Markets Data Volatility Heatmap Portfolio Calculator

VZ Deep Analytical Report

Verizon Communications Inc. | Category: Equity Mega Cap | Ann. Div Yield: 5.62% ($2.73) | Last Updated: 2026-02-22 | Data Range: 1983-11-01 → 2026-02-01 (508 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% 1.32% 1.31% 48.60 49.91 47.97 50.57
Weekly 3.14% 2.85% 3.06% 4.24% 2.91% 2.88% 47.84 50.70 46.47 52.20
Monthly 6.12% 5.58% 5.93% 9.18% 6.06% 6.00% 46.36 52.33 43.63 55.59
Quarterly 8.48% 8.74% 8.26% 15.21% 10.49% 10.39% 44.35 54.70 39.93 60.75
Annual — — — — 20.98% 20.78% 39.93 60.75 32.37 74.93
Option Time Horizon — — — — 8.07% 7.99% 45.43 53.39 41.91 57.88
Calculation Notes: Computed at 2026-02-22T14:18 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $49.25  |  Strike (K): $50.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $1.2100 (Bid $1.1700 / Ask $1.2500)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 5.62%  |  Binomial IV (Annual): 20.98% (CRR binomial tree, American, n=20 steps)  |  BS IV: 21.34% (European Black-Scholes)  |  Yahoo IV (Annual): 20.78% → 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%1050.99%1.73%
-3.30% to -2.18%3503.29%5.02%
-2.18% to -1.07%126911.92%16.94%
-1.07% to 0.05%364034.20%51.14%
0.05% to 1.16%345232.43%83.57%
1.16% to 2.28%116310.93%94.49%
2.28% to 3.39%3853.62%98.11%
3.39% to 4.50%1371.29%99.40%
Greater than 4.50%640.60%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.44%1.53% 77.52%68.27%
±2σ -2.92%3.02% 94.97%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 Variance2.209%
Kurtosis8.30
Skewness0.22
Range32.179%
Minimum-17.547%
Maximum14.632%
Count10644
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.092% 5268 49.49% 0.540%
Negative -1.047% 5013 47.10% -0.493%
Zero 0.000% 363 3.41% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.87%
20 1 Month 2.78%
60 1 Quarter 1.91%
250 1 Year 1.91%
750 3 Years 1.83%
1,250 5 Years 1.77%
2,500 10 Years 1.70%
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 21.95 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 -0.87%00.00%0.00%
-0.87% to 0.05%00.00%0.00%
0.05% to 0.96%174916.43%16.43%
0.96% to 1.88%497846.76%63.19%
1.88% to 2.79%234121.99%85.19%
2.79% to 3.71%8588.06%93.25%
3.71% to 4.62%3553.33%96.58%
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% 85.47%68.27%
±2σ -0.56%4.32% 95.78%95.45%
±3σ -1.78%5.54% 98.31%99.73%
Descriptive Statistics
Mean1.879%
Standard Error0.012%
Median1.570%
Mode1.323%
Standard Deviation1.220%
Sample Variance1.488%
Kurtosis21.95
Skewness3.16
Range21.498%
Minimum0.262%
Maximum21.760%
Count10645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.879% 10645 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 -3.92%750.70%0.70%
-3.92% to -2.94%1141.07%1.78%
-2.94% to -1.96%4023.78%5.55%
-1.96% to -0.99%126011.84%17.39%
-0.99% to -0.01%332531.24%48.62%
-0.01% to 0.96%358633.69%82.31%
0.96% to 1.94%130112.22%94.53%
1.94% to 2.91%3973.73%98.26%
2.91% to 3.89%1191.12%99.38%
Greater than 3.89%660.62%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.31%1.29% 76.51%68.27%
±2σ -2.61%2.59% 94.82%95.45%
±3σ -3.92%3.89% 98.67%99.73%
Descriptive Statistics
Mean-0.013%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.301%
Sample Variance1.692%
Kurtosis5.40
Skewness-0.17
Range23.063%
Minimum-12.319%
Maximum10.744%
Count10645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.956% 5058 47.52% 0.454%
Negative -0.961% 5176 48.62% -0.467%
Zero 0.000% 411 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 3.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.20%90.41%0.41%
-9.20% to -6.84%241.09%1.50%
-6.84% to -4.49%813.67%5.17%
-4.49% to -2.13%30613.88%19.05%
-2.13% to 0.23%69231.38%50.43%
0.23% to 2.58%67830.75%81.18%
2.58% to 4.94%29313.29%94.47%
4.94% to 7.29%783.54%98.00%
7.29% to 9.65%261.18%99.18%
Greater than 9.65%180.82%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.92%3.37% 75.60%68.27%
±2σ -6.06%6.51% 95.19%95.45%
±3σ -9.20%9.65% 98.78%99.73%
Descriptive Statistics
Mean0.225%
Standard Error0.067%
Median0.191%
Mode0.000%
Standard Deviation3.141%
Sample Variance9.865%
Kurtosis3.72
Skewness0.15
Range39.947%
Minimum-20.525%
Maximum19.422%
Count2205
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.389% 1166 52.88% 1.263%
Negative -2.255% 1016 46.08% -1.039%
Zero 0.000% 23 1.04% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 8.38%
12 1 Quarter 4.92%
52 1 Year 4.68%
156 3 Years 4.44%
260 5 Years 4.24%
520 10 Years 3.98%
1,040 20 Years 4.11%
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 16.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.94%00.00%0.00%
-3.94% to -1.80%00.00%0.00%
-1.80% to 0.34%00.00%0.00%
0.34% to 2.47%38517.45%17.45%
2.47% to 4.61%98444.61%62.06%
4.61% to 6.75%52923.98%86.04%
6.75% to 8.88%1607.25%93.29%
8.88% to 11.02%743.35%96.65%
11.02% to 13.16%391.77%98.41%
Greater than 13.16%351.59%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.76%7.46% 84.50%68.27%
±2σ -1.09%10.31% 95.65%95.45%
±3σ -3.94%13.16% 98.41%99.73%
Descriptive Statistics
Mean4.611%
Standard Error0.061%
Median3.979%
Mode6.250%
Standard Deviation2.849%
Sample Variance8.116%
Kurtosis16.80
Skewness2.99
Range32.115%
Minimum1.002%
Maximum33.117%
Count2206
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.611% 2206 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 0.39. Further, an Excess Kurtosis of 5.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.22%130.59%0.59%
-9.22% to -6.92%210.95%1.54%
-6.92% to -4.62%833.76%5.30%
-4.62% to -2.32%30713.92%19.22%
-2.32% to -0.03%71232.28%51.50%
-0.03% to 2.27%65429.65%81.14%
2.27% to 4.57%28212.78%93.93%
4.57% to 6.87%994.49%98.41%
6.87% to 9.17%221.00%99.41%
Greater than 9.17%130.59%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.09%3.04% 74.25%68.27%
±2σ -6.16%6.10% 95.47%95.45%
±3σ -9.22%9.17% 98.82%99.73%
Descriptive Statistics
Mean-0.025%
Standard Error0.065%
Median-0.135%
Mode0.000%
Standard Deviation3.065%
Sample Variance9.394%
Kurtosis5.04
Skewness0.39
Range43.536%
Minimum-16.263%
Maximum27.273%
Count2206
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.343% 1046 47.42% 1.111%
Negative -2.203% 1138 51.59% -1.136%
Zero 0.000% 22 1.00% 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 -12.81%30.59%0.79%
-12.81% to -8.22%265.13%5.92%
-8.22% to -3.63%7614.99%20.91%
-3.63% to 0.96%14929.39%50.30%
0.96% to 5.55%15229.98%80.28%
5.55% to 10.14%6512.82%93.10%
10.14% to 14.72%316.11%99.21%
14.72% to 19.31%00.00%99.21%
Greater than 19.31%40.79%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.16%7.08% 71.99%68.27%
±2σ -11.28%13.20% 96.45%95.45%
±3σ -17.39%19.31% 99.01%99.73%
Descriptive Statistics
Mean0.959%
Standard Error0.272%
Median0.901%
Mode-2.250%
Standard Deviation6.118%
Sample Variance37.429%
Kurtosis3.20
Skewness0.51
Range60.253%
Minimum-20.989%
Maximum39.264%
Count507
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.995% 287 56.61% 2.828%
Negative -4.305% 220 43.39% -1.868%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 11.57%
12 1 Year 9.36%
36 3 Years 9.72%
60 5 Years 9.18%
120 10 Years 8.67%
240 20 Years 8.81%
600 50 Years 9.59%
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 -2.34%00.00%0.00%
-2.34% to 1.84%00.00%0.00%
1.84% to 6.03%8817.32%17.32%
6.03% to 10.21%22644.49%61.81%
10.21% to 14.40%10821.26%83.07%
14.40% to 18.58%5110.04%93.11%
18.58% to 22.77%203.94%97.05%
22.77% to 26.95%50.98%98.03%
Greater than 26.95%101.97%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 4.63%15.79% 82.48%68.27%
±2σ -0.95%21.37% 95.87%95.45%
±3σ -6.53%26.95% 98.03%99.73%
Descriptive Statistics
Mean10.214%
Standard Error0.248%
Median8.668%
Mode5.000%
Standard Deviation5.580%
Sample Variance31.135%
Kurtosis11.62
Skewness2.52
Range51.837%
Minimum2.719%
Maximum54.556%
Count508
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.214% 508 100.00% 10.214%
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 0.19. 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 -13.40%20.39%0.59%
-13.40% to -8.96%265.12%5.71%
-8.96% to -4.51%7915.55%21.26%
-4.51% to -0.07%15630.71%51.97%
-0.07% to 4.38%14328.15%80.12%
4.38% to 8.82%6112.01%92.13%
8.82% to 13.27%295.71%97.83%
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 -5.99%5.86% 69.88%68.27%
±2σ -11.92%11.79% 96.06%95.45%
±3σ -17.85%17.71% 99.41%99.73%
Descriptive Statistics
Mean-0.066%
Standard Error0.263%
Median-0.283%
Mode0.000%
Standard Deviation5.927%
Sample Variance35.129%
Kurtosis1.18
Skewness0.19
Range51.257%
Minimum-27.119%
Maximum24.138%
Count508
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.811% 238 46.85% 2.254%
Negative -4.446% 265 52.16% -2.319%
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 0.02 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -22.81%00.00%0.00%
-22.81% to -16.45%31.78%1.78%
-16.45% to -10.09%84.73%6.51%
-10.09% to -3.73%2917.16%23.67%
-3.73% to 2.63%4828.40%52.07%
2.63% to 8.99%4023.67%75.74%
8.99% to 15.35%3017.75%93.49%
15.35% to 21.71%74.14%97.63%
21.71% to 28.07%42.37%100.00%
Greater than 28.07%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.85%11.11% 68.05%68.27%
±2σ -14.33%19.59% 95.27%95.45%
±3σ -22.81%28.07% 100.00%99.73%
Descriptive Statistics
Mean2.632%
Standard Error0.652%
Median2.144%
Mode-21.421%
Standard Deviation8.481%
Sample Variance71.934%
Kurtosis0.02
Skewness0.06
Range46.337%
Minimum-21.421%
Maximum24.916%
Count169
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.804% 105 62.13% 4.849%
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 13.79%
12 3 Years 15.50%
20 5 Years 15.21%
40 10 Years 14.37%
80 20 Years 14.78%
200 50 Years 15.90%
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 -8.49%00.00%0.00%
-8.49% to -1.94%00.00%0.00%
-1.94% to 4.62%00.00%0.00%
4.62% to 11.17%3218.82%18.82%
11.17% to 17.72%7141.76%60.59%
17.72% to 24.27%4425.88%86.47%
24.27% to 30.82%127.06%93.53%
30.82% to 37.38%52.94%96.47%
37.38% to 43.93%21.18%97.65%
Greater than 43.93%42.35%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 8.98%26.46% 82.94%68.27%
±2σ 0.25%35.19% 96.47%95.45%
±3σ -8.49%43.93% 97.65%99.73%
Descriptive Statistics
Mean17.721%
Standard Error0.670%
Median15.618%
Mode12.979%
Standard Deviation8.736%
Sample Variance76.321%
Kurtosis11.28
Skewness2.67
Range65.349%
Minimum6.623%
Maximum71.972%
Count170
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 17.721% 170 100.00% 17.721%
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 0.33 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.19%00.00%0.00%
-25.19% to -18.99%00.00%0.00%
-18.99% to -12.79%84.71%4.71%
-12.79% to -6.60%3218.82%23.53%
-6.60% to -0.40%4928.82%52.35%
-0.40% to 5.79%4627.06%79.41%
5.79% to 11.99%2414.12%93.53%
11.99% to 18.18%84.71%98.24%
18.18% to 24.38%21.18%99.41%
Greater than 24.38%10.59%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.66%7.86% 66.47%68.27%
±2σ -16.92%16.12% 95.88%95.45%
±3σ -25.19%24.38% 99.41%99.73%
Descriptive Statistics
Mean-0.403%
Standard Error0.634%
Median-1.105%
Mode0.487%
Standard Deviation8.261%
Sample Variance68.238%
Kurtosis0.33
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 -6.450% 92 54.12% -3.491%
Zero 0.000% 0 0.00% 0.000%