Markets Data Volatility Heatmap Portfolio Calculator

PG Deep Analytical Report

The Procter & Gamble Company | Category: Equity Mega Cap | Ann. Div Yield: 2.90% ($4.18) | Last Updated: 2026-03-24 | Data Range: 1962-01-01 → 2026-03-01 (771 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 1.34% 1.19% 1.14% 1.57% 1.69% 1.72% 141.14 146.00 138.77 148.50
Weekly 2.97% 2.92% 2.90% 3.58% 3.73% 3.78% 138.29 149.00 133.23 154.67
Monthly 5.47% 5.83% 5.60% 7.65% 7.76% 7.87% 132.83 155.14 122.90 167.66
Quarterly 8.38% 9.58% 8.70% 12.63% 13.45% 13.63% 125.49 164.21 109.70 187.85
Annual — — — — 26.89% 27.26% 109.70 187.85 83.83 245.81
Option Time Horizon — — — — 10.15% 10.29% 129.69 158.89 117.17 175.86
Calculation Notes: Computed at 2026-03-23T16:31 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $143.55  |  Strike (K): $145.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $5.2250 (Bid $5.1000 / Ask $5.3500)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 2.90%  |  Binomial IV (Annual): 26.89% (CRR binomial tree, American, n=20 steps)  |  BS IV: 27.02% (European Black-Scholes)  |  Yahoo IV (Annual): 27.26% → 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
2026-01-23 $1.0570
2025-10-24 $1.0570
2025-07-18 $1.0570
2025-04-21 $1.0570
2025-01-24 $1.0070
2024-10-18 $1.0070
2024-07-19 $1.0070
2024-04-18 $1.0070
2024-01-18 $0.9410
2023-10-19 $0.9410
2023-07-20 $0.9410
2023-04-20 $0.9410
2023-01-19 $0.9130
2022-10-20 $0.9130
2022-07-21 $0.9130
2022-04-21 $0.9130
2022-01-20 $0.8700
2021-10-21 $0.8700
2021-07-22 $0.8700
2021-04-22 $0.8700
2021-01-21 $0.7910
2020-10-22 $0.7910
2020-07-23 $0.7910
2020-04-23 $0.7910
2020-01-23 $0.7460
2019-10-17 $0.7460
2019-07-18 $0.7460
2019-04-17 $0.7460
2019-01-17 $0.7170
2018-10-18 $0.7170
2018-07-19 $0.7170
2018-04-19 $0.7170
2018-01-18 $0.6900
2017-10-19 $0.6900
2017-07-19 $0.6900
2017-04-19 $0.6900
2017-01-18 $0.6700
2016-10-19 $0.6700
2016-07-20 $0.6700
2016-04-14 $0.6700
2016-01-20 $0.6630
2015-10-21 $0.6630
2015-07-22 $0.6630
2015-04-23 $0.6630
2015-01-21 $0.6440
2014-10-22 $0.6440
2014-07-16 $0.6440
2014-04-23 $0.6440
2014-01-22 $0.6020
2013-10-16 $0.6020
2013-07-17 $0.6020
2013-04-24 $0.6020
2013-01-16 $0.5620
2012-10-17 $0.5620
2012-07-18 $0.5620
2012-04-25 $0.5620
2012-01-18 $0.5250
2011-10-19 $0.5250
2011-07-20 $0.5250
2011-04-27 $0.5250
2011-01-19 $0.4820
2010-10-20 $0.4820
2010-07-21 $0.4820
2010-04-28 $0.4820
2010-01-20 $0.4400
2009-10-21 $0.4400
2009-07-22 $0.4400
2009-04-22 $0.4400
2009-01-21 $0.4000
2008-10-22 $0.4000
2008-07-16 $0.4000
2008-04-16 $0.4000
2008-01-16 $0.3500
2007-10-17 $0.3500
2007-07-18 $0.3500
2007-04-25 $0.3500
2007-01-17 $0.3100
2006-10-18 $0.3100
2006-07-19 $0.3100
2006-04-19 $0.3100
2006-01-18 $0.2800
2005-10-19 $0.2800
2005-07-20 $0.2800
2005-04-20 $0.2800
2005-01-19 $0.2500
2004-10-20 $0.2500
2004-07-21 $0.2500
2004-04-21 $0.2500
2004-01-21 $0.2275
2003-10-22 $0.2275
2003-07-16 $0.2275
2003-04-15 $0.2050
2003-01-22 $0.2050
2002-10-16 $0.2050
2002-07-17 $0.2050
2002-06-03 $0.3450
2002-04-17 $0.1900
2002-01-16 $0.1900
2001-10-17 $0.1900
2001-07-18 $0.1900
2001-04-18 $0.1750
2001-01-17 $0.1750
2000-10-18 $0.1750
2000-07-19 $0.1750
2000-04-18 $0.1600
2000-01-19 $0.1600
1999-10-20 $0.1600
1999-07-21 $0.1600
1999-04-21 $0.1425
1999-01-20 $0.1425
1998-10-21 $0.1425
1998-07-22 $0.1425
1998-04-22 $0.1260
1998-01-21 $0.1260
1997-10-22 $0.1260
1997-07-16 $0.1263
1997-04-16 $0.1125
1997-01-22 $0.1125
1996-10-16 $0.1125
1996-07-17 $0.1125
1996-04-17 $0.1000
1996-01-17 $0.1000
1995-10-18 $0.1000
1995-07-19 $0.1000
1995-04-17 $0.0875
1995-01-13 $0.0875
1994-10-17 $0.0875
1994-07-18 $0.0875
1994-04-18 $0.0775
1994-01-14 $0.0775
1993-10-18 $0.0775
1993-07-19 $0.0775
1993-04-19 $0.0688
1993-01-15 $0.0688
1992-10-19 $0.0688
1992-07-20 $0.0688
1992-04-20 $0.0688
1992-01-17 $0.0625
1991-10-11 $0.0625
1991-07-15 $0.0625
1991-04-15 $0.0625
1991-01-14 $0.0625
1990-10-15 $0.0625
1990-07-16 $0.0563
1990-04-16 $0.0563
1990-01-12 $0.0563
1989-10-16 $0.0563
1989-07-17 $0.0500
1989-04-17 $0.0500
1989-01-13 $0.0500
1988-10-17 $0.0437
1988-07-18 $0.0437
1988-04-18 $0.0437
1988-01-15 $0.0437
1987-10-19 $0.0422
1987-07-20 $0.0422
1987-04-20 $0.0422
1987-01-16 $0.0422
1986-10-20 $0.0422
1986-07-14 $0.0422
1986-04-14 $0.0422
1986-01-17 $0.0406
1985-10-11 $0.0406
1985-07-15 $0.0406
1985-04-15 $0.0406
1985-01-14 $0.0406
1984-10-15 $0.0406
1984-07-16 $0.0406
1984-04-13 $0.0375
1984-01-16 $0.0375
1983-10-17 $0.0375
1983-07-18 $0.0375
1983-04-18 $0.0375
1983-01-17 $0.0187
1982-10-18 $0.0328
1982-07-19 $0.0328
1982-04-19 $0.0328
1982-01-18 $0.0328
1981-10-19 $0.0328
1981-07-20 $0.0297
1981-04-20 $0.0297
1981-01-19 $0.0297
1980-10-20 $0.0297
1980-07-14 $0.0297
1980-04-14 $0.0266
1980-01-14 $0.0266
1979-10-15 $0.0266
1979-07-16 $0.0266
1979-04-16 $0.0266
1979-01-15 $0.0234
1978-10-16 $0.0234
1978-07-17 $0.0234
1978-04-17 $0.0234
1978-01-16 $0.0203
1977-10-17 $0.0203
1977-07-18 $0.0203
1977-04-18 $0.0203
1977-01-17 $0.0203
1976-10-18 $0.0172
1976-07-19 $0.0172
1976-04-19 $0.0172
1976-01-19 $0.0156
1975-10-20 $0.0156
1975-07-14 $0.0156
1975-04-14 $0.0156
1975-01-20 $0.0156
1974-10-11 $0.0141
1974-07-15 $0.0141
1974-04-15 $0.0141
1974-01-14 $0.0141
1973-10-15 $0.0141
1973-07-16 $0.0141
1973-04-13 $0.0122
1973-01-15 $0.0122
1972-10-16 $0.0122
1972-07-17 $0.0122
1972-04-17 $0.0117
1972-01-17 $0.0117
1971-10-18 $0.0117
1971-07-19 $0.0117
1971-04-19 $0.0109
1971-01-18 $0.0109
1970-10-19 $0.0109
1970-07-20 $0.0109
1970-04-20 $0.0109
1970-01-19 $0.0102
1969-10-20 $0.0102
1969-07-14 $0.0102
1969-04-14 $0.0102
1969-01-20 $0.0102
1968-10-14 $0.0094
1968-07-15 $0.0094
1968-04-15 $0.0094
1968-01-16 $0.0094
1967-10-17 $0.0086
1967-07-18 $0.0086
1967-04-18 $0.0086
1967-01-17 $0.0086
1966-10-18 $0.0078
1966-07-19 $0.0078
1966-04-19 $0.0078
1966-01-18 $0.0078
1965-10-19 $0.0072
1965-07-20 $0.0072
1965-04-20 $0.0072
1965-01-19 $0.0072
1964-10-20 $0.0068
1964-07-21 $0.0068
1964-04-21 $0.0068
1964-01-21 $0.0068
1963-10-15 $0.0063
1963-07-16 $0.0063
1963-04-16 $0.0063
1963-01-15 $0.0063
1962-10-16 $0.0059
1962-07-17 $0.0059
1962-04-16 $0.0059
1962-01-16 $0.0059
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.83. Further, an Excess Kurtosis of 35.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.97%820.51%0.51%
-3.97% to -2.97%1540.95%1.46%
-2.97% to -1.96%5303.28%4.74%
-1.96% to -0.96%186111.52%16.26%
-0.96% to 0.05%575535.61%51.87%
0.05% to 1.05%511031.62%83.49%
1.05% to 2.06%182511.29%94.78%
2.06% to 3.06%5593.46%98.24%
3.06% to 4.07%1731.07%99.31%
Greater than 4.07%1110.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.29%1.39% 77.82%68.27%
±2σ -2.63%2.73% 95.28%95.45%
±3σ -3.97%4.07% 98.81%99.73%
Descriptive Statistics
Mean0.049%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.340%
Sample Variance1.795%
Kurtosis35.48
Skewness-0.83
Range52.436%
Minimum-30.236%
Maximum22.200%
Count16160
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.983% 7908 48.94% 0.481%
Negative -0.931% 7510 46.47% -0.433%
Zero 0.000% 742 4.59% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.80%
20 1 Month 2.07%
60 1 Quarter 1.79%
250 1 Year 1.69%
750 3 Years 1.50%
1,250 5 Years 1.57%
2,500 10 Years 1.54%
5,000 20 Years 1.54%
12,500 50 Years 1.76%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 11.81. Further, an Excess Kurtosis of 424.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.94%00.00%0.00%
-1.94% to -1.05%00.00%0.00%
-1.05% to -0.16%00.00%0.00%
-0.16% to 0.73%166610.31%10.31%
0.73% to 1.63%850452.62%62.93%
1.63% to 2.52%387423.97%86.90%
2.52% to 3.41%13018.05%94.95%
3.41% to 4.30%4582.83%97.78%
4.30% to 5.20%1711.06%98.84%
Greater than 5.20%1871.16%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.44%2.82% 89.62%68.27%
±2σ -0.75%4.01% 96.97%95.45%
±3σ -1.94%5.20% 98.84%99.73%
Descriptive Statistics
Mean1.628%
Standard Error0.009%
Median1.360%
Mode1.786%
Standard Deviation1.190%
Sample Variance1.416%
Kurtosis424.91
Skewness11.81
Range59.035%
Minimum0.147%
Maximum59.182%
Count16161
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.628% 16161 100.00% 1.628%
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 6.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.44%1070.66%0.66%
-3.44% to -2.59%1921.19%1.85%
-2.59% to -1.74%5873.63%5.48%
-1.74% to -0.89%188211.65%17.13%
-0.89% to -0.04%499430.90%48.03%
-0.04% to 0.81%567335.10%83.13%
0.81% to 1.66%188011.63%94.77%
1.66% to 2.52%5833.61%98.37%
2.52% to 3.37%1460.90%99.28%
Greater than 3.37%1170.72%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.17%1.10% 76.78%68.27%
±2σ -2.31%2.23% 94.92%95.45%
±3σ -3.44%3.37% 98.61%99.73%
Descriptive Statistics
Mean-0.038%
Standard Error0.009%
Median0.000%
Mode0.000%
Standard Deviation1.135%
Sample Variance1.289%
Kurtosis6.84
Skewness0.22
Range24.035%
Minimum-9.982%
Maximum14.053%
Count16161
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.834% 7359 45.54% 0.380%
Negative -0.860% 7860 48.64% -0.418%
Zero 0.000% 942 5.83% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.70. Further, an Excess Kurtosis of 17.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.67%170.51%0.51%
-8.67% to -6.44%320.96%1.46%
-6.44% to -4.22%972.90%4.36%
-4.22% to -1.99%41612.42%16.78%
-1.99% to 0.24%114634.21%50.99%
0.24% to 2.46%102630.63%81.61%
2.46% to 4.69%44513.28%94.90%
4.69% to 6.92%1173.49%98.39%
6.92% to 9.14%391.16%99.55%
Greater than 9.14%150.45%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.73%3.21% 76.81%68.27%
±2σ -5.70%6.17% 95.79%95.45%
±3σ -8.67%9.14% 99.04%99.73%
Descriptive Statistics
Mean0.237%
Standard Error0.051%
Median0.166%
Mode0.000%
Standard Deviation2.969%
Sample Variance8.818%
Kurtosis17.22
Skewness-0.70
Range66.078%
Minimum-36.547%
Maximum29.531%
Count3350
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.220% 1752 52.30% 1.161%
Negative -1.989% 1555 46.42% -0.923%
Zero 0.000% 43 1.28% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 5.20%
12 1 Quarter 4.71%
52 1 Year 4.01%
156 3 Years 3.43%
260 5 Years 3.58%
520 10 Years 3.51%
1,040 20 Years 3.48%
2,600 50 Years 4.04%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.12. Further, an Excess Kurtosis of 110.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.68%00.00%0.00%
-4.68% to -2.49%00.00%0.00%
-2.49% to -0.30%00.00%0.00%
-0.30% to 1.88%36710.95%10.95%
1.88% to 4.07%171451.15%62.10%
4.07% to 6.26%85525.51%87.62%
6.26% to 8.44%2667.94%95.55%
8.44% to 10.63%812.42%97.97%
10.63% to 12.82%230.69%98.66%
Greater than 12.82%451.34%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.15%6.98% 90.18%68.27%
±2σ -1.76%9.90% 97.52%95.45%
±3σ -4.68%12.82% 98.66%99.73%
Descriptive Statistics
Mean4.069%
Standard Error0.050%
Median3.483%
Mode2.128%
Standard Deviation2.916%
Sample Variance8.502%
Kurtosis110.14
Skewness7.12
Range64.672%
Minimum0.745%
Maximum65.417%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.069% 3351 100.00% 4.069%
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 3.01. Further, an Excess Kurtosis of 56.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.79%80.24%0.24%
-8.79% to -6.62%270.81%1.04%
-6.62% to -4.45%1183.52%4.57%
-4.45% to -2.28%44613.31%17.88%
-2.28% to -0.11%109432.65%50.52%
-0.11% to 2.06%109232.59%83.11%
2.06% to 4.24%41112.26%95.37%
4.24% to 6.41%932.78%98.15%
6.41% to 8.58%381.13%99.28%
Greater than 8.58%240.72%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.00%2.79% 77.62%68.27%
±2σ -5.90%5.68% 95.88%95.45%
±3σ -8.79%8.58% 99.05%99.73%
Descriptive Statistics
Mean-0.107%
Standard Error0.050%
Median-0.141%
Mode0.000%
Standard Deviation2.895%
Sample Variance8.379%
Kurtosis56.45
Skewness3.01
Range75.059%
Minimum-15.385%
Maximum59.674%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.031% 1556 46.43% 0.943%
Negative -2.030% 1732 51.69% -1.049%
Zero 0.000% 63 1.88% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.27. Further, an Excess Kurtosis of 2.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -15.42%10.13%0.13%
-15.42% to -11.32%131.69%1.82%
-11.32% to -7.21%344.42%6.23%
-7.21% to -3.11%9612.47%18.70%
-3.11% to 0.99%25833.51%52.21%
0.99% to 5.10%20526.62%78.83%
5.10% to 9.20%11815.32%94.16%
9.20% to 13.31%364.68%98.83%
13.31% to 17.41%70.91%99.74%
Greater than 17.41%20.26%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.48%6.47% 72.21%68.27%
±2σ -9.95%11.94% 94.94%95.45%
±3σ -15.42%17.41% 99.61%99.73%
Descriptive Statistics
Mean0.995%
Standard Error0.197%
Median0.751%
Mode0.000%
Standard Deviation5.472%
Sample Variance29.938%
Kurtosis2.94
Skewness-0.27
Range60.546%
Minimum-35.420%
Maximum25.126%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.666% 428 55.58% 2.594%
Negative -3.664% 336 43.64% -1.599%
Zero 0.000% 6 0.78% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 11.47%
12 1 Year 8.54%
36 3 Years 7.32%
60 5 Years 7.65%
120 10 Years 7.41%
240 20 Years 7.42%
600 50 Years 8.54%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.00. Further, an Excess Kurtosis of 43.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -8.50%00.00%0.00%
-8.50% to -4.12%00.00%0.00%
-4.12% to 0.25%00.00%0.00%
0.25% to 4.63%9512.32%12.32%
4.63% to 9.00%39050.58%62.91%
9.00% to 13.38%18423.87%86.77%
13.38% to 17.75%668.56%95.33%
17.75% to 22.12%172.20%97.54%
22.12% to 26.50%91.17%98.70%
Greater than 26.50%101.30%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 3.17%14.83% 89.62%68.27%
±2σ -2.67%20.67% 97.41%95.45%
±3σ -8.50%26.50% 98.70%99.73%
Descriptive Statistics
Mean9.001%
Standard Error0.210%
Median7.558%
Mode6.667%
Standard Deviation5.833%
Sample Variance34.024%
Kurtosis43.60
Skewness5.00
Range69.991%
Minimum2.509%
Maximum72.500%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 9.001% 771 100.00% 9.001%
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 1.48. Further, an Excess Kurtosis of 12.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -17.25%20.26%0.26%
-17.25% to -13.06%20.26%0.52%
-13.06% to -8.86%314.02%4.54%
-8.86% to -4.66%13116.99%21.53%
-4.66% to -0.47%22829.57%51.10%
-0.47% to 3.73%24231.39%82.49%
3.73% to 7.93%8611.15%93.64%
7.93% to 12.12%314.02%97.67%
12.12% to 16.32%151.95%99.61%
Greater than 16.32%30.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.06%5.13% 75.10%68.27%
±2σ -11.66%10.73% 95.72%95.45%
±3σ -17.25%16.32% 99.35%99.73%
Descriptive Statistics
Mean-0.466%
Standard Error0.202%
Median-0.600%
Mode0.000%
Standard Deviation5.596%
Sample Variance31.310%
Kurtosis12.61
Skewness1.48
Range76.137%
Minimum-21.071%
Maximum55.066%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.124% 340 44.10% 1.819%
Negative -4.163% 423 54.86% -2.284%
Zero 0.000% 8 1.04% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.25. Further, an Excess Kurtosis of 2.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -22.23%10.39%0.39%
-22.23% to -15.95%00.00%0.39%
-15.95% to -9.67%103.89%4.28%
-9.67% to -3.38%3915.18%19.46%
-3.38% to 2.90%8231.91%51.36%
2.90% to 9.18%6926.85%78.21%
9.18% to 15.47%4216.34%94.55%
15.47% to 21.75%83.11%97.67%
21.75% to 28.03%62.33%100.00%
Greater than 28.03%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.48%11.28% 72.37%68.27%
±2σ -13.85%19.65% 95.33%95.45%
±3σ -22.23%28.03% 99.61%99.73%
Descriptive Statistics
Mean2.900%
Standard Error0.523%
Median2.806%
Mode7.849%
Standard Deviation8.377%
Sample Variance70.172%
Kurtosis2.55
Skewness-0.25
Range66.533%
Minimum-40.603%
Maximum25.930%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 7.718% 160 62.26% 4.805%
Negative -5.047% 97 37.74% -1.905%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 11.86%
12 3 Years 11.05%
20 5 Years 12.63%
40 10 Years 12.44%
80 20 Years 12.42%
200 50 Years 14.48%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.76. Further, an Excess Kurtosis of 21.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -13.00%00.00%0.00%
-13.00% to -5.82%00.00%0.00%
-5.82% to 1.36%00.00%0.00%
1.36% to 8.55%3011.63%11.63%
8.55% to 15.73%13251.16%62.79%
15.73% to 22.91%6525.19%87.98%
22.91% to 30.09%186.98%94.96%
30.09% to 37.28%51.94%96.90%
37.28% to 44.46%41.55%98.45%
Greater than 44.46%41.55%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 6.15%25.31% 90.70%68.27%
±2σ -3.43%34.88% 95.35%95.45%
±3σ -13.00%44.46% 98.45%99.73%
Descriptive Statistics
Mean15.729%
Standard Error0.596%
Median13.905%
Mode9.836%
Standard Deviation9.577%
Sample Variance91.726%
Kurtosis21.41
Skewness3.76
Range86.514%
Minimum4.718%
Maximum91.232%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 15.729% 258 100.00% 15.729%
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 2.09. Further, an Excess Kurtosis of 15.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -27.49%00.00%0.00%
-27.49% to -20.96%10.39%0.39%
-20.96% to -14.44%72.71%3.10%
-14.44% to -7.91%4818.60%21.71%
-7.91% to -1.39%7428.68%50.39%
-1.39% to 5.14%8432.56%82.95%
5.14% to 11.67%3312.79%95.74%
11.67% to 18.19%62.33%98.06%
18.19% to 24.72%41.55%99.61%
Greater than 24.72%10.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.09%7.32% 75.58%68.27%
±2σ -18.79%16.02% 95.74%95.45%
±3σ -27.49%24.72% 99.61%99.73%
Descriptive Statistics
Mean-1.386%
Standard Error0.542%
Median-1.480%
Mode0.000%
Standard Deviation8.701%
Sample Variance75.706%
Kurtosis15.39
Skewness2.09
Range90.125%
Minimum-21.610%
Maximum68.515%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.009% 106 41.09% 2.469%
Negative -6.631% 150 58.14% -3.855%
Zero 0.000% 2 0.78% 0.000%