Markets Data Volatility Heatmap Portfolio Calculator

AXP Deep Analytical Report

American Express Company | Category: Equity Mega Cap | Ann. Div Yield: 1.11% ($3.28) | Last Updated: 2026-03-24 | Data Range: 1973-05-01 → 2026-03-01 (635 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 2.19% 1.80% 1.73% 2.41% 2.23% 2.31% 294.98 308.41 288.48 315.36
Weekly 4.78% 4.63% 4.67% 5.86% 4.90% 5.08% 287.19 316.77 273.45 332.69
Monthly 8.96% 10.05% 8.70% 12.37% 10.20% 10.58% 272.36 334.02 245.94 369.91
Quarterly 14.56% 19.38% 14.99% 22.57% 17.68% 18.33% 252.75 359.93 211.80 429.52
Annual — — — — 35.35% 36.66% 211.80 429.52 148.73 611.66
Option Time Horizon — — — — 13.34% 13.84% 263.94 344.67 230.98 393.87
Calculation Notes: Computed at 2026-03-23T16:32 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $301.62  |  Strike (K): $310.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $13.0500 (Bid $12.7500 / Ask $13.3500)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 1.11%  |  Binomial IV (Annual): 35.35% (CRR binomial tree, American, n=20 steps)  |  BS IV: 35.78% (European Black-Scholes)  |  Yahoo IV (Annual): 36.66% → 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 10.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.49%920.69%0.69%
-6.49% to -4.85%1160.87%1.56%
-4.85% to -3.21%4453.34%4.90%
-3.21% to -1.57%151711.38%16.28%
-1.57% to 0.07%479035.93%52.21%
0.07% to 1.70%423831.79%83.99%
1.70% to 3.34%144610.85%94.84%
3.34% to 4.98%4353.26%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% 78.36%68.27%
±2σ -4.30%4.44% 95.23%95.45%
±3σ -6.49%6.62% 98.51%99.73%
Descriptive Statistics
Mean0.065%
Standard Error0.019%
Median0.000%
Mode0.000%
Standard Deviation2.185%
Sample Variance4.775%
Kurtosis10.00
Skewness0.28
Range48.112%
Minimum-26.230%
Maximum21.882%
Count13332
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.596% 6475 48.57% 0.775%
Negative -1.508% 6276 47.08% -0.710%
Zero 0.000% 581 4.36% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.47%
20 1 Month 2.96%
60 1 Quarter 2.70%
250 1 Year 2.54%
750 3 Years 2.19%
1,250 5 Years 2.41%
2,500 10 Years 2.29%
5,000 20 Years 2.55%
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 48.99 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 -0.29%00.00%0.00%
-0.29% to 1.06%157511.81%11.81%
1.06% to 2.41%697452.31%64.12%
2.41% to 3.77%300722.55%86.67%
3.77% to 5.12%9947.46%94.13%
5.12% to 6.47%3932.95%97.07%
6.47% to 7.83%1671.25%98.33%
Greater than 7.83%2231.67%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.61%4.22% 89.33%68.27%
±2σ -1.20%6.02% 96.35%95.45%
±3σ -3.00%7.83% 98.33%99.73%
Descriptive Statistics
Mean2.413%
Standard Error0.016%
Median1.940%
Mode1.754%
Standard Deviation1.805%
Sample Variance3.259%
Kurtosis48.99
Skewness4.56
Range40.713%
Minimum0.251%
Maximum40.964%
Count13333
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.413% 13333 100.00% 2.413%
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 11.64 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 -2.56%4423.32%5.09%
-2.56% to -1.26%148611.15%16.23%
-1.26% to 0.04%501937.64%53.87%
0.04% to 1.34%395629.67%83.54%
1.34% to 2.64%155111.63%95.18%
2.64% to 3.94%3952.96%98.14%
3.94% to 5.24%1491.12%99.26%
Greater than 5.24%990.74%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.69%1.77% 78.64%68.27%
±2σ -3.42%3.50% 95.05%95.45%
±3σ -5.15%5.24% 98.57%99.73%
Descriptive Statistics
Mean0.042%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.731%
Sample Variance2.996%
Kurtosis11.64
Skewness0.39
Range41.271%
Minimum-13.493%
Maximum27.778%
Count13333
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.295% 6237 46.78% 0.606%
Negative -1.270% 5921 44.41% -0.564%
Zero 0.000% 1175 8.81% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.25. 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%311.12%1.70%
-10.44% to -6.86%963.48%5.18%
-6.86% to -3.27%33112.00%17.18%
-3.27% to 0.32%91133.02%50.20%
0.32% to 3.90%89632.48%82.67%
3.90% to 7.49%33011.96%94.64%
7.49% to 11.08%943.41%98.04%
11.08% to 14.66%321.16%99.20%
Greater than 14.66%220.80%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.47%5.10% 77.06%68.27%
±2σ -9.25%9.88% 94.85%95.45%
±3σ -14.03%14.66% 98.62%99.73%
Descriptive Statistics
Mean0.316%
Standard Error0.091%
Median0.303%
Mode0.000%
Standard Deviation4.782%
Sample Variance22.866%
Kurtosis5.51
Skewness0.25
Range71.130%
Minimum-36.170%
Maximum34.960%
Count2759
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.511% 1448 52.48% 1.843%
Negative -3.356% 1255 45.49% -1.527%
Zero 0.000% 56 2.03% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 6.70%
12 1 Quarter 6.46%
52 1 Year 6.21%
156 3 Years 5.28%
260 5 Years 5.86%
520 10 Years 5.49%
1,040 20 Years 6.00%
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 -7.42%00.00%0.00%
-7.42% to -3.94%00.00%0.00%
-3.94% to -0.47%00.00%0.00%
-0.47% to 3.00%39914.46%14.46%
3.00% to 6.48%137649.86%64.31%
6.48% to 9.95%59421.52%85.83%
9.95% to 13.43%2288.26%94.09%
13.43% to 16.90%853.08%97.17%
16.90% to 20.38%361.30%98.48%
Greater than 20.38%421.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.85%11.11% 87.50%68.27%
±2σ -2.79%15.75% 96.41%95.45%
±3σ -7.42%20.38% 98.48%99.73%
Descriptive Statistics
Mean6.479%
Standard Error0.088%
Median5.373%
Mode5.000%
Standard Deviation4.633%
Sample Variance21.461%
Kurtosis29.47
Skewness3.85
Range69.538%
Minimum1.050%
Maximum70.588%
Count2760
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.479% 2760 100.00% 6.479%
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 -13.96%100.36%0.36%
-13.96% to -10.46%270.98%1.34%
-10.46% to -6.95%873.15%4.49%
-6.95% to -3.45%34912.64%17.14%
-3.45% to 0.06%100836.52%53.66%
0.06% to 3.56%82830.00%83.66%
3.56% to 7.07%30210.94%94.60%
7.07% to 10.58%873.15%97.75%
10.58% to 14.08%391.41%99.17%
Greater than 14.08%230.83%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.62%4.73% 77.46%68.27%
±2σ -9.29%9.41% 94.75%95.45%
±3σ -13.96%14.08% 98.80%99.73%
Descriptive Statistics
Mean0.059%
Standard Error0.089%
Median-0.112%
Mode0.000%
Standard Deviation4.674%
Sample Variance21.845%
Kurtosis13.81
Skewness1.24
Range87.211%
Minimum-26.100%
Maximum61.111%
Count2760
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.527% 1288 46.67% 1.646%
Negative -3.118% 1405 50.91% -1.587%
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 1.26. Further, an Excess Kurtosis of 15.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.59%60.95%0.95%
-25.59% to -18.87%50.79%1.74%
-18.87% to -12.16%274.26%5.99%
-12.16% to -5.44%7011.04%17.03%
-5.44% to 1.28%20732.65%49.68%
1.28% to 7.99%20432.18%81.86%
7.99% to 14.71%9014.20%96.06%
14.71% 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 -7.68%10.23% 78.08%68.27%
±2σ -16.63%19.19% 95.74%95.45%
±3σ -25.59%28.14% 98.58%99.73%
Descriptive Statistics
Mean1.276%
Standard Error0.356%
Median1.281%
Mode0.000%
Standard Deviation8.955%
Sample Variance80.200%
Kurtosis15.05
Skewness1.26
Range119.915%
Minimum-32.406%
Maximum87.509%
Count634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.602% 364 57.41% 3.790%
Negative -5.993% 266 41.96% -2.514%
Zero 0.000% 4 0.63% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 12.01%
12 1 Year 12.63%
36 3 Years 11.45%
60 5 Years 12.37%
120 10 Years 11.87%
240 20 Years 12.64%
600 50 Years 13.04%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.52. Further, an Excess Kurtosis of 19.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.54%00.00%0.00%
-15.54% to -8.00%00.00%0.00%
-8.00% to -0.46%00.00%0.00%
-0.46% to 7.07%8613.54%13.54%
7.07% to 14.61%31148.98%62.52%
14.61% to 22.14%15824.88%87.40%
22.14% to 29.68%457.09%94.49%
29.68% to 37.22%172.68%97.17%
37.22% to 44.75%81.26%98.43%
Greater than 44.75%101.57%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.56%24.66% 88.66%68.27%
±2σ -5.49%34.70% 96.38%95.45%
±3σ -15.53%44.75% 98.43%99.73%
Descriptive Statistics
Mean14.609%
Standard Error0.399%
Median12.465%
Mode7.595%
Standard Deviation10.048%
Sample Variance100.961%
Kurtosis19.73
Skewness3.52
Range98.804%
Minimum2.496%
Maximum101.300%
Count635
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 14.609% 635 100.00% 14.609%
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 5.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -26.38%20.31%0.31%
-26.38% to -19.86%10.16%0.47%
-19.86% to -13.33%203.15%3.62%
-13.33% to -6.81%10716.85%20.47%
-6.81% to -0.28%21333.54%54.02%
-0.28% to 6.24%18829.61%83.62%
6.24% to 12.76%639.92%93.54%
12.76% to 19.29%243.78%97.32%
19.29% to 25.81%81.26%98.58%
Greater than 25.81%91.42%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.98%8.41% 77.01%68.27%
±2σ -17.68%17.11% 96.22%95.45%
±3σ -26.38%25.81% 98.27%99.73%
Descriptive Statistics
Mean-0.285%
Standard Error0.345%
Median-0.912%
Mode0.000%
Standard Deviation8.698%
Sample Variance75.651%
Kurtosis5.39
Skewness0.94
Range97.882%
Minimum-47.105%
Maximum50.777%
Count635
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.723% 278 43.78% 2.943%
Negative -5.824% 352 55.43% -3.228%
Zero 0.000% 5 0.79% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of 1.35 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -40.02%00.00%0.00%
-40.02% to -29.10%41.90%1.90%
-29.10% to -18.18%146.64%8.53%
-18.18% to -7.26%2210.43%18.96%
-7.26% to 3.66%6731.75%50.71%
3.66% to 14.58%6430.33%81.04%
14.58% to 25.50%2913.74%94.79%
25.50% to 36.42%73.32%98.10%
36.42% to 47.34%20.95%99.05%
Greater than 47.34%20.95%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.90%18.22% 75.36%68.27%
±2σ -25.46%32.78% 93.84%95.45%
±3σ -40.02%47.34% 99.05%99.73%
Descriptive Statistics
Mean3.660%
Standard Error1.002%
Median3.598%
Mode2.733%
Standard Deviation14.561%
Sample Variance212.030%
Kurtosis1.35
Skewness0.08
Range95.886%
Minimum-38.639%
Maximum57.247%
Count211
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.646% 135 63.98% 7.451%
Negative -10.524% 76 36.02% -3.791%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 21.73%
12 3 Years 23.32%
20 5 Years 22.57%
40 10 Years 21.55%
80 20 Years 22.03%
200 50 Years 22.57%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.41. Further, an Excess Kurtosis of 17.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.01%00.00%0.00%
-31.01% to -16.48%00.00%0.00%
-16.48% to -1.94%00.00%0.00%
-1.94% to 12.59%2210.38%10.38%
12.59% to 27.12%11755.19%65.57%
27.12% to 41.65%4822.64%88.21%
41.65% to 56.18%125.66%93.87%
56.18% to 70.72%52.36%96.23%
70.72% to 85.25%31.42%97.64%
Greater than 85.25%52.36%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 7.74%46.50% 90.09%68.27%
±2σ -11.63%65.87% 94.34%95.45%
±3σ -31.01%85.25% 97.64%99.73%
Descriptive Statistics
Mean27.120%
Standard Error1.331%
Median22.289%
Mode21.905%
Standard Deviation19.376%
Sample Variance375.428%
Kurtosis17.38
Skewness3.41
Range163.183%
Minimum7.981%
Maximum171.164%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 27.120% 212 100.00% 27.120%
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 1.28. Further, an Excess Kurtosis of 2.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -45.84%00.00%0.00%
-45.84% to -34.60%10.47%0.47%
-34.60% to -23.36%52.36%2.83%
-23.36% to -12.12%3416.04%18.87%
-12.12% to -0.88%8540.09%58.96%
-0.88% to 10.36%5525.94%84.91%
10.36% to 21.61%136.13%91.04%
21.61% to 32.85%94.25%95.28%
32.85% to 44.09%73.30%98.58%
Greater than 44.09%31.42%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.87%14.11% 77.83%68.27%
±2σ -30.85%29.10% 93.87%95.45%
±3σ -45.84%44.09% 98.58%99.73%
Descriptive Statistics
Mean-0.877%
Standard Error1.029%
Median-2.971%
Mode-14.286%
Standard Deviation14.988%
Sample Variance224.641%
Kurtosis2.82
Skewness1.28
Range98.410%
Minimum-35.170%
Maximum63.240%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.377% 79 37.26% 4.985%
Negative -9.344% 133 62.74% -5.862%
Zero 0.000% 0 0.00% 0.000%