Markets Data Volatility Heatmap Portfolio Calculator

TRV Deep Analytical Report

The Travelers Companies, Inc. | Category: Equity Mega Cap | Ann. Div Yield: 1.47% ($4.35) | Last Updated: 2026-03-24 | Data Range: 1976-01-01 → 2026-03-01 (603 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 1.71% 1.49% 1.43% 1.92% 1.76% 1.90% 292.29 302.78 287.19 308.16
Weekly 3.83% 4.16% 4.26% 4.35% 3.88% 4.18% 286.17 309.26 275.28 321.49
Monthly 7.48% 9.10% 8.32% 9.32% 8.07% 8.71% 274.41 322.51 253.13 349.63
Quarterly 11.47% 16.79% 14.44% 15.01% 13.99% 15.08% 258.66 342.15 224.90 393.50
Annual — — — — 27.97% 30.16% 224.90 393.50 170.03 520.51
Option Time Horizon — — — — 10.56% 11.38% 267.68 330.62 240.86 367.43
Calculation Notes: Computed at 2026-03-23T16:34 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $297.49  |  Strike (K): $300.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $11.8000 (Bid $11.0000 / Ask $12.6000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 1.47%  |  Binomial IV (Annual): 27.97% (CRR binomial tree, American, n=20 steps)  |  BS IV: 28.03% (European Black-Scholes)  |  Yahoo IV (Annual): 30.16% → 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
2026-03-10 $1.1000
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 81.28 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 -3.80%1140.90%1.50%
-3.80% to -2.52%3552.81%4.31%
-2.52% to -1.23%133210.54%14.85%
-1.23% to 0.05%473237.45%52.30%
0.05% to 1.34%418533.12%85.43%
1.34% to 2.62%12579.95%95.38%
2.62% to 3.91%3782.99%98.37%
3.91% to 5.19%1250.99%99.36%
Greater than 5.19%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%5.19% 98.77%99.73%
Descriptive Statistics
Mean0.052%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.714%
Sample Variance2.937%
Kurtosis81.28
Skewness-2.06
Range77.633%
Minimum-52.078%
Maximum25.555%
Count12634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.184% 6142 48.62% 0.576%
Negative -1.167% 5669 44.87% -0.524%
Zero 0.000% 823 6.51% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.88%
20 1 Month 2.00%
60 1 Quarter 1.97%
250 1 Year 1.94%
750 3 Years 1.84%
1,250 5 Years 1.92%
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 4.63. Further, an Excess Kurtosis of 42.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.61%00.00%0.00%
-2.61% to -1.50%00.00%0.00%
-1.50% to -0.38%00.00%0.00%
-0.38% to 0.74%142311.26%11.26%
0.74% to 1.86%705355.82%67.08%
1.86% to 2.97%253020.02%87.11%
2.97% to 4.09%8877.02%94.13%
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% 87.77%68.27%
±2σ -1.12%4.84% 96.29%95.45%
±3σ -2.61%6.33% 98.37%99.73%
Descriptive Statistics
Mean1.857%
Standard Error0.013%
Median1.493%
Mode1.527%
Standard Deviation1.490%
Sample Variance2.220%
Kurtosis42.27
Skewness4.63
Range28.379%
Minimum0.179%
Maximum28.558%
Count12635
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.857% 12635 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 -3.19%1651.31%2.03%
-3.19% to -2.12%3793.00%5.03%
-2.12% to -1.04%130110.30%15.32%
-1.04% to 0.03%498139.42%54.74%
0.03% to 1.11%373829.58%84.33%
1.11% to 2.18%140611.13%95.46%
2.18% to 3.26%3672.90%98.36%
3.26% to 4.33%1100.87%99.23%
Greater than 4.33%970.77%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.40%1.46% 79.60%68.27%
±2σ -2.84%2.90% 94.96%95.45%
±3σ -4.27%4.33% 98.51%99.73%
Descriptive Statistics
Mean0.031%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.434%
Sample Variance2.057%
Kurtosis14.34
Skewness0.43
Range33.110%
Minimum-12.832%
Maximum20.278%
Count12635
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.048% 5786 45.79% 0.480%
Negative -1.067% 5319 42.10% -0.449%
Zero 0.000% 1530 12.11% 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 19.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.22%100.38%0.38%
-11.22% to -8.35%260.99%1.38%
-8.35% to -5.48%873.33%4.70%
-5.48% to -2.61%30911.81%16.51%
-2.61% to 0.26%91034.79%51.30%
0.26% to 3.12%83732.00%83.30%
3.12% to 6.00%29711.35%94.65%
6.00% to 8.86%823.13%97.78%
8.86% to 11.73%371.41%99.20%
Greater than 11.73%210.80%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.57%4.08% 77.91%68.27%
±2σ -7.40%7.91% 94.84%95.45%
±3σ -11.22%11.73% 98.81%99.73%
Descriptive Statistics
Mean0.256%
Standard Error0.075%
Median0.160%
Mode0.000%
Standard Deviation3.826%
Sample Variance14.637%
Kurtosis19.34
Skewness-0.98
Range73.681%
Minimum-54.593%
Maximum19.088%
Count2616
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.785% 1354 51.76% 1.441%
Negative -2.554% 1215 46.45% -1.186%
Zero 0.000% 47 1.80% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.34%
12 1 Quarter 4.53%
52 1 Year 4.41%
156 3 Years 4.28%
260 5 Years 4.35%
520 10 Years 4.33%
1,040 20 Years 4.52%
2,600 50 Years 4.82%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 10.27. Further, an Excess Kurtosis of 237.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.55%00.00%0.00%
-7.55% to -4.43%00.00%0.00%
-4.43% to -1.32%00.00%0.00%
-1.32% to 1.80%1586.04%6.04%
1.80% to 4.92%150457.47%63.51%
4.92% to 8.04%65224.91%88.42%
8.04% to 11.15%1786.80%95.22%
11.15% to 14.27%672.56%97.78%
14.27% 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%9.07% 91.02%68.27%
±2σ -3.39%13.23% 97.36%95.45%
±3σ -7.55%17.39% 98.70%99.73%
Descriptive Statistics
Mean4.918%
Standard Error0.081%
Median3.984%
Mode2.564%
Standard Deviation4.156%
Sample Variance17.272%
Kurtosis237.67
Skewness10.27
Range119.814%
Minimum0.535%
Maximum120.349%
Count2617
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.918% 2617 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 235.82 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%3.32%
-6.41% to -3.21%28110.74%14.06%
-3.21% to -0.01%97437.22%51.28%
-0.01% to 3.19%90534.58%85.86%
3.19% to 6.38%28410.85%96.71%
6.38% to 9.58%572.18%98.89%
9.58% to 12.78%200.76%99.66%
Greater than 12.78%90.34%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.28%4.25% 82.27%68.27%
±2σ -8.54%8.52% 96.68%95.45%
±3σ -12.81%12.78% 99.31%99.73%
Descriptive Statistics
Mean-0.012%
Standard Error0.083%
Median-0.136%
Mode0.000%
Standard Deviation4.265%
Sample Variance18.192%
Kurtosis235.82
Skewness8.75
Range134.687%
Minimum-15.612%
Maximum119.075%
Count2617
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.728% 1225 46.81% 1.277%
Negative -2.509% 1344 51.36% -1.289%
Zero 0.000% 48 1.83% 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 9.05 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 -4.54%8213.62%18.94%
-4.54% to 1.07%16627.57%46.51%
1.07% to 6.68%22136.71%83.22%
6.68% to 12.28%8013.29%96.51%
12.28% to 17.89%121.99%98.50%
17.89% to 23.50%50.83%99.34%
Greater than 23.50%40.66%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.41%8.55% 77.91%68.27%
±2σ -13.88%16.02% 95.68%95.45%
±3σ -21.36%23.50% 98.84%99.73%
Descriptive Statistics
Mean1.070%
Standard Error0.305%
Median1.591%
Mode0.000%
Standard Deviation7.476%
Sample Variance55.887%
Kurtosis9.05
Skewness-0.06
Range107.369%
Minimum-53.470%
Maximum53.899%
Count602
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.526% 356 59.14% 3.268%
Negative -5.561% 238 39.53% -2.199%
Zero 0.000% 8 1.33% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 7.92%
12 1 Year 8.56%
36 3 Years 9.08%
60 5 Years 9.32%
120 10 Years 9.44%
240 20 Years 9.53%
600 50 Years 10.69%
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 67.97 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.76%00.00%0.00%
-15.76% to -8.94%00.00%0.00%
-8.94% to -2.12%00.00%0.00%
-2.12% to 4.70%345.64%5.64%
4.70% to 11.53%36961.19%66.83%
11.53% to 18.35%13522.39%89.22%
18.35% to 25.17%396.47%95.69%
25.17% to 31.99%162.65%98.34%
31.99% to 38.81%30.50%98.84%
Greater than 38.81%71.16%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.43%20.62% 91.87%68.27%
±2σ -6.67%29.72% 97.84%95.45%
±3σ -15.76%38.81% 98.84%99.73%
Descriptive Statistics
Mean11.526%
Standard Error0.370%
Median9.513%
Mode16.667%
Standard Deviation9.096%
Sample Variance82.730%
Kurtosis67.97
Skewness6.35
Range133.886%
Minimum2.699%
Maximum136.585%
Count603
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.526% 603 100.00% 11.526%
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 4.54. Further, an Excess Kurtosis of 59.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.17%10.17%0.17%
-25.17% to -18.93%30.50%0.66%
-18.93% to -12.69%81.33%1.99%
-12.69% to -6.44%7512.44%14.43%
-6.44% to -0.20%25141.63%56.05%
-0.20% to 6.04%17929.68%85.74%
6.04% to 12.29%579.45%95.19%
12.29% to 18.53%213.48%98.67%
18.53% to 24.77%50.83%99.50%
Greater than 24.77%30.50%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.52%8.12% 83.08%68.27%
±2σ -16.85%16.45% 96.52%95.45%
±3σ -25.17%24.77% 99.34%99.73%
Descriptive Statistics
Mean-0.199%
Standard Error0.339%
Median-1.193%
Mode0.000%
Standard Deviation8.324%
Sample Variance69.288%
Kurtosis59.82
Skewness4.54
Range148.431%
Minimum-34.066%
Maximum114.365%
Count603
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.193% 252 41.79% 2.588%
Negative -4.915% 342 56.72% -2.788%
Zero 0.000% 9 1.49% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.52. Further, an Excess Kurtosis of 5.61 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 -22.75%10.50%1.49%
-22.75% to -14.14%52.49%3.98%
-14.14% to -5.54%2914.43%18.41%
-5.54% to 3.07%6130.35%48.76%
3.07% to 11.67%6532.34%81.09%
11.67% to 20.28%2914.43%95.52%
20.28% to 28.88%83.98%99.50%
28.88% to 37.48%00.00%99.50%
Greater than 37.48%10.50%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.41%14.54% 77.11%68.27%
±2σ -19.88%26.01% 97.01%95.45%
±3σ -31.35%37.49% 98.51%99.73%
Descriptive Statistics
Mean3.066%
Standard Error0.809%
Median3.409%
Mode-57.963%
Standard Deviation11.473%
Sample Variance131.639%
Kurtosis5.61
Skewness-0.52
Range112.508%
Minimum-57.963%
Maximum54.545%
Count201
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 9.217% 128 63.68% 5.870%
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 11.82%
12 3 Years 15.27%
20 5 Years 15.01%
40 10 Years 16.07%
80 20 Years 16.24%
200 50 Years 18.65%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.58. Further, an Excess Kurtosis of 28.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -29.04%00.00%0.00%
-29.04% to -16.45%00.00%0.00%
-16.45% to -3.85%00.00%0.00%
-3.85% to 8.74%52.48%2.48%
8.74% to 21.34%13566.83%69.31%
21.34% to 33.93%4823.76%93.07%
33.93% to 46.52%52.48%95.54%
46.52% to 59.12%31.49%97.03%
59.12% to 71.71%20.99%98.02%
Greater than 71.71%41.98%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.54%38.13% 94.06%68.27%
±2σ -12.25%54.92% 96.53%95.45%
±3σ -29.04%71.71% 98.02%99.73%
Descriptive Statistics
Mean21.335%
Standard Error1.181%
Median17.569%
Mode10.705%
Standard Deviation16.792%
Sample Variance281.964%
Kurtosis28.09
Skewness4.58
Range152.588%
Minimum3.906%
Maximum156.494%
Count202
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 21.335% 202 100.00% 21.335%
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 43.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -44.20%00.00%0.00%
-44.20% to -33.37%10.50%0.50%
-33.37% to -22.54%00.00%0.50%
-22.54% to -11.70%2411.88%12.38%
-11.70% to -0.87%9346.04%58.42%
-0.87% to 9.96%6029.70%88.12%
9.96% to 20.80%209.90%98.02%
20.80% to 31.63%10.50%98.51%
31.63% 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 -15.32%13.57% 86.63%68.27%
±2σ -29.76%28.02% 97.52%95.45%
±3σ -44.20%42.46% 98.51%99.73%
Descriptive Statistics
Mean-0.871%
Standard Error1.016%
Median-2.380%
Mode-34.244%
Standard Deviation14.444%
Sample Variance208.636%
Kurtosis43.15
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 -7.597% 125 61.88% -4.701%
Zero 0.000% 1 0.49% 0.000%