Markets Data Volatility Heatmap Portfolio Calculator

PEP Deep Analytical Report

PepsiCo, Inc. | Category: Equity Mega Cap | Ann. Div Yield: 3.42% ($5.62) | Last Updated: 2026-02-22 | Data Range: 1972-06-01 → 2026-02-01 (645 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 1.53% 1.38% 1.31% 1.63% 1.28% 1.31% 162.85 167.06 160.78 169.20
Weekly 3.26% 3.31% 3.14% 3.72% 2.81% 2.89% 160.37 169.64 155.93 174.47
Monthly 6.13% 6.91% 6.18% 7.74% 5.85% 6.02% 155.57 174.87 146.73 185.41
Quarterly 9.08% 11.02% 8.81% 12.59% 10.13% 10.43% 149.05 182.52 134.69 201.98
Annual — — — — 20.26% 20.86% 134.69 201.98 109.99 247.34
Option Time Horizon — — — — 7.79% 8.02% 152.58 178.31 141.14 192.76
Calculation Notes: Computed at 2026-02-22T14:17 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $164.94  |  Strike (K): $165.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $5.0500 (Bid $4.8000 / Ask $5.3000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.42%  |  Binomial IV (Annual): 20.26% (CRR binomial tree, American, n=20 steps)  |  BS IV: 20.03% (European Black-Scholes)  |  Yahoo IV (Annual): 20.86% → 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
2025-12-05 $1.4230
2025-09-05 $1.4230
2025-06-06 $1.4230
2025-03-07 $1.3550
2024-12-06 $1.3550
2024-09-06 $1.3550
2024-06-07 $1.3550
2024-02-29 $1.2650
2023-11-30 $1.2650
2023-08-31 $1.2650
2023-06-01 $1.2650
2023-03-02 $1.1500
2022-12-01 $1.1500
2022-09-01 $1.1500
2022-06-02 $1.1500
2022-03-03 $1.0750
2021-12-02 $1.0750
2021-09-02 $1.0750
2021-06-03 $1.0750
2021-03-04 $1.0230
2020-12-03 $1.0230
2020-09-03 $1.0230
2020-06-04 $1.0230
2020-03-05 $0.9550
2019-12-05 $0.9550
2019-09-05 $0.9550
2019-06-06 $0.9550
2019-02-28 $0.9280
2018-12-06 $0.9280
2018-09-06 $0.9280
2018-05-31 $0.9280
2018-03-01 $0.8050
2017-11-30 $0.8050
2017-08-30 $0.8050
2017-05-31 $0.8050
2017-03-01 $0.7530
2016-11-30 $0.7530
2016-08-31 $0.7530
2016-06-01 $0.7530
2016-03-02 $0.7030
2015-12-02 $0.7030
2015-09-02 $0.7030
2015-06-03 $0.7030
2015-03-04 $0.6550
2014-12-03 $0.6550
2014-09-03 $0.6550
2014-06-04 $0.6550
2014-03-05 $0.5680
2013-12-04 $0.5680
2013-09-04 $0.5680
2013-06-05 $0.5680
2013-02-27 $0.5370
2012-12-05 $0.5370
2012-09-05 $0.5380
2012-05-30 $0.5380
2012-02-29 $0.5150
2011-11-30 $0.5150
2011-08-31 $0.5150
2011-06-01 $0.5150
2011-03-02 $0.4800
2010-12-01 $0.4800
2010-09-01 $0.4800
2010-06-02 $0.4800
2010-03-03 $0.4500
2009-12-02 $0.4500
2009-09-02 $0.4500
2009-06-03 $0.4500
2009-03-04 $0.4250
2008-12-03 $0.4250
2008-09-03 $0.4250
2008-06-04 $0.4250
2008-03-05 $0.3750
2007-12-05 $0.3750
2007-09-05 $0.3750
2007-06-06 $0.3750
2007-03-07 $0.3000
2006-12-06 $0.3000
2006-09-06 $0.3000
2006-06-07 $0.3000
2006-03-08 $0.2600
2005-12-07 $0.2600
2005-09-07 $0.2600
2005-06-08 $0.2600
2005-03-09 $0.2300
2004-12-08 $0.2300
2004-09-08 $0.2300
2004-06-09 $0.2300
2004-03-10 $0.1600
2003-12-10 $0.1600
2003-09-10 $0.1600
2003-06-11 $0.1600
2003-03-12 $0.1500
2002-12-04 $0.1500
2002-09-04 $0.1500
2002-06-05 $0.1500
2002-03-06 $0.1450
2001-12-05 $0.1450
2001-09-05 $0.1450
2001-06-06 $0.1450
2001-03-07 $0.1400
2000-12-06 $0.1400
2000-09-06 $0.1400
2000-06-07 $0.1400
2000-03-08 $0.1350
1999-12-08 $0.1350
1999-09-08 $0.1350
1999-06-09 $0.1350
1999-03-10 $0.1300
1998-12-09 $0.1300
1998-09-09 $0.1300
1998-06-10 $0.1300
1998-03-11 $0.1250
1997-12-10 $0.1250
1997-10-07 $3.2000
1997-09-17 $0.1250
1997-06-11 $0.1250
1997-03-12 $0.1150
1996-12-04 $0.1150
1996-09-04 $0.1150
1996-06-05 $0.1150
1996-03-06 $0.1000
1995-12-06 $0.1000
1995-09-06 $0.1000
1995-06-06 $0.1000
1995-03-06 $0.0900
1994-12-05 $0.0900
1994-09-02 $0.0900
1994-06-06 $0.0900
1994-03-07 $0.0800
1993-12-06 $0.0800
1993-09-03 $0.0800
1993-06-07 $0.0800
1993-03-08 $0.0650
1992-12-07 $0.0650
1992-09-04 $0.0650
1992-06-08 $0.0650
1992-03-09 $0.0600
1991-12-09 $0.0600
1991-09-09 $0.0600
1991-06-10 $0.0600
1991-03-04 $0.0500
1990-12-10 $0.0500
1990-09-10 $0.0500
1990-06-04 $0.0500
1990-03-05 $0.0417
1989-12-04 $0.0417
1989-09-01 $0.0417
1989-06-05 $0.0417
1989-03-06 $0.0350
1988-12-05 $0.0350
1988-09-02 $0.0350
1988-06-06 $0.0350
1988-03-07 $0.0283
1987-12-07 $0.0283
1987-09-04 $0.0283
1987-06-08 $0.0283
1987-03-09 $0.0267
1986-12-08 $0.0267
1986-09-08 $0.0267
1986-06-09 $0.0267
1986-03-10 $0.0247
1985-12-09 $0.0247
1985-09-09 $0.0247
1985-06-10 $0.0247
1985-03-04 $0.0233
1984-12-10 $0.0233
1984-09-10 $0.0233
1984-06-04 $0.0233
1984-03-05 $0.0225
1983-12-05 $0.0225
1983-09-02 $0.0225
1983-06-06 $0.0225
1983-03-07 $0.0225
1982-12-06 $0.0225
1982-09-03 $0.0225
1982-06-07 $0.0225
1982-03-08 $0.0203
1981-12-07 $0.0203
1981-09-04 $0.0203
1981-06-08 $0.0203
1981-03-09 $0.0181
1980-12-08 $0.0181
1980-09-08 $0.0181
1980-06-09 $0.0181
1980-03-10 $0.0158
1979-12-10 $0.0158
1979-09-10 $0.0158
1979-06-04 $0.0158
1979-03-05 $0.0139
1978-12-04 $0.0139
1978-09-01 $0.0139
1978-06-05 $0.0139
1978-03-06 $0.0125
1977-12-05 $0.0125
1977-09-02 $0.0111
1977-06-03 $0.0111
1977-03-04 $0.0111
1976-12-06 $0.0093
1976-09-02 $0.0093
1976-06-03 $0.0093
1976-03-04 $0.0074
1975-12-04 $0.0074
1975-09-03 $0.0074
1975-06-03 $0.0065
1975-03-04 $0.0065
1974-12-04 $0.0065
1974-09-03 $0.0065
1974-06-03 $0.0056
1974-03-05 $0.0056
1973-12-04 $0.0056
1973-08-31 $0.0056
1973-06-04 $0.0050
1973-03-05 $0.0050
1972-12-04 $0.0046
1972-09-01 $0.0046
1972-06-05 $0.0046
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.18. Further, an Excess Kurtosis of 7.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.53%890.66%0.66%
-4.53% to -3.39%1351.00%1.67%
-3.39% to -2.24%4673.47%5.14%
-2.24% to -1.09%152011.30%16.44%
-1.09% to 0.06%500537.22%53.67%
0.06% to 1.20%397129.53%83.20%
1.20% to 2.35%152811.36%94.56%
2.35% to 3.50%4753.53%98.10%
3.50% to 4.65%1511.12%99.22%
Greater than 4.65%1050.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.47%1.59% 77.90%68.27%
±2σ -3.00%3.12% 94.82%95.45%
±3σ -4.53%4.65% 98.56%99.73%
Descriptive Statistics
Mean0.057%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.530%
Sample Variance2.340%
Kurtosis7.32
Skewness0.18
Range30.430%
Minimum-14.286%
Maximum16.144%
Count13446
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.168% 6403 47.62% 0.556%
Negative -1.098% 6113 45.46% -0.499%
Zero 0.000% 930 6.92% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.11%
20 1 Month 2.35%
60 1 Quarter 1.83%
250 1 Year 1.93%
750 3 Years 1.64%
1,250 5 Years 1.63%
2,500 10 Years 1.58%
5,000 20 Years 1.56%
12,500 50 Years 2.00%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 9.48. Further, an Excess Kurtosis of 323.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.23%00.00%0.00%
-2.23% to -1.19%00.00%0.00%
-1.19% to -0.16%00.00%0.00%
-0.16% to 0.88%170212.66%12.66%
0.88% to 1.91%675450.23%62.88%
1.91% to 2.95%307322.85%85.74%
2.95% to 3.99%11258.37%94.10%
3.99% to 5.02%4663.47%97.57%
5.02% to 6.06%1571.17%98.74%
Greater than 6.06%1701.26%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.53%3.29% 88.29%68.27%
±2σ -0.85%4.68% 96.71%95.45%
±3σ -2.23%6.06% 98.74%99.73%
Descriptive Statistics
Mean1.914%
Standard Error0.012%
Median1.577%
Mode1.531%
Standard Deviation1.381%
Sample Variance1.906%
Kurtosis323.08
Skewness9.48
Range63.806%
Minimum0.148%
Maximum63.954%
Count13447
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.914% 13447 100.00% 1.914%
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 0.22. Further, an Excess Kurtosis of 6.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.00%880.65%0.65%
-4.00% to -3.01%1651.23%1.88%
-3.01% to -2.03%4803.57%5.45%
-2.03% to -1.04%157411.71%17.16%
-1.04% to -0.06%397229.54%46.69%
-0.06% to 0.93%494336.76%83.45%
0.93% to 1.91%149911.15%94.60%
1.91% to 2.90%4713.50%98.10%
2.90% to 3.88%1581.17%99.28%
Greater than 3.88%970.72%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.37%1.26% 76.75%68.27%
±2σ -2.68%2.57% 94.60%95.45%
±3σ -4.00%3.88% 98.62%99.73%
Descriptive Statistics
Mean-0.057%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.313%
Sample Variance1.724%
Kurtosis6.73
Skewness0.22
Range26.241%
Minimum-11.443%
Maximum14.798%
Count13447
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.979% 5887 43.78% 0.429%
Negative -1.011% 6456 48.01% -0.485%
Zero 0.000% 1104 8.21% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.33. Further, an Excess Kurtosis of 5.30 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.52%150.54%0.54%
-9.52% to -7.07%291.03%1.57%
-7.07% to -4.62%1013.60%5.17%
-4.62% to -2.18%33411.92%17.09%
-2.18% to 0.27%93133.21%50.30%
0.27% to 2.72%90932.43%82.73%
2.72% to 5.17%32911.74%94.47%
5.17% to 7.61%1073.82%98.29%
7.61% to 10.06%260.93%99.22%
Greater than 10.06%220.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.99%3.53% 77.10%68.27%
±2σ -6.25%6.80% 95.01%95.45%
±3σ -9.52%10.06% 98.68%99.73%
Descriptive Statistics
Mean0.271%
Standard Error0.062%
Median0.248%
Mode0.000%
Standard Deviation3.263%
Sample Variance10.650%
Kurtosis5.30
Skewness0.33
Range44.773%
Minimum-19.677%
Maximum25.096%
Count2803
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.447% 1474 52.59% 1.287%
Negative -2.296% 1241 44.27% -1.017%
Zero 0.000% 88 3.14% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 6.63%
12 1 Quarter 4.91%
52 1 Year 4.60%
156 3 Years 3.86%
260 5 Years 3.72%
520 10 Years 3.55%
1,040 20 Years 3.46%
2,600 50 Years 4.57%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.00. Further, an Excess Kurtosis of 95.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.21%00.00%0.00%
-5.21% to -2.73%00.00%0.00%
-2.73% to -0.24%00.00%0.00%
-0.24% to 2.24%39514.09%14.09%
2.24% to 4.72%135948.47%62.55%
4.72% to 7.20%64022.82%85.38%
7.20% to 9.69%2599.24%94.61%
9.69% to 12.17%863.07%97.68%
12.17% to 14.65%311.11%98.79%
Greater than 14.65%341.21%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.41%8.03% 87.09%68.27%
±2σ -1.90%11.34% 97.08%95.45%
±3σ -5.21%14.65% 98.79%99.73%
Descriptive Statistics
Mean4.722%
Standard Error0.063%
Median3.975%
Mode4.000%
Standard Deviation3.310%
Sample Variance10.957%
Kurtosis95.31
Skewness6.00
Range77.147%
Minimum0.760%
Maximum77.907%
Count2804
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.722% 2804 100.00% 4.722%
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 5.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.54%180.64%0.64%
-9.54% to -7.18%210.75%1.39%
-7.18% to -4.83%1093.89%5.28%
-4.83% to -2.47%36212.91%18.19%
-2.47% to -0.11%91232.52%50.71%
-0.11% to 2.25%90132.13%82.85%
2.25% to 4.60%32611.63%94.47%
4.60% to 6.96%1003.57%98.04%
6.96% to 9.32%331.18%99.22%
Greater than 9.32%220.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.25%3.03% 76.50%68.27%
±2σ -6.40%6.17% 95.04%95.45%
±3σ -9.54%9.32% 98.57%99.73%
Descriptive Statistics
Mean-0.112%
Standard Error0.059%
Median-0.164%
Mode0.000%
Standard Deviation3.143%
Sample Variance9.879%
Kurtosis5.18
Skewness0.45
Range43.380%
Minimum-20.062%
Maximum23.318%
Count2804
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.348% 1265 45.11% 1.059%
Negative -2.259% 1453 51.82% -1.171%
Zero 0.000% 86 3.07% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.02. Further, an Excess Kurtosis of 3.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.24%50.78%0.78%
-17.24% to -12.65%60.93%1.71%
-12.65% to -8.05%223.42%5.12%
-8.05% to -3.46%8312.89%18.01%
-3.46% to 1.14%21433.23%51.24%
1.14% to 5.74%19830.75%81.99%
5.74% to 10.33%8312.89%94.88%
10.33% to 14.93%203.11%97.98%
14.93% to 19.52%101.55%99.53%
Greater than 19.52%30.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.99%7.27% 76.71%68.27%
±2σ -11.12%13.40% 94.72%95.45%
±3σ -17.24%19.52% 98.76%99.73%
Descriptive Statistics
Mean1.140%
Standard Error0.241%
Median0.991%
Mode0.000%
Standard Deviation6.128%
Sample Variance37.548%
Kurtosis3.67
Skewness0.02
Range64.154%
Minimum-28.411%
Maximum35.743%
Count644
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.795% 378 58.70% 2.814%
Negative -4.164% 259 40.22% -1.675%
Zero 0.000% 7 1.09% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 10.23%
12 1 Year 9.94%
36 3 Years 8.17%
60 5 Years 7.74%
120 10 Years 7.52%
240 20 Years 7.30%
600 50 Years 9.43%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.01. Further, an Excess Kurtosis of 30.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.35%00.00%0.00%
-10.35% to -5.17%00.00%0.00%
-5.17% to 0.01%00.00%0.00%
0.01% to 5.19%8212.71%12.71%
5.19% to 10.37%32350.08%62.79%
10.37% to 15.55%15524.03%86.82%
15.55% to 20.72%497.60%94.42%
20.72% to 25.90%152.33%96.74%
25.90% to 31.08%101.55%98.29%
Greater than 31.08%111.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 3.46%17.27% 88.06%68.27%
±2σ -3.44%24.18% 96.43%95.45%
±3σ -10.35%31.08% 98.29%99.73%
Descriptive Statistics
Mean10.367%
Standard Error0.272%
Median8.682%
Mode12.500%
Standard Deviation6.905%
Sample Variance47.677%
Kurtosis30.91
Skewness4.01
Range86.142%
Minimum2.811%
Maximum88.953%
Count645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.367% 645 100.00% 10.367%
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 1.05. Further, an Excess Kurtosis of 5.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -19.09%10.16%0.16%
-19.09% to -14.46%91.40%1.55%
-14.46% to -9.82%192.95%4.50%
-9.82% to -5.19%8413.02%17.52%
-5.19% to -0.56%21633.49%51.01%
-0.56% to 4.07%21433.18%84.19%
4.07% to 8.71%6810.54%94.73%
8.71% to 13.34%192.95%97.67%
13.34% to 17.97%71.09%98.76%
Greater than 17.97%81.24%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.74%5.62% 77.98%68.27%
±2σ -12.91%11.79% 94.57%95.45%
±3σ -19.09%17.97% 98.60%99.73%
Descriptive Statistics
Mean-0.559%
Standard Error0.243%
Median-0.709%
Mode0.000%
Standard Deviation6.176%
Sample Variance38.147%
Kurtosis5.94
Skewness1.05
Range65.569%
Minimum-26.331%
Maximum39.238%
Count645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.554% 270 41.86% 1.906%
Negative -4.381% 363 56.28% -2.466%
Zero 0.000% 12 1.86% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.05. Further, an Excess Kurtosis of 0.52 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -23.98%10.47%0.47%
-23.98% to -17.17%10.47%0.93%
-17.17% to -10.36%136.05%6.98%
-10.36% to -3.55%2511.63%18.60%
-3.55% to 3.26%6429.77%48.37%
3.26% to 10.07%6831.63%80.00%
10.07% to 16.88%3114.42%94.42%
16.88% to 23.69%73.26%97.67%
23.69% to 30.50%41.86%99.53%
Greater than 30.50%10.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.82%12.34% 68.84%68.27%
±2σ -14.90%21.42% 94.42%95.45%
±3σ -23.98%30.50% 99.07%99.73%
Descriptive Statistics
Mean3.262%
Standard Error0.619%
Median3.340%
Mode-24.079%
Standard Deviation9.080%
Sample Variance82.455%
Kurtosis0.52
Skewness0.05
Range55.121%
Minimum-24.079%
Maximum31.042%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.228% 140 65.12% 5.358%
Negative -6.008% 75 34.88% -2.096%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 13.22%
12 3 Years 13.11%
20 5 Years 12.59%
40 10 Years 12.66%
80 20 Years 12.40%
200 50 Years 15.93%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.85. Further, an Excess Kurtosis of 13.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.01%00.00%0.00%
-15.01% to -6.74%00.00%0.00%
-6.74% to 1.52%00.00%0.00%
1.52% to 9.78%3214.81%14.81%
9.78% to 18.04%10347.69%62.50%
18.04% to 26.31%4520.83%83.33%
26.31% to 34.57%188.33%91.67%
34.57% to 42.83%125.56%97.22%
42.83% to 51.09%31.39%98.61%
Greater than 51.09%31.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 7.03%29.06% 85.65%68.27%
±2σ -3.99%40.08% 96.76%95.45%
±3σ -15.01%51.09% 98.61%99.73%
Descriptive Statistics
Mean18.044%
Standard Error0.750%
Median14.707%
Mode13.027%
Standard Deviation11.017%
Sample Variance121.372%
Kurtosis13.86
Skewness2.85
Range91.072%
Minimum5.440%
Maximum96.512%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 18.044% 216 100.00% 18.044%
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 0.61. Further, an Excess Kurtosis of 1.01 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -28.26%00.00%0.00%
-28.26% to -21.66%20.93%0.93%
-21.66% to -15.05%73.24%4.17%
-15.05% to -8.44%3817.59%21.76%
-8.44% to -1.83%7132.87%54.63%
-1.83% to 4.77%5927.31%81.94%
4.77% to 11.38%219.72%91.67%
11.38% to 17.98%125.56%97.22%
17.98% to 24.59%41.85%99.07%
Greater than 24.59%20.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.64%6.97% 71.30%68.27%
±2σ -19.45%15.78% 93.98%95.45%
±3σ -28.26%24.59% 99.07%99.73%
Descriptive Statistics
Mean-1.835%
Standard Error0.599%
Median-2.788%
Mode-6.897%
Standard Deviation8.809%
Sample Variance77.603%
Kurtosis1.01
Skewness0.61
Range54.910%
Minimum-23.541%
Maximum31.369%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.000% 79 36.57% 2.560%
Negative -6.981% 136 62.96% -4.395%
Zero 0.000% 1 0.46% 0.000%