Markets Data Volatility Heatmap Portfolio Calculator

AXP Deep Analytical Report

American Express Company | Category: Equity Mega Cap | Ann. Div Yield: 0.96% ($3.28) | Last Updated: 2026-02-22 | Data Range: 1973-05-01 → 2026-02-01 (634 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 2.18% 1.80% 1.73% 2.40% 1.81% 1.91% 339.99 352.49 333.91 358.91
Weekly 4.78% 4.63% 4.67% 5.84% 3.97% 4.21% 332.69 360.21 319.73 374.81
Monthly 8.95% 10.05% 8.69% 12.31% 8.27% 8.75% 318.70 376.03 293.40 408.46
Quarterly 14.52% 19.41% 14.95% 21.92% 14.33% 15.16% 299.97 399.51 259.93 461.05
Annual — — — — 28.65% 30.32% 259.93 461.05 195.17 614.02
Option Time Horizon — — — — 11.02% 11.66% 310.05 386.52 277.70 431.55
Calculation Notes: Computed at 2026-02-22T14:17 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $346.18  |  Strike (K): $350.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $14.1500 (Bid $13.8000 / Ask $14.5000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.96%  |  Binomial IV (Annual): 28.65% (CRR binomial tree, American, n=20 steps)  |  BS IV: 28.79% (European Black-Scholes)  |  Yahoo IV (Annual): 30.32% → 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
2026-01-02 $0.8200
2025-10-10 $0.8200
2025-07-03 $0.8200
2025-04-04 $0.8200
2025-01-03 $0.7000
2024-10-04 $0.7000
2024-07-05 $0.7000
2024-04-04 $0.7000
2024-01-04 $0.6000
2023-10-05 $0.6000
2023-07-06 $0.6000
2023-04-05 $0.6000
2023-01-05 $0.5200
2022-10-13 $0.5200
2022-06-30 $0.5200
2022-04-07 $0.5200
2022-01-06 $0.4300
2021-10-07 $0.4300
2021-07-01 $0.4300
2021-03-31 $0.4300
2021-01-07 $0.4300
2020-10-08 $0.4300
2020-07-01 $0.4300
2020-04-02 $0.4300
2020-01-02 $0.4300
2019-10-03 $0.4300
2019-07-03 $0.3900
2019-04-04 $0.3900
2019-01-03 $0.3900
2018-10-04 $0.3900
2018-07-05 $0.3500
2018-04-05 $0.3500
2018-01-04 $0.3500
2017-10-05 $0.3500
2017-07-05 $0.3200
2017-04-05 $0.3200
2017-01-04 $0.3200
2016-10-05 $0.3200
2016-06-29 $0.2900
2016-04-06 $0.2900
2016-01-06 $0.2900
2015-10-07 $0.2900
2015-06-30 $0.2900
2015-03-31 $0.2600
2015-01-07 $0.2600
2014-10-01 $0.2600
2014-07-09 $0.2600
2014-04-02 $0.2300
2014-01-08 $0.2300
2013-10-02 $0.2300
2013-07-02 $0.2300
2013-04-03 $0.2000
2013-01-02 $0.2000
2012-10-03 $0.2000
2012-07-03 $0.2000
2012-04-03 $0.2000
2012-01-04 $0.1800
2011-10-05 $0.1800
2011-06-29 $0.1800
2011-04-06 $0.1800
2011-01-05 $0.1800
2010-10-06 $0.1800
2010-06-30 $0.1800
2010-03-30 $0.1800
2010-01-07 $0.1800
2009-09-30 $0.1800
2009-06-30 $0.1800
2009-04-01 $0.1800
2009-01-07 $0.1800
2008-10-01 $0.1800
2008-07-09 $0.1800
2008-04-09 $0.1800
2008-01-02 $0.1800
2007-10-03 $0.1500
2007-07-03 $0.1500
2007-04-03 $0.1500
2007-01-03 $0.1500
2006-10-04 $0.1500
2006-07-05 $0.1500
2006-04-05 $0.1200
2006-01-04 $0.1200
2005-10-05 $0.1200
2005-06-29 $0.1050
2005-03-30 $0.1050
2005-01-05 $0.1050
2004-10-06 $0.1050
2004-06-30 $0.0875
2004-03-31 $0.0875
2003-12-30 $0.0875
2003-10-01 $0.0875
2003-07-01 $0.0875
2003-04-02 $0.0700
2002-12-31 $0.0700
2002-10-02 $0.0700
2002-07-02 $0.0700
2002-04-03 $0.0700
2002-01-02 $0.0700
2001-10-03 $0.0700
2001-07-03 $0.0700
2001-04-04 $0.0700
2001-01-03 $0.0700
2000-10-04 $0.0700
2000-07-05 $0.0700
2000-04-20 $0.0700
2000-01-05 $0.0656
1999-10-06 $0.0656
1999-06-30 $0.0659
1999-03-30 $0.0656
1999-01-06 $0.0656
1998-10-07 $0.0656
1998-06-30 $0.0656
1998-04-07 $0.0656
1997-12-30 $0.0656
1997-10-01 $0.0656
1997-07-01 $0.0656
1997-04-02 $0.0656
1996-12-31 $0.0656
1996-10-09 $0.0656
1996-07-02 $0.0656
1996-04-02 $0.0656
1996-01-03 $0.0656
1995-10-11 $0.0656
1995-07-05 $0.0656
1995-04-03 $0.0656
1994-12-30 $0.0656
1994-10-03 $0.0656
1994-07-01 $0.0656
1994-04-04 $0.0644
1994-01-03 $0.0644
1993-10-04 $0.0644
1993-07-02 $0.0644
1993-03-29 $0.0644
1993-01-04 $0.0644
1992-09-28 $0.0644
1992-06-26 $0.0644
1992-03-30 $0.0644
1991-12-27 $0.0644
1991-09-30 $0.0644
1991-06-28 $0.0592
1991-04-01 $0.0592
1990-12-28 $0.0592
1990-10-01 $0.0592
1990-06-29 $0.0592
1990-04-02 $0.0592
1989-12-29 $0.0592
1989-10-02 $0.0541
1989-06-30 $0.0541
1989-04-03 $0.0541
1988-12-30 $0.0541
1988-10-03 $0.0489
1988-07-01 $0.0489
1988-04-04 $0.0489
1988-01-04 $0.0489
1987-12-31 $0.0489
1987-10-05 $0.0489
1987-09-29 $0.0875
1987-06-26 $0.0489
1987-03-30 $0.0489
1986-12-26 $0.0463
1986-09-29 $0.0438
1986-06-27 $0.0438
1986-03-27 $0.0438
1985-12-27 $0.0438
1985-09-30 $0.0438
1985-06-28 $0.0412
1985-03-29 $0.0412
1984-12-28 $0.0412
1984-10-01 $0.0412
1984-06-29 $0.0412
1984-04-02 $0.0412
1983-12-30 $0.0412
1983-10-03 $0.0412
1983-07-01 $0.0412
1983-04-04 $0.0386
1983-01-03 $0.0386
1982-10-04 $0.0354
1982-07-02 $0.0354
1982-01-04 $0.0354
1981-10-05 $0.0322
1981-06-29 $0.0322
1981-03-30 $0.0322
1980-12-26 $0.0322
1980-09-29 $0.0322
1980-06-27 $0.0322
1980-03-28 $0.0322
1979-12-28 $0.0290
1979-10-01 $0.0290
1979-06-29 $0.0290
1979-04-02 $0.0290
1978-12-29 $0.0257
1978-10-02 $0.0257
1978-06-30 $0.0257
1978-04-03 $0.0225
1977-12-30 $0.0225
1977-10-03 $0.0225
1977-07-01 $0.0193
1977-04-01 $0.0193
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.28. Further, an Excess Kurtosis of 10.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.49%900.68%0.68%
-6.49% to -4.85%1160.87%1.55%
-4.85% to -3.21%4493.37%4.92%
-3.21% to -1.57%151211.36%16.28%
-1.57% to 0.07%478335.93%52.21%
0.07% to 1.70%423031.78%83.99%
1.70% to 3.34%144310.84%94.83%
3.34% to 4.98%4353.27%98.10%
4.98% to 6.62%1461.10%99.20%
Greater than 6.62%1070.80%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.12%2.25% 78.33%68.27%
±2σ -4.30%4.43% 95.24%95.45%
±3σ -6.49%6.62% 98.52%99.73%
Descriptive Statistics
Mean0.066%
Standard Error0.019%
Median0.000%
Mode0.000%
Standard Deviation2.184%
Sample Variance4.771%
Kurtosis10.01
Skewness0.28
Range48.112%
Minimum-26.230%
Maximum21.882%
Count13311
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.596% 6465 48.57% 0.775%
Negative -1.506% 6265 47.07% -0.709%
Zero 0.000% 581 4.37% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.17%
20 1 Month 2.54%
60 1 Quarter 2.24%
250 1 Year 2.54%
750 3 Years 2.18%
1,250 5 Years 2.40%
2,500 10 Years 2.28%
5,000 20 Years 2.54%
12,500 50 Years 2.63%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.56. Further, an Excess Kurtosis of 49.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.00%00.00%0.00%
-3.00% to -1.65%00.00%0.00%
-1.65% to -0.30%00.00%0.00%
-0.30% to 1.06%157011.79%11.79%
1.06% to 2.41%696352.31%64.10%
2.41% to 3.77%300022.54%86.64%
3.77% to 5.12%9977.49%94.13%
5.12% to 6.47%3932.95%97.08%
6.47% to 7.83%1671.25%98.33%
Greater than 7.83%2221.67%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.61%4.22% 89.36%68.27%
±2σ -1.20%6.02% 96.35%95.45%
±3σ -3.00%7.83% 98.33%99.73%
Descriptive Statistics
Mean2.412%
Standard Error0.016%
Median1.938%
Mode1.754%
Standard Deviation1.805%
Sample Variance3.260%
Kurtosis49.03
Skewness4.56
Range40.713%
Minimum0.251%
Maximum40.964%
Count13312
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.412% 13312 100.00% 2.412%
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 0.39. Further, an Excess Kurtosis of 11.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.15%920.69%0.69%
-5.15% to -3.85%1441.08%1.77%
-3.85% to -2.55%4413.31%5.09%
-2.55% to -1.25%148511.16%16.24%
-1.25% to 0.04%500837.62%53.86%
0.04% to 1.34%395229.69%83.55%
1.34% to 2.64%154811.63%95.18%
2.64% to 3.93%3942.96%98.14%
3.93% to 5.23%1501.13%99.26%
Greater than 5.23%980.74%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.69%1.77% 78.62%68.27%
±2σ -3.42%3.50% 95.05%95.45%
±3σ -5.15%5.23% 98.57%99.73%
Descriptive Statistics
Mean0.042%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.730%
Sample Variance2.993%
Kurtosis11.67
Skewness0.39
Range41.271%
Minimum-13.493%
Maximum27.778%
Count13312
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.294% 6228 46.78% 0.605%
Negative -1.270% 5909 44.39% -0.564%
Zero 0.000% 1175 8.83% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.24. Further, an Excess Kurtosis of 5.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -14.03%160.58%0.58%
-14.03% to -10.44%311.13%1.71%
-10.44% to -6.85%973.52%5.23%
-6.85% to -3.27%32811.91%17.13%
-3.27% to 0.32%90932.99%50.13%
0.32% to 3.91%89732.56%82.69%
3.91% to 7.50%33011.98%94.66%
7.50% to 11.08%933.38%98.04%
11.08% to 14.67%321.16%99.20%
Greater than 14.67%220.80%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.46%5.10% 77.13%68.27%
±2σ -9.25%9.89% 94.85%95.45%
±3σ -14.03%14.67% 98.62%99.73%
Descriptive Statistics
Mean0.321%
Standard Error0.091%
Median0.307%
Mode0.000%
Standard Deviation4.783%
Sample Variance22.880%
Kurtosis5.51
Skewness0.24
Range71.130%
Minimum-36.170%
Maximum34.960%
Count2755
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.512% 1448 52.56% 1.846%
Negative -3.357% 1251 45.41% -1.524%
Zero 0.000% 56 2.03% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 5.44%
12 1 Quarter 5.18%
52 1 Year 6.15%
156 3 Years 5.25%
260 5 Years 5.84%
520 10 Years 5.45%
1,040 20 Years 5.98%
2,600 50 Years 6.20%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.85. Further, an Excess Kurtosis of 29.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.43%00.00%0.00%
-7.43% to -3.95%00.00%0.00%
-3.95% to -0.48%00.00%0.00%
-0.48% to 3.00%39714.40%14.40%
3.00% to 6.48%137549.89%64.30%
6.48% to 9.95%59421.55%85.85%
9.95% to 13.43%2278.24%94.09%
13.43% to 16.91%853.08%97.17%
16.91% to 20.38%361.31%98.48%
Greater than 20.38%421.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.84%11.11% 87.52%68.27%
±2σ -2.79%15.75% 96.41%95.45%
±3σ -7.43%20.38% 98.48%99.73%
Descriptive Statistics
Mean6.476%
Standard Error0.088%
Median5.370%
Mode5.000%
Standard Deviation4.635%
Sample Variance21.480%
Kurtosis29.47
Skewness3.85
Range69.538%
Minimum1.050%
Maximum70.588%
Count2756
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.476% 2756 100.00% 6.476%
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 1.24. Further, an Excess Kurtosis of 13.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -13.97%100.36%0.36%
-13.97% to -10.46%270.98%1.34%
-10.46% to -6.96%873.16%4.50%
-6.96% to -3.45%34612.55%17.05%
-3.45% to 0.05%101136.68%53.74%
0.05% to 3.56%82629.97%83.71%
3.56% to 7.07%30010.89%94.59%
7.07% to 10.57%873.16%97.75%
10.57% to 14.08%391.42%99.17%
Greater than 14.08%230.83%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.62%4.73% 77.47%68.27%
±2σ -9.30%9.40% 94.70%95.45%
±3σ -13.97%14.08% 98.80%99.73%
Descriptive Statistics
Mean0.054%
Standard Error0.089%
Median-0.116%
Mode0.000%
Standard Deviation4.675%
Sample Variance21.858%
Kurtosis13.81
Skewness1.24
Range87.211%
Minimum-26.100%
Maximum61.111%
Count2756
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.528% 1284 46.59% 1.644%
Negative -3.118% 1405 50.98% -1.590%
Zero 0.000% 67 2.43% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.27. Further, an Excess Kurtosis of 15.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.54%60.95%0.95%
-25.54% to -18.83%50.79%1.74%
-18.83% to -12.12%264.11%5.85%
-12.12% to -5.41%7011.06%16.90%
-5.41% to 1.30%21133.33%50.24%
1.30% to 8.01%20131.75%81.99%
8.01% to 14.72%8914.06%96.05%
14.72% to 21.43%193.00%99.05%
21.43% to 28.14%30.47%99.53%
Greater than 28.14%30.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.65%10.24% 78.20%68.27%
±2σ -16.59%19.19% 95.73%95.45%
±3σ -25.54%28.14% 98.58%99.73%
Descriptive Statistics
Mean1.298%
Standard Error0.356%
Median1.281%
Mode0.000%
Standard Deviation8.946%
Sample Variance80.033%
Kurtosis15.13
Skewness1.27
Range119.915%
Minimum-32.406%
Maximum87.509%
Count633
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.602% 364 57.50% 3.796%
Negative -5.969% 265 41.86% -2.499%
Zero 0.000% 4 0.63% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 9.70%
12 1 Year 12.74%
36 3 Years 11.44%
60 5 Years 12.31%
120 10 Years 11.83%
240 20 Years 12.60%
600 50 Years 13.03%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.53. Further, an Excess Kurtosis of 19.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.55%00.00%0.00%
-15.55% to -8.01%00.00%0.00%
-8.01% to -0.47%00.00%0.00%
-0.47% to 7.07%8513.41%13.41%
7.07% to 14.60%31249.21%62.62%
14.60% to 22.14%15724.76%87.38%
22.14% to 29.68%457.10%94.48%
29.68% to 37.22%172.68%97.16%
37.22% to 44.76%81.26%98.42%
Greater than 44.76%101.58%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.55%24.66% 88.64%68.27%
±2σ -5.50%34.71% 96.37%95.45%
±3σ -15.55%44.76% 98.42%99.73%
Descriptive Statistics
Mean14.604%
Standard Error0.399%
Median12.463%
Mode7.595%
Standard Deviation10.051%
Sample Variance101.025%
Kurtosis19.74
Skewness3.53
Range98.804%
Minimum2.496%
Maximum101.300%
Count634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 14.604% 634 100.00% 14.604%
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 0.94. Further, an Excess Kurtosis of 5.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -26.37%20.32%0.32%
-26.37% to -19.85%10.16%0.47%
-19.85% to -13.34%203.15%3.63%
-13.34% to -6.82%10716.88%20.50%
-6.82% to -0.30%21133.28%53.79%
-0.30% to 6.21%18929.81%83.60%
6.21% to 12.73%6410.09%93.69%
12.73% to 19.24%233.63%97.32%
19.24% to 25.76%81.26%98.58%
Greater than 25.76%91.42%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.99%8.38% 76.97%68.27%
±2σ -17.68%17.07% 96.21%95.45%
±3σ -26.37%25.76% 98.26%99.73%
Descriptive Statistics
Mean-0.305%
Standard Error0.345%
Median-0.914%
Mode0.000%
Standard Deviation8.688%
Sample Variance75.476%
Kurtosis5.44
Skewness0.94
Range97.882%
Minimum-47.105%
Maximum50.777%
Count634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.703% 277 43.69% 2.929%
Negative -5.824% 352 55.52% -3.234%
Zero 0.000% 5 0.79% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.07. Further, an Excess Kurtosis of 1.40 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -39.83%00.00%0.00%
-39.83% to -28.94%41.90%1.90%
-28.94% to -18.05%146.64%8.53%
-18.05% to -7.17%219.95%18.48%
-7.17% to 3.72%6932.70%51.18%
3.72% to 14.61%6329.86%81.04%
14.61% to 25.49%2913.74%94.79%
25.49% to 36.38%73.32%98.10%
36.38% to 47.26%20.95%99.05%
Greater than 47.26%20.95%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.80%18.23% 75.83%68.27%
±2σ -25.31%32.75% 93.84%95.45%
±3σ -39.83%47.26% 99.05%99.73%
Descriptive Statistics
Mean3.719%
Standard Error0.999%
Median3.598%
Mode2.733%
Standard Deviation14.515%
Sample Variance210.682%
Kurtosis1.40
Skewness0.07
Range95.886%
Minimum-38.639%
Maximum57.247%
Count211
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.646% 135 63.98% 7.451%
Negative -10.362% 76 36.02% -3.732%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 18.51%
12 3 Years 22.25%
20 5 Years 21.92%
40 10 Years 21.23%
80 20 Years 21.86%
200 50 Years 22.51%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.40. Further, an Excess Kurtosis of 17.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.20%00.00%0.00%
-31.20% to -16.64%00.00%0.00%
-16.64% to -2.08%00.00%0.00%
-2.08% to 12.48%2210.38%10.38%
12.48% to 27.04%11654.72%65.09%
27.04% to 41.60%4923.11%88.21%
41.60% to 56.16%125.66%93.87%
56.16% to 70.72%52.36%96.23%
70.72% to 85.28%31.42%97.64%
Greater than 85.28%52.36%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 7.63%46.45% 90.09%68.27%
±2σ -11.78%65.86% 94.34%95.45%
±3σ -31.20%85.28% 97.64%99.73%
Descriptive Statistics
Mean27.039%
Standard Error1.333%
Median22.212%
Mode21.905%
Standard Deviation19.412%
Sample Variance376.827%
Kurtosis17.29
Skewness3.40
Range163.183%
Minimum7.981%
Maximum171.164%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 27.039% 212 100.00% 27.039%
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 1.30. Further, an Excess Kurtosis of 2.90 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -45.78%00.00%0.00%
-45.78% to -34.57%10.47%0.47%
-34.57% to -23.36%52.36%2.83%
-23.36% to -12.15%3416.04%18.87%
-12.15% to -0.94%8540.09%58.96%
-0.94% to 10.26%5525.94%84.91%
10.26% to 21.47%136.13%91.04%
21.47% to 32.68%94.25%95.28%
32.68% to 43.89%73.30%98.58%
Greater than 43.89%31.42%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.89%14.00% 78.30%68.27%
±2σ -30.84%28.95% 93.87%95.45%
±3σ -45.78%43.89% 98.58%99.73%
Descriptive Statistics
Mean-0.945%
Standard Error1.026%
Median-2.971%
Mode-14.286%
Standard Deviation14.945%
Sample Variance223.363%
Kurtosis2.90
Skewness1.30
Range98.410%
Minimum-35.170%
Maximum63.240%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.195% 79 37.26% 4.917%
Negative -9.344% 133 62.74% -5.862%
Zero 0.000% 0 0.00% 0.000%