00%
-2.03% to 0.66%00.00%0.00%
0.66% to 3.35%62818.74%18.74%
3.35% to 6.04%142442.49%61.24%
6.04% to 8.72%78323.37%84.60%
8.72% to 11.41%2798.33%92.93%
11.41% to 14.10%1293.85%96.78%
14.10% 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% 81.17%68.27%
±2σ -1.13%13.20% 95.82%95.45%
±3σ -4.71%16.78% 98.48%99.73%
Descriptive Statistics
Mean6.035%
Standard Error0.062%
Median5.208%
Mode4.167%
Standard Deviation3.583%
Sample Variance12.836%
Kurtosis16.36
Skewness2.78
Range42.779%
Minimum0.971%
Maximum43.750%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.035% 3351 100.00% 6.035%
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 4.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.92%160.48%0.48%
-12.92% to -9.70%210.63%1.10%
-9.70% to -6.49%1394.15%5.25%
-6.49% to -3.27%49414.74%19.99%
-3.27% to -0.06%105531.48%51.48%
-0.06% to 3.16%101130.17%81.65%
3.16% to 6.38%41812.47%94.12%
6.38% to 9.59%1333.97%98.09%
9.59% to 12.81%421.25%99.34%
Greater than 12.81%220.66%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.34%4.23% 74.07%68.27%
±2σ -8.63%8.52% 95.46%95.45%
±3σ -12.92%12.81% 98.87%99.73%
Descriptive Statistics
Mean-0.055%
Standard Error0.074%
Median-0.224%
Mode0.000%
Standard Deviation4.288%
Sample Variance18.386%
Kurtosis4.03
Skewness0.61
Range53.437%
Minimum-17.230%
Maximum36.207%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.318% 1565 46.70% 1.550%
Negative -3.107% 1730 51.63% -1.604%
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%13617.66%22.34%
-5.04% to 1.30%22228.83%51.17%
1.30% to 7.65%21227.53%78.70%
7.65% to 14.00%12516.23%94.94%
14.00% to 20.34%253.25%98.18%
20.34% to 26.69%81.04%99.22%
Greater than 26.69%60.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.16%9.76% 71.43%68.27%
±2σ -15.62%18.23% 95.58%95.45%
±3σ -24.09%26.69% 98.83%99.73%
Descriptive Statistics
Mean1.302%
Standard Error0.305%
Median1.131%
Mode0.000%
Standard Deviation8.463%
Sample Variance71.617%
Kurtosis1.71
Skewness0.12
Range76.081%
Minimum-35.260%
Maximum40.821%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.997% 435 56.49% 3.953%
Negative -6.147% 332 43.12% -2.650%
Zero 0.000% 3 0.39% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 17.09%
12 1 Year 15.76%
36 3 Years 13.72%
60 5 Years 13.99%
120 10 Years 13.48%
240 20 Years 13.79%
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 19.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.58%00.00%0.00%
-8.58% to -2.95%00.00%0.00%
-2.95% to 2.69%00.00%0.00%
2.69% to 8.33%13517.51%17.51%
8.33% to 13.97%34044.10%61.61%
13.97% to 19.61%17422.57%84.18%
19.61% to 25.24%749.60%93.77%
25.24% to 30.88%303.89%97.67%
30.88% to 36.52%60.78%98.44%
Greater than 36.52%121.56%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 6.45%21.48% 82.62%68.27%
±2σ -1.07%29.00% 96.76%95.45%
±3σ -8.58%36.52% 98.44%99.73%
Descriptive Statistics
Mean13.967%
Standard Error0.271%
Median12.400%
Mode15.615%
Standard Deviation7.517%
Sample Variance56.499%
Kurtosis19.71
Skewness3.17
Range81.704%
Minimum3.053%
Maximum84.757%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.967% 771 100.00% 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 4.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.97%10.13%0.13%
-25.97% to -19.57%50.65%0.78%
-19.57% to -13.17%232.98%3.76%
-13.17% to -6.76%14418.68%22.44%
-6.76% to -0.36%24431.65%54.09%
-0.36% to 6.04%20526.59%80.67%
6.04% to 12.45%10814.01%94.68%
12.45% to 18.85%263.37%98.05%
18.85% to 25.25%91.17%99.22%
Greater than 25.25%60.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.90%8.18% 73.54%68.27%
±2σ -17.43%16.71% 95.85%95.45%
±3σ -25.97%25.25% 99.09%99.73%
Descriptive Statistics
Mean-0.360%
Standard Error0.307%
Median-1.075%
Mode0.000%
Standard Deviation8.537%
Sample Variance72.879%
Kurtosis4.30
Skewness0.96
Range81.749%
Minimum-28.058%
Maximum53.691%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.885% 343 44.49% 3.063%
Negative -6.223% 424 54.99% -3.422%
Zero 0.000% 4 0.52% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.16. Further, an Excess Kurtosis of 0.11 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -38.19%10.39%0.39%
-38.19% to -27.69%00.00%0.39%
-27.69% to -17.19%135.06%5.45%
-17.19% to -6.69%4417.12%22.57%
-6.69% to 3.81%7027.24%49.81%
3.81% to 14.31%7228.02%77.82%
14.31% to 24.81%3814.79%92.61%
24.81% to 35.31%166.23%98.83%
35.31% to 45.81%20.78%99.61%
Greater than 45.81%10.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.19%17.81% 68.09%68.27%
±2σ -24.19%31.81% 96.89%95.45%
±3σ -38.19%45.81% 99.22%99.73%
Descriptive Statistics
Mean3.812%
Standard Error0.873%
Median3.898%
Mode-8.878%
Standard Deviation13.999%
Sample Variance195.965%
Kurtosis0.11
Skewness0.16
Range93.853%
Minimum-44.498%
Maximum49.355%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.980% 142 55.25% 7.724%
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 3.96 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -43.33%00.00%0.00%
-43.33% to -32.82%00.00%0.00%
-32.82% to -22.31%114.26%4.26%
-22.31% to -11.80%5019.38%23.64%
-11.80% to -1.29%7328.29%51.94%
-1.29% to 9.22%6926.74%78.68%
9.22% to 19.73%3814.73%93.41%
19.73% to 30.25%135.04%98.45%
30.25% to 40.76%31.16%99.61%
Greater than 40.76%10.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.30%12.73% 70.16%68.27%
±2σ -29.32%26.74% 97.67%95.45%
±3σ -43.33%40.76% 99.61%99.73%
Descriptive Statistics
Mean-1.289%
Standard Error0.873%
Median-2.665%
Mode-32.524%
Standard Deviation14.015%
Sample Variance196.415%
Kurtosis3.96
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 -11.574% 139 53.88% -6.236%
Zero 0.000% 0 0.00% 0.000%