Markets Data Volatility Heatmap Portfolio Calculator

PEP Deep Analytical Report

PepsiCo, Inc. | Category: Equity Mega Cap | Ann. Div Yield: 3.75% ($5.62) | Last Updated: 2026-03-24 | Data Range: 1972-06-01 → 2026-03-01 (646 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% 1.89% 1.91% 147.50 153.18 144.74 156.10
Weekly 3.26% 3.31% 3.14% 3.72% 4.16% 4.20% 144.19 156.70 138.32 163.35
Monthly 6.14% 6.90% 6.20% 7.73% 8.66% 8.75% 137.85 163.91 126.42 178.72
Quarterly 9.08% 11.01% 8.81% 12.71% 14.99% 15.16% 129.39 174.63 111.37 202.87
Annual — — — — 29.98% 30.32% 111.37 202.87 82.52 273.80
Option Time Horizon — — — — 11.32% 11.44% 134.23 168.33 119.87 188.50
Calculation Notes: Computed at 2026-03-23T16:31 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $150.32  |  Strike (K): $155.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $4.8500 (Bid $4.7000 / Ask $5.0000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.75%  |  Binomial IV (Annual): 29.98% (CRR binomial tree, American, n=20 steps)  |  BS IV: 30.34% (European Black-Scholes)  |  Yahoo IV (Annual): 30.32% → 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
2026-03-06 $1.4230
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 -3.38%1351.00%1.66%
-3.38% to -2.24%4673.47%5.13%
-2.24% to -1.09%152111.29%16.43%
-1.09% to 0.06%501837.26%53.69%
0.06% to 1.20%397329.50%83.19%
1.20% to 2.35%153311.38%94.57%
2.35% to 3.50%4733.51%98.08%
3.50% to 4.64%1531.14%99.22%
Greater than 4.64%1050.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.47%1.58% 77.83%68.27%
±2σ -3.00%3.11% 94.82%95.45%
±3σ -4.53%4.64% 98.56%99.73%
Descriptive Statistics
Mean0.056%
Standard Error0.013%
Median0.000%
Mode0.000%
Standard Deviation1.529%
Sample Variance2.339%
Kurtosis7.32
Skewness0.18
Range30.430%
Minimum-14.286%
Maximum16.144%
Count13467
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.168% 6410 47.60% 0.556%
Negative -1.098% 6127 45.50% -0.500%
Zero 0.000% 930 6.91% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.86%
20 1 Month 1.95%
60 1 Quarter 1.97%
250 1 Year 1.90%
750 3 Years 1.65%
1,250 5 Years 1.63%
2,500 10 Years 1.58%
5,000 20 Years 1.57%
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 323.47 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%170612.67%12.67%
0.88% to 1.91%676250.21%62.87%
1.91% to 2.95%308222.88%85.76%
2.95% to 3.98%11258.35%94.11%
3.98% to 5.02%4653.45%97.56%
5.02% to 6.05%1581.17%98.74%
Greater than 6.05%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%4.67% 96.70%95.45%
±3σ -2.23%6.05% 98.74%99.73%
Descriptive Statistics
Mean1.914%
Standard Error0.012%
Median1.577%
Mode1.531%
Standard Deviation1.380%
Sample Variance1.904%
Kurtosis323.47
Skewness9.48
Range63.806%
Minimum0.148%
Maximum63.954%
Count13468
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.914% 13468 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 6.72 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%4813.57%5.45%
-2.03% to -1.04%158011.73%17.18%
-1.04% to -0.06%397429.51%46.69%
-0.06% to 0.93%494936.75%83.43%
0.93% to 1.91%150511.17%94.61%
1.91% to 2.90%4713.50%98.11%
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% 76.76%68.27%
±2σ -2.68%2.57% 94.61%95.45%
±3σ -4.00%3.88% 98.63%99.73%
Descriptive Statistics
Mean-0.056%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.313%
Sample Variance1.724%
Kurtosis6.72
Skewness0.22
Range26.241%
Minimum-11.443%
Maximum14.798%
Count13468
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.979% 5900 43.81% 0.429%
Negative -1.011% 6464 47.99% -0.485%
Zero 0.000% 1104 8.20% 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 5.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.52%150.53%0.53%
-9.52% to -7.08%281.00%1.53%
-7.08% to -4.63%1023.63%5.17%
-4.63% to -2.18%33611.97%17.14%
-2.18% to 0.27%93133.17%50.30%
0.27% to 2.71%91132.45%82.76%
2.71% to 5.16%32911.72%94.48%
5.16% to 7.61%1073.81%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 -3.00%3.53% 77.16%68.27%
±2σ -6.26%6.79% 95.01%95.45%
±3σ -9.52%10.06% 98.68%99.73%
Descriptive Statistics
Mean0.267%
Standard Error0.062%
Median0.247%
Mode0.000%
Standard Deviation3.263%
Sample Variance10.650%
Kurtosis5.29
Skewness0.33
Range44.773%
Minimum-19.677%
Maximum25.096%
Count2807
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.447% 1475 52.55% 1.286%
Negative -2.299% 1244 44.32% -1.019%
Zero 0.000% 88 3.13% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.68%
12 1 Quarter 5.17%
52 1 Year 4.57%
156 3 Years 3.89%
260 5 Years 3.72%
520 10 Years 3.57%
1,040 20 Years 3.47%
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 95.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.20%00.00%0.00%
-5.20% to -2.72%00.00%0.00%
-2.72% to -0.24%00.00%0.00%
-0.24% to 2.24%39614.10%14.10%
2.24% to 4.72%135948.40%62.50%
4.72% to 7.21%64322.90%85.40%
7.21% to 9.69%2599.22%94.62%
9.69% to 12.17%863.06%97.69%
12.17% to 14.65%311.10%98.79%
Greater than 14.65%341.21%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.41%8.03% 87.11%68.27%
±2σ -1.90%11.34% 97.08%95.45%
±3σ -5.20%14.65% 98.79%99.73%
Descriptive Statistics
Mean4.723%
Standard Error0.062%
Median3.975%
Mode4.000%
Standard Deviation3.309%
Sample Variance10.947%
Kurtosis95.34
Skewness6.00
Range77.147%
Minimum0.760%
Maximum77.907%
Count2808
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.723% 2808 100.00% 4.723%
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 5.16 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 -4.82%1093.88%5.27%
-4.82% to -2.46%36212.89%18.16%
-2.46% to -0.11%91632.62%50.78%
-0.11% to 2.25%89932.02%82.80%
2.25% to 4.61%32711.65%94.44%
4.61% to 6.96%1013.60%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% 76.35%68.27%
±2σ -6.39%6.18% 95.05%95.45%
±3σ -9.54%9.32% 98.58%99.73%
Descriptive Statistics
Mean-0.108%
Standard Error0.059%
Median-0.163%
Mode0.000%
Standard Deviation3.143%
Sample Variance9.881%
Kurtosis5.16
Skewness0.45
Range43.380%
Minimum-20.062%
Maximum23.318%
Count2808
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.350% 1268 45.16% 1.061%
Negative -2.259% 1454 51.78% -1.170%
Zero 0.000% 86 3.06% 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 3.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.31%50.78%0.78%
-17.31% to -12.70%60.93%1.71%
-12.70% to -8.09%233.57%5.27%
-8.09% to -3.48%8212.71%17.98%
-3.48% to 1.12%21433.18%51.16%
1.12% to 5.73%19830.70%81.86%
5.73% to 10.34%8413.02%94.88%
10.34% to 14.95%203.10%97.98%
14.95% to 19.56%101.55%99.53%
Greater than 19.56%30.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.02%7.27% 76.59%68.27%
±2σ -11.16%13.41% 94.73%95.45%
±3σ -17.31%19.56% 98.76%99.73%
Descriptive Statistics
Mean1.125%
Standard Error0.242%
Median0.970%
Mode0.000%
Standard Deviation6.144%
Sample Variance37.751%
Kurtosis3.61
Skewness0.02
Range64.154%
Minimum-28.411%
Maximum35.743%
Count645
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.801% 378 58.60% 2.814%
Negative -4.188% 260 40.31% -1.688%
Zero 0.000% 7 1.08% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 12.14%
12 1 Year 10.09%
36 3 Years 8.29%
60 5 Years 7.73%
120 10 Years 7.57%
240 20 Years 7.33%
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 30.93 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.33%00.00%0.00%
-10.33% to -5.16%00.00%0.00%
-5.16% to 0.02%00.00%0.00%
0.02% to 5.20%8312.85%12.85%
5.20% to 10.37%32249.85%62.69%
10.37% to 15.55%15624.15%86.84%
15.55% to 20.72%497.59%94.43%
20.72% to 25.90%152.32%96.75%
25.90% to 31.07%101.55%98.30%
Greater than 31.07%111.70%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 3.47%17.27% 87.93%68.27%
±2σ -3.43%24.17% 96.44%95.45%
±3σ -10.33%31.07% 98.30%99.73%
Descriptive Statistics
Mean10.372%
Standard Error0.271%
Median8.703%
Mode12.500%
Standard Deviation6.901%
Sample Variance47.618%
Kurtosis30.93
Skewness4.01
Range86.142%
Minimum2.811%
Maximum88.953%
Count646
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.372% 646 100.00% 10.372%
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 1.04. Further, an Excess Kurtosis of 5.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -19.13%10.15%0.15%
-19.13% to -14.49%91.39%1.55%
-14.49% to -9.84%192.94%4.49%
-9.84% to -5.19%8413.00%17.49%
-5.19% to -0.54%21733.59%51.08%
-0.54% to 4.11%21332.97%84.06%
4.11% to 8.75%6910.68%94.74%
8.75% to 13.40%203.10%97.83%
13.40% to 18.05%60.93%98.76%
Greater than 18.05%81.24%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.74%5.65% 77.86%68.27%
±2σ -12.94%11.85% 94.43%95.45%
±3σ -19.13%18.05% 98.61%99.73%
Descriptive Statistics
Mean-0.543%
Standard Error0.244%
Median-0.693%
Mode0.000%
Standard Deviation6.197%
Sample Variance38.406%
Kurtosis5.83
Skewness1.04
Range65.569%
Minimum-26.331%
Maximum39.238%
Count646
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.583% 271 41.95% 1.923%
Negative -4.388% 363 56.19% -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 0.06. Further, an Excess Kurtosis of 0.52 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -24.03%10.47%0.47%
-24.03% to -17.22%10.47%0.93%
-17.22% to -10.41%136.05%6.98%
-10.41% to -3.59%2511.63%18.60%
-3.59% to 3.22%6530.23%48.84%
3.22% to 10.03%6630.70%79.53%
10.03% to 16.84%3214.88%94.42%
16.84% to 23.66%73.26%97.67%
23.66% to 30.47%41.86%99.53%
Greater than 30.47%10.47%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.86%12.30% 68.84%68.27%
±2σ -14.95%21.39% 94.42%95.45%
±3σ -24.03%30.47% 99.07%99.73%
Descriptive Statistics
Mean3.219%
Standard Error0.619%
Median3.323%
Mode-24.079%
Standard Deviation9.083%
Sample Variance82.506%
Kurtosis0.52
Skewness0.06
Range55.121%
Minimum-24.079%
Maximum31.042%
Count215
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.235% 139 64.65% 5.324%
Negative -5.955% 76 35.35% -2.105%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 13.84%
12 3 Years 13.32%
20 5 Years 12.71%
40 10 Years 12.72%
80 20 Years 12.43%
200 50 Years 15.94%
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 13.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -14.97%00.00%0.00%
-14.97% to -6.72%00.00%0.00%
-6.72% to 1.54%00.00%0.00%
1.54% to 9.80%3315.28%15.28%
9.80% to 18.06%10247.22%62.50%
18.06% to 26.32%4520.83%83.33%
26.32% 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 7.05%29.07% 85.65%68.27%
±2σ -3.96%40.08% 96.76%95.45%
±3σ -14.98%51.09% 98.61%99.73%
Descriptive Statistics
Mean18.058%
Standard Error0.749%
Median14.721%
Mode13.027%
Standard Deviation11.011%
Sample Variance121.246%
Kurtosis13.88
Skewness2.85
Range91.072%
Minimum5.440%
Maximum96.512%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 18.058% 216 100.00% 18.058%
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 0.60. 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 -28.22%00.00%0.00%
-28.22% to -21.61%20.93%0.93%
-21.61% to -15.01%73.24%4.17%
-15.01% to -8.40%3817.59%21.76%
-8.40% to -1.79%7032.41%54.17%
-1.79% to 4.81%6027.78%81.94%
4.81% to 11.42%2210.19%92.13%
11.42% to 18.02%115.09%97.22%
18.02% to 24.63%41.85%99.07%
Greater than 24.63%20.93%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.60%7.01% 71.30%68.27%
±2σ -19.41%15.82% 93.98%95.45%
±3σ -28.22%24.63% 99.07%99.73%
Descriptive Statistics
Mean-1.794%
Standard Error0.599%
Median-2.680%
Mode-6.897%
Standard Deviation8.808%
Sample Variance77.578%
Kurtosis1.01
Skewness0.60
Range54.910%
Minimum-23.541%
Maximum31.369%
Count216
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.942% 80 37.04% 2.571%
Negative -6.984% 135 62.50% -4.365%
Zero 0.000% 1 0.46% 0.000%