Markets Data Volatility Heatmap Portfolio Calculator

TRV Deep Analytical Report

The Travelers Companies, Inc. | Category: Equity Mega Cap | Ann. Div Yield: 1.45% ($4.35) | Last Updated: 2026-02-22 | Data Range: 1976-01-01 → 2026-02-01 (602 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 1.72% 1.49% 1.44% 1.93% 1.36% 1.57% 300.80 309.11 296.73 313.36
Weekly 3.83% 4.16% 4.27% 4.37% 3.00% 3.46% 295.92 314.22 287.17 323.79
Monthly 7.48% 9.10% 8.33% 9.37% 6.25% 7.19% 286.47 324.58 269.12 345.50
Quarterly 11.48% 16.80% 14.45% 14.87% 10.82% 12.46% 273.67 339.77 245.61 378.58
Annual — — — — 21.63% 24.92% 245.61 378.58 197.83 470.02
Option Time Horizon — — — — 8.32% 9.59% 280.58 331.39 258.18 360.15
Calculation Notes: Computed at 2026-02-22T14:19 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $304.93  |  Strike (K): $310.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $8.4000 (Bid $7.3000 / Ask $9.5000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 1.45%  |  Binomial IV (Annual): 21.63% (CRR binomial tree, American, n=20 steps)  |  BS IV: 21.89% (European Black-Scholes)  |  Yahoo IV (Annual): 24.92% → 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
2025-12-10 $1.1000
2025-09-10 $1.1000
2025-06-10 $1.1000
2025-03-10 $1.0500
2024-12-10 $1.0500
2024-09-10 $1.0500
2024-06-10 $1.0500
2024-03-07 $1.0000
2023-12-07 $1.0000
2023-09-07 $1.0000
2023-06-08 $1.0000
2023-03-09 $0.9300
2022-12-08 $0.9300
2022-09-08 $0.9300
2022-06-09 $0.9300
2022-03-09 $0.8800
2021-12-09 $0.8800
2021-09-09 $0.8800
2021-06-09 $0.8800
2021-03-09 $0.8500
2020-12-09 $0.8500
2020-09-09 $0.8500
2020-06-09 $0.8500
2020-03-09 $0.8200
2019-12-09 $0.8200
2019-09-09 $0.8200
2019-06-07 $0.8200
2019-03-08 $0.7700
2018-12-07 $0.7700
2018-09-07 $0.7700
2018-06-07 $0.7700
2018-03-08 $0.7200
2017-12-08 $0.7200
2017-09-07 $0.7200
2017-06-07 $0.7200
2017-03-08 $0.6700
2016-12-07 $0.6700
2016-09-07 $0.6700
2016-06-08 $0.6700
2016-03-08 $0.6100
2015-12-08 $0.6100
2015-09-08 $0.6100
2015-06-08 $0.6100
2015-03-06 $0.5500
2014-12-08 $0.5500
2014-09-08 $0.5500
2014-06-06 $0.5500
2014-03-06 $0.5000
2013-12-06 $0.5000
2013-09-06 $0.5000
2013-06-06 $0.5000
2013-03-06 $0.4600
2012-12-06 $0.4600
2012-09-06 $0.4600
2012-06-06 $0.4600
2012-03-07 $0.4100
2011-12-07 $0.4100
2011-09-07 $0.4100
2011-06-08 $0.4100
2011-03-08 $0.3600
2010-12-08 $0.3600
2010-09-08 $0.3600
2010-06-08 $0.3600
2010-03-08 $0.3300
2009-12-08 $0.3300
2009-09-08 $0.3000
2009-06-08 $0.3000
2009-03-06 $0.3000
2008-12-08 $0.3000
2008-09-08 $0.3000
2008-06-06 $0.3000
2008-03-06 $0.2900
2007-12-06 $0.2900
2007-09-06 $0.2900
2007-06-06 $0.2900
2007-03-07 $0.2600
2006-12-06 $0.2600
2006-09-06 $0.2600
2006-06-07 $0.2600
2006-03-08 $0.2300
2005-12-07 $0.2300
2005-09-07 $0.2300
2005-06-08 $0.2300
2005-03-08 $0.2200
2004-12-08 $0.2200
2004-09-08 $0.2200
2004-06-08 $0.2200
2004-04-02 $0.2100
2004-03-29 $0.2900
2003-12-29 $0.2900
2003-09-26 $0.2900
2003-06-26 $0.2900
2003-03-27 $0.2900
2002-12-27 $0.2900
2002-09-26 $0.2900
2002-06-26 $0.2900
2002-03-26 $0.2900
2001-12-27 $0.2800
2001-09-26 $0.2800
2001-06-27 $0.2800
2001-03-28 $0.2800
2000-12-27 $0.2700
2000-09-27 $0.2700
2000-06-28 $0.2700
2000-03-29 $0.2700
1999-12-29 $0.2600
1999-09-28 $0.2600
1999-06-28 $0.2600
1999-03-29 $0.2600
1998-12-29 $0.2500
1998-09-28 $0.2500
1998-06-26 $0.2500
1998-03-27 $0.2500
1997-12-29 $0.2350
1997-09-26 $0.2350
1997-06-26 $0.2350
1997-03-26 $0.2350
1996-12-27 $0.2200
1996-09-26 $0.2200
1996-06-26 $0.2200
1996-03-27 $0.2200
1995-12-27 $0.2000
1995-09-27 $0.2000
1995-06-28 $0.2000
1995-03-27 $0.2000
1994-12-23 $0.1875
1994-09-26 $0.1875
1994-06-24 $0.1875
1994-03-25 $0.1875
1993-12-27 $0.1750
1993-09-24 $0.1750
1993-06-24 $0.1750
1993-03-25 $0.1750
1992-12-24 $0.1700
1992-09-24 $0.1700
1992-06-24 $0.1700
1992-03-25 $0.1700
1991-12-24 $0.1625
1991-09-24 $0.1625
1991-06-24 $0.1625
1991-03-22 $0.1625
1990-12-24 $0.1500
1990-09-24 $0.1500
1990-06-25 $0.1500
1990-03-26 $0.1500
1989-12-22 $0.1375
1989-09-25 $0.1375
1989-06-26 $0.1375
1989-03-27 $0.1375
1988-12-23 $0.1250
1988-09-26 $0.1250
1988-06-24 $0.1250
1988-03-25 $0.1250
1987-12-24 $0.1100
1987-08-24 $0.0440
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Highly Left Skewed (Extreme Negative Tail Risk) with a Skewness factor of -2.06. Further, an Excess Kurtosis of 81.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.09%750.59%0.59%
-5.09% to -3.81%1140.90%1.50%
-3.81% to -2.52%3552.81%4.31%
-2.52% to -1.23%133010.54%14.86%
-1.23% to 0.05%472637.47%52.33%
0.05% to 1.34%417433.09%85.42%
1.34% to 2.63%12569.96%95.38%
2.63% to 3.91%3783.00%98.37%
3.91% to 5.20%1240.98%99.36%
Greater than 5.20%810.64%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.66%1.77% 80.73%68.27%
±2σ -3.38%3.48% 95.70%95.45%
±3σ -5.09%5.20% 98.76%99.73%
Descriptive Statistics
Mean0.053%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.715%
Sample Variance2.941%
Kurtosis81.21
Skewness-2.06
Range77.633%
Minimum-52.078%
Maximum25.555%
Count12613
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.186% 6129 48.59% 0.576%
Negative -1.167% 5661 44.88% -0.524%
Zero 0.000% 823 6.53% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.87%
20 1 Month 2.11%
60 1 Quarter 1.78%
250 1 Year 1.96%
750 3 Years 1.86%
1,250 5 Years 1.93%
2,500 10 Years 1.89%
5,000 20 Years 2.03%
12,500 50 Years 2.01%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.62. Further, an Excess Kurtosis of 42.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.62%00.00%0.00%
-2.62% to -1.50%00.00%0.00%
-1.50% to -0.38%00.00%0.00%
-0.38% to 0.74%142011.26%11.26%
0.74% to 1.86%704755.87%67.12%
1.86% to 2.98%252019.98%87.10%
2.98% to 4.09%8857.02%94.12%
4.09% to 5.21%3712.94%97.06%
5.21% to 6.33%1651.31%98.37%
Greater than 6.33%2061.63%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.37%3.35% 87.78%68.27%
±2σ -1.13%4.84% 96.28%95.45%
±3σ -2.62%6.33% 98.37%99.73%
Descriptive Statistics
Mean1.857%
Standard Error0.013%
Median1.493%
Mode1.527%
Standard Deviation1.491%
Sample Variance2.223%
Kurtosis42.21
Skewness4.62
Range28.379%
Minimum0.179%
Maximum28.558%
Count12614
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.857% 12614 100.00% 1.857%
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 0.43. Further, an Excess Kurtosis of 14.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.27%910.72%0.72%
-4.27% to -3.20%1641.30%2.02%
-3.20% to -2.12%3793.00%5.03%
-2.12% to -1.04%129910.30%15.32%
-1.04% to 0.03%497239.42%54.74%
0.03% to 1.11%373529.61%84.35%
1.11% to 2.18%140011.10%95.45%
2.18% to 3.26%3672.91%98.36%
3.26% to 4.34%1100.87%99.23%
Greater than 4.34%970.77%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.40%1.47% 79.61%68.27%
±2σ -2.84%2.90% 94.98%95.45%
±3σ -4.27%4.34% 98.51%99.73%
Descriptive Statistics
Mean0.031%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.435%
Sample Variance2.059%
Kurtosis14.34
Skewness0.43
Range33.110%
Minimum-12.832%
Maximum20.278%
Count12614
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.048% 5776 45.79% 0.480%
Negative -1.068% 5308 42.08% -0.449%
Zero 0.000% 1530 12.13% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.98. Further, an Excess Kurtosis of 19.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.23%100.38%0.38%
-11.23% to -8.36%261.00%1.38%
-8.36% to -5.49%873.33%4.71%
-5.49% to -2.61%30911.83%16.54%
-2.61% to 0.26%90934.80%51.34%
0.26% to 3.13%83632.01%83.35%
3.13% to 6.00%29511.29%94.64%
6.00% to 8.87%823.14%97.78%
8.87% to 11.74%381.45%99.23%
Greater than 11.74%200.77%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.57%4.08% 77.87%68.27%
±2σ -7.40%7.91% 94.83%95.45%
±3σ -11.23%11.74% 98.85%99.73%
Descriptive Statistics
Mean0.257%
Standard Error0.075%
Median0.160%
Mode0.000%
Standard Deviation3.828%
Sample Variance14.653%
Kurtosis19.33
Skewness-0.98
Range73.681%
Minimum-54.593%
Maximum19.088%
Count2612
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.788% 1352 51.76% 1.443%
Negative -2.554% 1213 46.44% -1.186%
Zero 0.000% 47 1.80% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.61%
12 1 Quarter 4.06%
52 1 Year 4.44%
156 3 Years 4.30%
260 5 Years 4.37%
520 10 Years 4.32%
1,040 20 Years 4.52%
2,600 50 Years 4.83%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 10.26. Further, an Excess Kurtosis of 237.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.56%00.00%0.00%
-7.56% to -4.44%00.00%0.00%
-4.44% to -1.32%00.00%0.00%
-1.32% to 1.80%1586.05%6.05%
1.80% to 4.92%150157.44%63.49%
4.92% to 8.04%65124.91%88.40%
8.04% to 11.16%1786.81%95.22%
11.16% to 14.28%672.56%97.78%
14.28% to 17.39%240.92%98.70%
Greater than 17.39%341.30%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.76%9.08% 91.01%68.27%
±2σ -3.40%13.24% 97.36%95.45%
±3σ -7.56%17.39% 98.70%99.73%
Descriptive Statistics
Mean4.918%
Standard Error0.081%
Median3.981%
Mode2.564%
Standard Deviation4.159%
Sample Variance17.298%
Kurtosis237.30
Skewness10.26
Range119.814%
Minimum0.535%
Maximum120.349%
Count2613
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.918% 2613 100.00% 4.918%
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 8.75. Further, an Excess Kurtosis of 235.68 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.81%90.34%0.34%
-12.81% to -9.61%230.88%1.22%
-9.61% to -6.41%552.10%3.33%
-6.41% to -3.21%28110.75%14.08%
-3.21% to -0.01%97237.20%51.28%
-0.01% to 3.19%90434.60%85.88%
3.19% to 6.39%28310.83%96.71%
6.39% to 9.59%572.18%98.89%
9.59% to 12.79%200.77%99.66%
Greater than 12.79%90.34%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.28%4.25% 82.24%68.27%
±2σ -8.55%8.52% 96.71%95.45%
±3σ -12.81%12.79% 99.31%99.73%
Descriptive Statistics
Mean-0.013%
Standard Error0.083%
Median-0.136%
Mode0.000%
Standard Deviation4.267%
Sample Variance18.212%
Kurtosis235.68
Skewness8.75
Range134.687%
Minimum-15.612%
Maximum119.075%
Count2613
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.728% 1223 46.80% 1.277%
Negative -2.511% 1342 51.36% -1.290%
Zero 0.000% 48 1.84% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.06. Further, an Excess Kurtosis of 9.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -21.36%30.50%0.50%
-21.36% to -15.75%50.83%1.33%
-15.75% to -10.14%243.99%5.32%
-10.14% to -4.53%8213.64%18.97%
-4.53% to 1.07%16527.45%46.42%
1.07% to 6.68%22136.77%83.19%
6.68% to 12.29%8013.31%96.51%
12.29% to 17.90%122.00%98.50%
17.90% to 23.51%50.83%99.33%
Greater than 23.51%40.67%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.40%8.55% 77.87%68.27%
±2σ -13.88%16.03% 95.67%95.45%
±3σ -21.36%23.51% 98.84%99.73%
Descriptive Statistics
Mean1.075%
Standard Error0.305%
Median1.594%
Mode0.000%
Standard Deviation7.479%
Sample Variance55.929%
Kurtosis9.06
Skewness-0.06
Range107.369%
Minimum-53.470%
Maximum53.899%
Count601
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.523% 356 59.23% 3.272%
Negative -5.570% 237 39.43% -2.196%
Zero 0.000% 8 1.33% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 7.26%
12 1 Year 8.49%
36 3 Years 9.22%
60 5 Years 9.37%
120 10 Years 9.45%
240 20 Years 9.52%
600 50 Years 10.70%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.35. Further, an Excess Kurtosis of 67.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.78%00.00%0.00%
-15.78% to -8.95%00.00%0.00%
-8.95% to -2.12%00.00%0.00%
-2.12% to 4.70%345.65%5.65%
4.70% to 11.53%36861.13%66.78%
11.53% to 18.36%13522.43%89.20%
18.36% to 25.18%396.48%95.68%
25.18% to 32.01%162.66%98.34%
32.01% to 38.84%30.50%98.84%
Greater than 38.84%71.16%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.43%20.63% 91.86%68.27%
±2σ -6.67%29.73% 97.84%95.45%
±3σ -15.78%38.84% 98.84%99.73%
Descriptive Statistics
Mean11.531%
Standard Error0.371%
Median9.514%
Mode16.667%
Standard Deviation9.102%
Sample Variance82.845%
Kurtosis67.88
Skewness6.35
Range133.886%
Minimum2.699%
Maximum136.585%
Count602
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.531% 602 100.00% 11.531%
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 4.55. Further, an Excess Kurtosis of 59.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.19%10.17%0.17%
-25.19% to -18.94%30.50%0.66%
-18.94% to -12.70%81.33%1.99%
-12.70% to -6.45%7412.29%14.29%
-6.45% to -0.20%25241.86%56.15%
-0.20% to 6.04%17829.57%85.71%
6.04% to 12.29%579.47%95.18%
12.29% to 18.53%213.49%98.67%
18.53% to 24.78%50.83%99.50%
Greater than 24.78%30.50%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.53%8.12% 83.06%68.27%
±2σ -16.86%16.45% 96.51%95.45%
±3σ -25.19%24.78% 99.34%99.73%
Descriptive Statistics
Mean-0.204%
Standard Error0.339%
Median-1.198%
Mode0.000%
Standard Deviation8.328%
Sample Variance69.356%
Kurtosis59.81
Skewness4.55
Range148.431%
Minimum-34.066%
Maximum114.365%
Count602
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.204% 251 41.69% 2.587%
Negative -4.911% 342 56.81% -2.790%
Zero 0.000% 9 1.50% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.53. Further, an Excess Kurtosis of 5.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -31.35%21.00%1.00%
-31.35% to -22.74%10.50%1.49%
-22.74% to -14.14%52.49%3.98%
-14.14% to -5.53%2914.43%18.41%
-5.53% to 3.08%6130.35%48.76%
3.08% to 11.69%6532.34%81.09%
11.69% to 20.29%2914.43%95.52%
20.29% to 28.90%83.98%99.50%
28.90% to 37.51%00.00%99.50%
Greater than 37.51%10.50%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.40%14.56% 77.11%68.27%
±2σ -19.88%26.03% 97.01%95.45%
±3σ -31.35%37.51% 98.51%99.73%
Descriptive Statistics
Mean3.079%
Standard Error0.809%
Median3.409%
Mode-57.963%
Standard Deviation11.477%
Sample Variance131.713%
Kurtosis5.60
Skewness-0.53
Range112.508%
Minimum-57.963%
Maximum54.545%
Count201
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 9.238% 128 63.68% 5.883%
Negative -7.827% 72 35.82% -2.804%
Zero 0.000% 1 0.50% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 11.11%
12 3 Years 15.03%
20 5 Years 14.87%
40 10 Years 16.00%
80 20 Years 16.20%
200 50 Years 18.63%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.57. Further, an Excess Kurtosis of 28.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -29.09%00.00%0.00%
-29.09% to -16.48%00.00%0.00%
-16.48% to -3.88%00.00%0.00%
-3.88% to 8.72%62.97%2.97%
8.72% to 21.32%13466.34%69.31%
21.32% to 33.92%4823.76%93.07%
33.92% to 46.52%52.48%95.54%
46.52% to 59.12%31.49%97.03%
59.12% to 71.73%20.99%98.02%
Greater than 71.73%41.98%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.52%38.12% 94.06%68.27%
±2σ -12.28%54.92% 96.53%95.45%
±3σ -29.09%71.73% 98.02%99.73%
Descriptive Statistics
Mean21.320%
Standard Error1.182%
Median17.569%
Mode10.705%
Standard Deviation16.802%
Sample Variance282.316%
Kurtosis28.03
Skewness4.57
Range152.588%
Minimum3.906%
Maximum156.494%
Count202
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 21.320% 202 100.00% 21.320%
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 4.91. Further, an Excess Kurtosis of 43.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -44.23%00.00%0.00%
-44.23% to -33.39%10.50%0.50%
-33.39% to -22.55%00.00%0.50%
-22.55% to -11.72%2411.88%12.38%
-11.72% to -0.88%9346.04%58.42%
-0.88% to 9.95%6029.70%88.12%
9.95% to 20.79%209.90%98.02%
20.79% to 31.62%10.50%98.51%
31.62% to 42.46%00.00%98.51%
Greater than 42.46%31.49%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.33%13.57% 86.63%68.27%
±2σ -29.78%28.01% 97.52%95.45%
±3σ -44.23%42.46% 98.51%99.73%
Descriptive Statistics
Mean-0.883%
Standard Error1.017%
Median-2.380%
Mode-34.244%
Standard Deviation14.448%
Sample Variance208.734%
Kurtosis43.12
Skewness4.91
Range172.132%
Minimum-34.244%
Maximum137.888%
Count202
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.179% 76 37.62% 3.830%
Negative -7.616% 125 61.88% -4.713%
Zero 0.000% 1 0.49% 0.000%