Markets Data Volatility Heatmap Portfolio Calculator

VZ Deep Analytical Report

Verizon Communications Inc. | Category: Equity Mega Cap | Ann. Div Yield: 5.47% ($2.73) | Last Updated: 2026-03-24 | Data Range: 1983-11-01 → 2026-03-01 (509 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 1.49% 1.22% 1.30% 1.77% 1.55% 1.51% 49.70 51.26 48.93 52.07
Weekly 3.14% 2.85% 3.06% 4.25% 3.42% 3.32% 48.78 52.23 47.14 54.04
Monthly 6.12% 5.58% 5.93% 9.14% 7.11% 6.92% 47.01 54.20 43.78 58.19
Quarterly 8.50% 8.73% 8.28% 15.37% 12.32% 11.99% 44.63 57.09 39.45 64.58
Annual — — — — 24.64% 23.98% 39.45 64.58 30.84 82.62
Option Time Horizon — — — — 9.30% 9.05% 45.99 55.39 41.91 60.79
Calculation Notes: Computed at 2026-03-23T16:32 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $50.47  |  Strike (K): $52.50 (first OTM call ≥ spot)  |  Observed Mid-Price: $1.0100 (Bid $0.9700 / Ask $1.0500)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 5.47%  |  Binomial IV (Annual): 24.64% (CRR binomial tree, American, n=20 steps)  |  BS IV: 24.55% (European Black-Scholes)  |  Yahoo IV (Annual): 23.98% → 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
2026-01-12 $0.6900
2025-10-10 $0.6900
2025-07-10 $0.6780
2025-04-10 $0.6780
2025-01-10 $0.6780
2024-10-10 $0.6780
2024-07-10 $0.6650
2024-04-09 $0.6650
2024-01-09 $0.6650
2023-10-06 $0.6650
2023-07-07 $0.6530
2023-04-06 $0.6530
2023-01-09 $0.6530
2022-10-06 $0.6530
2022-07-07 $0.6400
2022-04-07 $0.6400
2022-01-07 $0.6400
2021-10-07 $0.6400
2021-07-08 $0.6280
2021-04-08 $0.6280
2021-01-07 $0.6280
2020-10-08 $0.6280
2020-07-09 $0.6150
2020-04-09 $0.6150
2020-01-09 $0.6150
2019-10-09 $0.6150
2019-07-09 $0.6030
2019-04-09 $0.6030
2019-01-09 $0.6030
2018-10-09 $0.6030
2018-07-09 $0.5900
2018-04-09 $0.5900
2018-01-09 $0.5900
2017-10-06 $0.5900
2017-07-06 $0.5780
2017-04-06 $0.5780
2017-01-06 $0.5780
2016-10-05 $0.5780
2016-07-06 $0.5650
2016-04-06 $0.5650
2016-01-06 $0.5650
2015-10-07 $0.5650
2015-07-08 $0.5500
2015-04-08 $0.5500
2015-01-07 $0.5500
2014-10-08 $0.5500
2014-07-08 $0.5300
2014-04-08 $0.5300
2014-01-08 $0.5300
2013-10-08 $0.5300
2013-07-08 $0.5150
2013-04-08 $0.5150
2013-01-08 $0.5150
2012-10-05 $0.5150
2012-07-06 $0.5000
2012-04-05 $0.5000
2012-01-06 $0.5000
2011-10-05 $0.5000
2011-07-06 $0.4880
2011-04-06 $0.4880
2011-01-06 $0.4880
2010-10-06 $0.4880
2010-07-07 $0.4750
2010-04-07 $0.4455
2010-01-06 $0.4455
2009-10-07 $0.4455
2009-07-08 $0.4314
2009-04-07 $0.4314
2009-01-07 $0.4314
2008-10-08 $0.4314
2008-07-08 $0.4033
2008-04-08 $0.4033
2008-01-08 $0.4014
2007-10-05 $0.4014
2007-07-06 $0.3781
2007-04-05 $0.3781
2007-01-08 $0.3781
2006-10-05 $0.3642
2006-07-06 $0.3642
2006-04-06 $0.3642
2006-01-06 $0.3642
2005-10-05 $0.3642
2005-07-06 $0.3642
2005-04-06 $0.3642
2005-01-06 $0.3462
2004-10-06 $0.3462
2004-07-07 $0.3462
2004-04-06 $0.3462
2004-01-07 $0.3462
2003-10-08 $0.3462
2003-07-08 $0.3462
2003-04-08 $0.3462
2003-01-08 $0.3462
2002-10-08 $0.3462
2002-07-08 $0.3462
2002-04-08 $0.3462
2002-01-08 $0.3462
2001-10-05 $0.3462
2001-07-06 $0.3462
2001-04-06 $0.3462
2001-01-08 $0.3462
2000-10-05 $0.3462
2000-07-06 $0.0423
2000-07-03 $0.3462
2000-04-06 $0.3462
2000-01-06 $0.3462
1999-10-06 $0.3462
1999-07-07 $0.3471
1999-04-07 $0.3462
1999-01-06 $0.3462
1998-10-07 $0.3462
1998-07-08 $0.3462
1998-04-07 $0.3462
1998-01-07 $0.3462
1997-10-08 $0.3462
1997-04-08 $0.3327
1997-01-08 $0.3238
1996-10-08 $0.3238
1996-07-08 $0.3238
1996-04-08 $0.3238
1996-01-08 $0.3148
1995-10-05 $0.3148
1995-07-06 $0.3148
1995-04-04 $0.3148
1995-01-04 $0.3103
1994-10-04 $0.3103
1994-07-05 $0.3103
1994-04-05 $0.3103
1994-01-04 $0.3013
1993-07-02 $0.3013
1993-04-02 $0.3013
1993-01-05 $0.2923
1992-10-05 $0.2923
1992-07-06 $0.2923
1992-04-06 $0.2923
1992-01-06 $0.2833
1991-10-04 $0.2833
1991-07-03 $0.2833
1991-04-04 $0.2833
1991-01-04 $0.2653
1990-10-03 $0.2653
1990-07-03 $0.2653
1990-04-04 $0.2653
1990-01-04 $0.2473
1989-10-03 $0.2473
1989-07-03 $0.2473
1989-04-04 $0.2473
1988-12-23 $0.2293
1988-09-26 $0.2293
1988-06-24 $0.2293
1988-03-25 $0.2293
1987-12-24 $0.2158
1987-09-24 $0.2158
1987-06-24 $0.2158
1987-03-25 $0.2158
1986-12-24 $0.2023
1986-09-24 $0.2023
1986-06-24 $0.2023
1986-03-24 $0.2023
1985-12-24 $0.1911
1985-09-24 $0.1911
1985-06-24 $0.0191
1985-03-25 $0.1911
1984-12-21 $0.1799
1984-09-24 $0.1799
1984-06-25 $0.1799
1984-03-26 $0.1799
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.22. Further, an Excess Kurtosis of 8.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.41%790.74%0.74%
-4.41% to -3.30%1050.98%1.73%
-3.30% to -2.18%3503.28%5.01%
-2.18% to -1.07%127211.93%16.93%
-1.07% to 0.05%364934.21%51.15%
0.05% to 1.16%345832.42%83.57%
1.16% to 2.28%116510.92%94.50%
2.28% to 3.39%3863.62%98.12%
3.39% to 4.50%1371.28%99.40%
Greater than 4.50%640.60%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.44%1.53% 77.53%68.27%
±2σ -2.92%3.02% 94.98%95.45%
±3σ -4.41%4.50% 98.66%99.73%
Descriptive Statistics
Mean0.047%
Standard Error0.014%
Median0.000%
Mode0.000%
Standard Deviation1.486%
Sample Variance2.207%
Kurtosis8.30
Skewness0.22
Range32.179%
Minimum-17.547%
Maximum14.632%
Count10665
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.092% 5277 49.48% 0.540%
Negative -1.046% 5025 47.12% -0.493%
Zero 0.000% 363 3.40% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.16%
20 1 Month 1.93%
60 1 Quarter 2.06%
250 1 Year 1.84%
750 3 Years 1.83%
1,250 5 Years 1.77%
2,500 10 Years 1.71%
5,000 20 Years 1.81%
12,500 50 Years 1.97%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.16. Further, an Excess Kurtosis of 21.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.78%00.00%0.00%
-1.78% to -0.86%00.00%0.00%
-0.86% to 0.05%00.00%0.00%
0.05% to 0.96%175616.46%16.46%
0.96% to 1.88%498346.72%63.18%
1.88% to 2.79%234521.99%85.17%
2.79% to 3.71%8638.09%93.26%
3.71% to 4.62%3553.33%96.59%
4.62% to 5.54%1841.73%98.31%
Greater than 5.54%1801.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.66%3.10% 85.48%68.27%
±2σ -0.56%4.32% 95.79%95.45%
±3σ -1.78%5.54% 98.31%99.73%
Descriptive Statistics
Mean1.879%
Standard Error0.012%
Median1.570%
Mode1.323%
Standard Deviation1.219%
Sample Variance1.485%
Kurtosis21.98
Skewness3.16
Range21.498%
Minimum0.262%
Maximum21.760%
Count10666
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.879% 10666 100.00% 1.879%
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 -0.17. Further, an Excess Kurtosis of 5.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.91%760.71%0.71%
-3.91% to -2.94%1131.06%1.77%
-2.94% to -1.96%4033.78%5.55%
-1.96% to -0.99%126211.83%17.38%
-0.99% to -0.01%333431.26%48.64%
-0.01% to 0.96%358833.64%82.28%
0.96% to 1.94%130712.25%94.53%
1.94% to 2.91%3973.72%98.26%
2.91% to 3.89%1201.13%99.38%
Greater than 3.89%660.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.31%1.29% 76.50%68.27%
±2σ -2.61%2.59% 94.82%95.45%
±3σ -3.91%3.89% 98.67%99.73%
Descriptive Statistics
Mean-0.014%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.300%
Sample Variance1.691%
Kurtosis5.40
Skewness-0.17
Range23.063%
Minimum-12.319%
Maximum10.744%
Count10666
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.956% 5066 47.50% 0.454%
Negative -0.961% 5188 48.64% -0.467%
Zero 0.000% 412 3.86% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.15. Further, an Excess Kurtosis of 3.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.19%90.41%0.41%
-9.19% to -6.84%241.09%1.49%
-6.84% to -4.48%813.67%5.16%
-4.48% to -2.13%30613.85%19.01%
-2.13% to 0.23%69331.37%50.38%
0.23% to 2.58%68130.83%81.21%
2.58% to 4.93%29313.26%94.48%
4.93% to 7.29%783.53%98.01%
7.29% to 9.64%261.18%99.19%
Greater than 9.64%180.81%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.91%3.36% 75.65%68.27%
±2σ -6.05%6.50% 95.20%95.45%
±3σ -9.19%9.64% 98.78%99.73%
Descriptive Statistics
Mean0.225%
Standard Error0.067%
Median0.193%
Mode0.000%
Standard Deviation3.138%
Sample Variance9.849%
Kurtosis3.73
Skewness0.15
Range39.947%
Minimum-20.525%
Maximum19.422%
Count2209
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.386% 1169 52.92% 1.263%
Negative -2.253% 1017 46.04% -1.037%
Zero 0.000% 23 1.04% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 3.81%
12 1 Quarter 5.20%
52 1 Year 4.45%
156 3 Years 4.46%
260 5 Years 4.25%
520 10 Years 3.99%
1,040 20 Years 4.12%
2,600 50 Years 4.54%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.99. Further, an Excess Kurtosis of 16.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.93%00.00%0.00%
-3.93% to -1.79%00.00%0.00%
-1.79% to 0.34%00.00%0.00%
0.34% to 2.48%38517.42%17.42%
2.48% to 4.61%98644.62%62.04%
4.61% to 6.75%53124.03%86.06%
6.75% to 8.88%1607.24%93.30%
8.88% to 11.02%743.35%96.65%
11.02% to 13.15%391.76%98.42%
Greater than 13.15%351.58%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.76%7.46% 84.52%68.27%
±2σ -1.08%10.30% 95.66%95.45%
±3σ -3.93%13.15% 98.42%99.73%
Descriptive Statistics
Mean4.611%
Standard Error0.061%
Median3.979%
Mode6.250%
Standard Deviation2.847%
Sample Variance8.103%
Kurtosis16.83
Skewness2.99
Range32.115%
Minimum1.002%
Maximum33.117%
Count2210
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.611% 2210 100.00% 4.611%
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 0.40. Further, an Excess Kurtosis of 5.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.21%130.59%0.59%
-9.21% to -6.92%210.95%1.54%
-6.92% to -4.62%833.76%5.29%
-4.62% to -2.32%30713.89%19.19%
-2.32% to -0.03%71632.40%51.58%
-0.03% to 2.27%65429.59%81.18%
2.27% to 4.57%28212.76%93.94%
4.57% to 6.87%994.48%98.42%
6.87% to 9.16%221.00%99.41%
Greater than 9.16%130.59%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.09%3.04% 74.30%68.27%
±2σ -6.15%6.10% 95.48%95.45%
±3σ -9.21%9.16% 98.82%99.73%
Descriptive Statistics
Mean-0.026%
Standard Error0.065%
Median-0.139%
Mode0.000%
Standard Deviation3.063%
Sample Variance9.380%
Kurtosis5.05
Skewness0.40
Range43.536%
Minimum-16.263%
Maximum27.273%
Count2210
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.345% 1046 47.33% 1.110%
Negative -2.198% 1142 51.67% -1.136%
Zero 0.000% 22 0.99% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.51. Further, an Excess Kurtosis of 3.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.39%10.20%0.20%
-17.39% to -12.80%30.59%0.79%
-12.80% to -8.22%265.12%5.91%
-8.22% to -3.63%7614.96%20.87%
-3.63% to 0.96%15029.53%50.39%
0.96% to 5.55%15229.92%80.31%
5.55% to 10.14%6512.80%93.11%
10.14% to 14.73%316.10%99.21%
14.73% to 19.32%00.00%99.21%
Greater than 19.32%40.79%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.16%7.08% 72.05%68.27%
±2σ -11.28%13.20% 96.26%95.45%
±3σ -17.39%19.32% 99.02%99.73%
Descriptive Statistics
Mean0.963%
Standard Error0.271%
Median0.880%
Mode-2.250%
Standard Deviation6.119%
Sample Variance37.439%
Kurtosis3.20
Skewness0.51
Range60.253%
Minimum-20.989%
Maximum39.264%
Count508
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.987% 288 56.69% 2.827%
Negative -4.305% 220 43.31% -1.864%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 11.64%
12 1 Year 8.66%
36 3 Years 9.68%
60 5 Years 9.14%
120 10 Years 8.66%
240 20 Years 8.81%
600 50 Years 9.58%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 11.62 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.53%00.00%0.00%
-6.53% to -2.35%00.00%0.00%
-2.35% to 1.84%00.00%0.00%
1.84% to 6.02%8917.49%17.49%
6.02% to 10.21%22544.20%61.69%
10.21% to 14.39%10921.41%83.10%
14.39% to 18.57%5110.02%93.12%
18.57% to 22.76%203.93%97.05%
22.76% to 26.94%50.98%98.04%
Greater than 26.94%101.96%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.63%15.79% 82.51%68.27%
±2σ -0.95%21.36% 95.87%95.45%
±3σ -6.53%26.94% 98.04%99.73%
Descriptive Statistics
Mean10.206%
Standard Error0.247%
Median8.657%
Mode5.000%
Standard Deviation5.579%
Sample Variance31.124%
Kurtosis11.62
Skewness2.52
Range51.837%
Minimum2.719%
Maximum54.556%
Count509
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.206% 509 100.00% 10.206%
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 0.18. Further, an Excess Kurtosis of 1.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.85%10.20%0.20%
-17.85% to -13.41%20.39%0.59%
-13.41% to -8.96%265.11%5.70%
-8.96% to -4.52%7915.52%21.22%
-4.52% to -0.07%15630.65%51.87%
-0.07% to 4.37%14428.29%80.16%
4.37% to 8.82%6111.98%92.14%
8.82% to 13.27%295.70%97.84%
13.27% to 17.71%91.77%99.61%
Greater than 17.71%20.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.00%5.86% 70.14%68.27%
±2σ -11.92%11.78% 96.07%95.45%
±3σ -17.85%17.71% 99.41%99.73%
Descriptive Statistics
Mean-0.071%
Standard Error0.263%
Median-0.288%
Mode0.000%
Standard Deviation5.927%
Sample Variance35.126%
Kurtosis1.18
Skewness0.18
Range51.257%
Minimum-27.119%
Maximum24.138%
Count509
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.811% 238 46.76% 2.250%
Negative -4.440% 266 52.26% -2.320%
Zero 0.000% 5 0.98% 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 0.01 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -22.85%00.00%0.00%
-22.85% to -16.48%31.78%1.78%
-16.48% to -10.10%84.73%6.51%
-10.10% to -3.73%2917.16%23.67%
-3.73% to 2.65%4828.40%52.07%
2.65% to 9.02%4023.67%75.74%
9.02% to 15.40%3017.75%93.49%
15.40% to 21.77%74.14%97.63%
21.77% to 28.15%42.37%100.00%
Greater than 28.15%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.85%11.15% 67.46%68.27%
±2σ -14.35%19.65% 95.27%95.45%
±3σ -22.85%28.15% 100.00%99.73%
Descriptive Statistics
Mean2.648%
Standard Error0.654%
Median2.144%
Mode-21.421%
Standard Deviation8.500%
Sample Variance72.250%
Kurtosis0.01
Skewness0.06
Range46.337%
Minimum-21.421%
Maximum24.916%
Count169
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.831% 105 62.13% 4.865%
Negative -5.854% 64 37.87% -2.217%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 14.59%
12 3 Years 15.77%
20 5 Years 15.37%
40 10 Years 14.45%
80 20 Years 14.82%
200 50 Years 15.92%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.67. Further, an Excess Kurtosis of 11.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.46%00.00%0.00%
-8.46% to -1.91%00.00%0.00%
-1.91% to 4.64%00.00%0.00%
4.64% to 11.19%3218.82%18.82%
11.19% to 17.74%7141.76%60.59%
17.74% to 24.29%4425.88%86.47%
24.29% to 30.84%127.06%93.53%
30.84% to 37.39%52.94%96.47%
37.39% to 43.94%21.18%97.65%
Greater than 43.94%42.35%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 9.01%26.47% 82.94%68.27%
±2σ 0.27%35.21% 96.47%95.45%
±3σ -8.46%43.94% 97.65%99.73%
Descriptive Statistics
Mean17.740%
Standard Error0.670%
Median15.681%
Mode12.979%
Standard Deviation8.733%
Sample Variance76.259%
Kurtosis11.28
Skewness2.67
Range65.349%
Minimum6.623%
Maximum71.972%
Count170
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 17.740% 170 100.00% 17.740%
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 0.45. Further, an Excess Kurtosis of 0.32 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.25%00.00%0.00%
-25.25% to -19.04%00.00%0.00%
-19.04% to -12.83%84.71%4.71%
-12.83% to -6.62%3218.82%23.53%
-6.62% to -0.42%4928.82%52.35%
-0.42% to 5.79%4627.06%79.41%
5.79% to 12.00%2414.12%93.53%
12.00% to 18.21%84.71%98.24%
18.21% to 24.41%21.18%99.41%
Greater than 24.41%10.59%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.69%7.86% 66.47%68.27%
±2σ -16.97%16.14% 95.88%95.45%
±3σ -25.25%24.41% 99.41%99.73%
Descriptive Statistics
Mean-0.416%
Standard Error0.635%
Median-1.105%
Mode0.487%
Standard Deviation8.277%
Sample Variance68.511%
Kurtosis0.32
Skewness0.45
Range44.749%
Minimum-18.011%
Maximum26.738%
Count170
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.730% 78 45.88% 3.088%
Negative -6.475% 92 54.12% -3.504%
Zero 0.000% 0 0.00% 0.000%