Markets Data Volatility Heatmap Portfolio Calculator

MRK Deep Analytical Report

Merck & Co., Inc. | Category: Equity Mega Cap | Ann. Div Yield: 2.66% ($3.24) | Last Updated: 2026-02-22 | Data Range: 1962-01-01 → 2026-02-01 (770 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 1.57% 1.20% 1.34% 2.04% 1.62% 1.70% 120.30 124.26 118.36 126.29
Weekly 3.56% 2.98% 3.47% 4.77% 3.57% 3.73% 117.98 126.70 113.84 131.30
Monthly 6.75% 5.63% 6.70% 10.21% 7.42% 7.77% 113.51 131.68 105.39 141.83
Quarterly 10.85% 9.02% 10.51% 17.60% 12.86% 13.46% 107.51 139.04 94.54 158.11
Annual — — — — 25.72% 26.93% 94.54 158.11 73.10 204.48
Option Time Horizon — — — — 9.89% 10.36% 110.75 134.97 100.32 149.01
Calculation Notes: Computed at 2026-02-22T14:17 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $122.26  |  Strike (K): $125.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.7500 (Bid $3.6000 / Ask $3.9000)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 2.66%  |  Binomial IV (Annual): 25.72% (CRR binomial tree, American, n=20 steps)  |  BS IV: 26.03% (European Black-Scholes)  |  Yahoo IV (Annual): 26.93% → 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
2025-12-15 $0.8500
2025-09-15 $0.8100
2025-06-16 $0.8100
2025-03-17 $0.8100
2024-12-16 $0.8100
2024-09-16 $0.7700
2024-06-17 $0.7700
2024-03-14 $0.7700
2023-12-14 $0.7700
2023-09-14 $0.7300
2023-06-14 $0.7300
2023-03-14 $0.7300
2022-12-14 $0.7300
2022-09-14 $0.6900
2022-06-14 $0.6900
2022-03-14 $0.6900
2021-12-14 $0.6900
2021-09-14 $0.6500
2021-06-14 $0.6500
2021-03-12 $0.6202
2020-12-14 $0.6202
2020-09-14 $0.5821
2020-06-12 $0.5821
2020-03-13 $0.5821
2019-12-13 $0.5821
2019-09-13 $0.5248
2019-06-14 $0.5248
2019-03-14 $0.5248
2018-12-14 $0.5248
2018-09-14 $0.4580
2018-06-14 $0.4580
2018-03-14 $0.4580
2017-12-14 $0.4580
2017-09-14 $0.4485
2017-06-13 $0.4485
2017-03-13 $0.4485
2016-12-13 $0.4485
2016-09-13 $0.4389
2016-06-13 $0.4389
2016-03-11 $0.4389
2015-12-11 $0.4389
2015-09-11 $0.4294
2015-06-11 $0.4294
2015-03-12 $0.4294
2014-12-11 $0.4294
2014-09-11 $0.4198
2014-06-12 $0.4198
2014-03-13 $0.4198
2013-12-12 $0.4198
2013-09-12 $0.4103
2013-06-13 $0.4103
2013-03-13 $0.4103
2012-12-13 $0.4103
2012-09-13 $0.4008
2012-06-13 $0.4008
2012-03-13 $0.4008
2011-12-13 $0.4008
2011-09-13 $0.3626
2011-06-13 $0.3626
2011-03-11 $0.3626
2010-12-13 $0.3626
2010-09-13 $0.3626
2010-06-11 $0.3626
2010-03-11 $0.3626
2009-12-11 $0.3626
2009-09-02 $0.3626
2009-06-04 $0.3626
2009-03-04 $0.3626
2008-12-03 $0.3626
2008-09-03 $0.3626
2008-06-04 $0.3626
2008-03-05 $0.3626
2007-12-05 $0.3626
2007-09-05 $0.3626
2007-06-06 $0.3626
2007-03-07 $0.3626
2006-12-06 $0.3626
2006-08-30 $0.3626
2006-05-31 $0.3626
2006-03-08 $0.3626
2005-11-30 $0.3626
2005-08-31 $0.3626
2005-06-01 $0.3626
2005-03-02 $0.3626
2004-12-01 $0.3626
2004-09-01 $0.3626
2004-06-02 $0.3531
2004-03-03 $0.3531
2003-12-03 $0.3531
2003-09-03 $0.3531
2003-08-20 $2.7443
2003-06-04 $0.3435
2003-03-05 $0.3435
2002-12-04 $0.3435
2002-09-04 $0.3435
2002-06-05 $0.3340
2002-03-06 $0.3340
2001-12-05 $0.3340
2001-08-30 $0.3340
2001-05-31 $0.3244
2001-03-07 $0.3244
2000-12-06 $0.3244
2000-08-30 $0.3244
2000-05-31 $0.2767
2000-03-01 $0.2767
1999-12-01 $0.2767
1999-09-01 $0.2767
1999-06-02 $0.2576
1999-03-03 $0.2576
1998-12-02 $0.2576
1998-09-02 $0.2576
1998-06-03 $0.2147
1998-03-04 $0.2147
1997-12-03 $0.2147
1997-09-03 $0.2147
1997-06-05 $0.2004
1997-03-05 $0.2004
1996-12-05 $0.1908
1996-09-04 $0.1908
1996-06-06 $0.1622
1996-03-06 $0.1622
1995-12-06 $0.1622
1995-09-05 $0.1622
1995-06-02 $0.1431
1995-03-03 $0.1431
1994-12-02 $0.1431
1994-09-02 $0.1431
1994-06-02 $0.1336
1994-03-02 $0.1336
1993-12-02 $0.1336
1993-09-02 $0.1336
1993-06-02 $0.1193
1993-03-02 $0.1193
1992-12-02 $0.1193
1992-08-31 $0.1193
1992-06-02 $0.1097
1992-03-02 $0.1097
1991-12-02 $0.1002
1991-08-30 $0.1002
1991-06-03 $0.0891
1991-03-04 $0.0891
1990-12-03 $0.0891
1990-08-28 $0.0891
1990-05-29 $0.0716
1990-03-05 $0.0716
1989-12-04 $0.0716
1989-08-29 $0.0716
1989-05-30 $0.0652
1989-03-02 $0.0652
1988-11-29 $0.0588
1988-08-29 $0.0469
1988-06-03 $0.0509
1988-02-29 $0.0509
1987-12-01 $0.0424
1987-08-28 $0.0424
1987-06-02 $0.0292
1987-03-02 $0.0292
1986-12-02 $0.0292
1986-09-02 $0.0292
1986-06-03 $0.0239
1986-02-27 $0.0239
1985-12-03 $0.0239
1985-08-30 $0.0212
1985-06-03 $0.0212
1985-02-28 $0.0212
1984-12-03 $0.0212
1984-08-31 $0.0199
1984-05-29 $0.0199
1984-03-01 $0.0199
1983-11-29 $0.0199
1983-08-29 $0.0186
1983-05-31 $0.0186
1983-02-28 $0.0186
1982-11-30 $0.0186
1982-08-30 $0.0186
1982-06-01 $0.0186
1982-03-01 $0.0186
1981-12-01 $0.0186
1981-08-31 $0.0172
1981-06-01 $0.0172
1981-03-02 $0.0172
1980-12-02 $0.0172
1980-08-29 $0.0152
1980-06-02 $0.0152
1980-02-28 $0.0152
1979-12-03 $0.0152
1979-08-31 $0.0126
1979-05-25 $0.0126
1979-03-01 $0.0126
1978-12-04 $0.0126
1978-08-28 $0.0113
1978-05-26 $0.0113
1978-03-02 $0.0113
1977-11-28 $0.0113
1977-08-29 $0.0099
1977-05-31 $0.0099
1977-03-01 $0.0099
1976-11-30 $0.0099
1976-08-30 $0.0093
1976-06-01 $0.0093
1976-03-02 $0.0093
1975-12-01 $0.0093
1975-08-29 $0.0093
1975-06-02 $0.0093
1975-03-03 $0.0093
1974-08-30 $0.0093
1974-06-03 $0.0093
1974-03-04 $0.0093
1973-12-03 $0.0093
1973-08-31 $0.0078
1973-06-05 $0.0078
1973-03-05 $0.0078
1972-12-05 $0.0078
1972-06-09 $0.0073
1972-03-02 $0.0073
1971-12-06 $0.0073
1971-09-03 $0.0073
1971-06-07 $0.0073
1971-03-02 $0.0073
1970-12-01 $0.0073
1970-09-02 $0.0066
1970-06-02 $0.0066
1969-12-01 $0.0093
1969-09-02 $0.0060
1969-06-03 $0.0060
1969-03-03 $0.0060
1968-12-02 $0.0086
1968-08-30 $0.0053
1968-06-04 $0.0053
1968-03-04 $0.0053
1967-12-07 $0.0080
1967-09-05 $0.0046
1967-06-06 $0.0046
1967-03-07 $0.0046
1966-11-30 $0.0073
1966-09-06 $0.0040
1966-06-07 $0.0040
1966-03-08 $0.0040
1965-11-30 $0.0066
1965-09-07 $0.0033
1965-06-08 $0.0033
1965-03-09 $0.0033
1964-12-01 $0.0066
1964-09-08 $0.0024
1964-06-09 $0.0024
1964-03-10 $0.0022
1963-12-03 $0.0031
1963-09-03 $0.0020
1963-03-05 $0.0020
1962-12-04 $0.0020
1962-09-05 $0.0018
1962-06-05 $0.0018
1962-03-06 $0.0018
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.29. Further, an Excess Kurtosis of 10.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.64%980.61%0.61%
-4.64% to -3.47%1590.99%1.59%
-3.47% to -2.29%5293.28%4.87%
-2.29% to -1.12%205712.74%17.61%
-1.12% to 0.06%549734.06%51.67%
0.06% to 1.23%493030.55%82.22%
1.23% to 2.41%197012.21%94.42%
2.41% to 3.58%6163.82%98.24%
3.58% to 4.76%1801.12%99.36%
Greater than 4.76%1040.64%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.51%1.63% 76.10%68.27%
±2σ -3.07%3.19% 95.20%95.45%
±3σ -4.64%4.76% 98.75%99.73%
Descriptive Statistics
Mean0.059%
Standard Error0.012%
Median0.000%
Mode0.000%
Standard Deviation1.567%
Sample Variance2.457%
Kurtosis10.50
Skewness-0.29
Range39.814%
Minimum-26.781%
Maximum13.033%
Count16140
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.194% 7910 49.01% 0.585%
Negative -1.116% 7606 47.12% -0.526%
Zero 0.000% 624 3.87% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 1.97%
20 1 Month 2.62%
60 1 Quarter 2.50%
250 1 Year 2.61%
750 3 Years 2.12%
1,250 5 Years 2.04%
2,500 10 Years 1.93%
5,000 20 Years 2.06%
12,500 50 Years 2.12%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.34. Further, an Excess Kurtosis of 24.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -1.63%00.00%0.00%
-1.63% to -0.73%00.00%0.00%
-0.73% to 0.16%00.00%0.00%
0.16% to 1.06%277317.18%17.18%
1.06% to 1.96%717244.43%61.61%
1.96% to 2.86%373323.13%84.74%
2.86% to 3.76%14478.96%93.71%
3.76% to 4.65%5453.38%97.08%
4.65% to 5.55%2311.43%98.51%
Greater than 5.55%2401.49%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.76%3.16% 83.76%68.27%
±2σ -0.43%4.35% 96.24%95.45%
±3σ -1.63%5.55% 98.51%99.73%
Descriptive Statistics
Mean1.960%
Standard Error0.009%
Median1.687%
Mode1.818%
Standard Deviation1.197%
Sample Variance1.432%
Kurtosis24.81
Skewness3.34
Range19.603%
Minimum0.194%
Maximum19.797%
Count16141
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.960% 16141 100.00% 1.960%
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 0.13. Further, an Excess Kurtosis of 4.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.04%850.53%0.53%
-4.04% to -3.03%1931.20%1.72%
-3.03% to -2.03%6443.99%5.71%
-2.03% to -1.02%199412.35%18.07%
-1.02% to -0.02%477529.58%47.65%
-0.02% to 0.98%555134.39%82.04%
0.98% to 1.99%201912.51%94.55%
1.99% to 2.99%6083.77%98.31%
2.99% to 3.99%1701.05%99.37%
Greater than 3.99%1020.63%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.36%1.32% 75.76%68.27%
±2σ -2.70%2.66% 95.07%95.45%
±3σ -4.04%3.99% 98.84%99.73%
Descriptive Statistics
Mean-0.021%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.338%
Sample Variance1.790%
Kurtosis4.99
Skewness0.13
Range22.255%
Minimum-10.380%
Maximum11.875%
Count16141
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.998% 7608 47.13% 0.470%
Negative -1.027% 7715 47.80% -0.491%
Zero 0.000% 818 5.07% 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 3.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.39%230.69%0.69%
-10.39% to -7.72%320.96%1.64%
-7.72% to -5.05%1173.50%5.14%
-5.05% to -2.38%46313.84%18.98%
-2.38% to 0.29%106231.74%50.72%
0.29% to 2.96%101430.30%81.02%
2.96% to 5.63%43913.12%94.14%
5.63% to 8.31%1374.09%98.24%
8.31% to 10.98%401.20%99.43%
Greater than 10.98%190.57%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.27%3.85% 74.09%68.27%
±2σ -6.83%7.42% 94.89%95.45%
±3σ -10.39%10.98% 98.74%99.73%
Descriptive Statistics
Mean0.292%
Standard Error0.062%
Median0.246%
Mode0.000%
Standard Deviation3.562%
Sample Variance12.685%
Kurtosis3.18
Skewness0.02
Range47.878%
Minimum-23.009%
Maximum24.869%
Count3346
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.764% 1767 52.81% 1.460%
Negative -2.555% 1529 45.70% -1.168%
Zero 0.000% 50 1.49% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 6.43%
12 1 Quarter 5.38%
52 1 Year 5.95%
156 3 Years 4.89%
260 5 Years 4.77%
520 10 Years 4.47%
1,040 20 Years 4.74%
2,600 50 Years 5.00%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 18.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -3.88%00.00%0.00%
-3.88% to -1.65%00.00%0.00%
-1.65% to 0.59%00.00%0.00%
0.59% to 2.82%55916.70%16.70%
2.82% to 5.06%153545.86%62.56%
5.06% to 7.29%74822.35%84.91%
7.29% to 9.53%2858.52%93.43%
9.53% to 11.76%1183.53%96.95%
11.76% to 14.00%511.52%98.48%
Greater than 14.00%511.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.08%8.04% 83.18%68.27%
±2σ -0.90%11.02% 96.24%95.45%
±3σ -3.88%14.00% 98.48%99.73%
Descriptive Statistics
Mean5.056%
Standard Error0.052%
Median4.365%
Mode5.263%
Standard Deviation2.980%
Sample Variance8.878%
Kurtosis18.79
Skewness3.09
Range39.018%
Minimum0.662%
Maximum39.680%
Count3347
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.056% 3347 100.00% 5.056%
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 4.70 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -10.49%110.33%0.33%
-10.49% to -7.89%381.14%1.46%
-7.89% to -5.29%1293.85%5.32%
-5.29% to -2.68%44413.27%18.58%
-2.68% to -0.08%108732.48%51.06%
-0.08% to 2.53%102530.62%81.69%
2.53% to 5.13%43112.88%94.56%
5.13% to 7.73%1153.44%98.00%
7.73% to 10.34%351.05%99.04%
Greater than 10.34%320.96%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.55%3.39% 74.90%68.27%
±2σ -7.02%6.87% 95.22%95.45%
±3σ -10.49%10.34% 98.72%99.73%
Descriptive Statistics
Mean-0.078%
Standard Error0.060%
Median-0.154%
Mode0.000%
Standard Deviation3.472%
Sample Variance12.054%
Kurtosis4.70
Skewness0.61
Range48.688%
Minimum-18.159%
Maximum30.529%
Count3347
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.612% 1570 46.91% 1.225%
Negative -2.529% 1725 51.54% -1.303%
Zero 0.000% 52 1.55% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.04. Further, an Excess Kurtosis of 0.96 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -19.04%40.52%0.52%
-19.04% to -13.97%81.04%1.56%
-13.97% to -8.91%354.55%6.11%
-8.91% to -3.84%11114.43%20.55%
-3.84% to 1.22%22529.26%49.80%
1.22% to 6.29%22929.78%79.58%
6.29% to 11.36%11114.43%94.02%
11.36% to 16.42%354.55%98.57%
16.42% to 21.49%81.04%99.61%
Greater than 21.49%30.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.53%7.98% 71.00%68.27%
±2σ -12.28%14.73% 94.54%95.45%
±3σ -19.04%21.49% 99.09%99.73%
Descriptive Statistics
Mean1.224%
Standard Error0.244%
Median1.284%
Mode-3.018%
Standard Deviation6.754%
Sample Variance45.616%
Kurtosis0.96
Skewness-0.04
Range57.335%
Minimum-25.992%
Maximum31.343%
Count769
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.649% 445 57.87% 3.269%
Negative -4.868% 323 42.00% -2.045%
Zero 0.000% 1 0.13% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 10.40%
12 1 Year 12.65%
36 3 Years 10.37%
60 5 Years 10.21%
120 10 Years 9.51%
240 20 Years 10.03%
600 50 Years 10.77%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.04. Further, an Excess Kurtosis of 6.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.47%00.00%0.00%
-5.47% to -1.24%00.00%0.00%
-1.24% to 2.98%00.00%0.00%
2.98% to 7.20%16221.04%21.04%
7.20% to 11.42%29538.31%59.35%
11.42% to 15.65%18724.29%83.64%
15.65% to 19.87%7710.00%93.64%
19.87% to 24.09%253.25%96.88%
24.09% to 28.31%111.43%98.31%
Greater than 28.31%131.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 5.79%17.05% 79.61%68.27%
±2σ 0.16%22.68% 95.84%95.45%
±3σ -5.47%28.31% 98.31%99.73%
Descriptive Statistics
Mean11.424%
Standard Error0.203%
Median9.994%
Mode10.526%
Standard Deviation5.630%
Sample Variance31.696%
Kurtosis6.88
Skewness2.04
Range41.309%
Minimum3.256%
Maximum44.565%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.424% 770 100.00% 11.424%
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 1.71 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -20.59%10.13%0.13%
-20.59% to -15.56%30.39%0.52%
-15.56% to -10.54%395.06%5.58%
-10.54% to -5.51%11915.45%21.04%
-5.51% to -0.48%24832.21%53.25%
-0.48% to 4.54%20726.88%80.13%
4.54% to 9.56%10313.38%93.51%
9.56% to 14.59%344.42%97.92%
14.59% to 19.61%121.56%99.48%
Greater than 19.61%40.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.19%6.21% 71.43%68.27%
±2σ -13.88%12.92% 94.94%95.45%
±3σ -20.59%19.62% 99.35%99.73%
Descriptive Statistics
Mean-0.485%
Standard Error0.241%
Median-0.848%
Mode-10.714%
Standard Deviation6.700%
Sample Variance44.885%
Kurtosis1.71
Skewness0.61
Range58.985%
Minimum-23.864%
Maximum35.121%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.369% 335 43.51% 2.336%
Negative -5.016% 433 56.23% -2.821%
Zero 0.000% 2 0.26% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.11. Further, an Excess Kurtosis of -0.10 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -28.98%10.39%0.39%
-28.98% to -20.84%10.39%0.78%
-20.84% to -12.70%166.23%7.00%
-12.70% to -4.56%4316.73%23.74%
-4.56% to 3.58%7428.79%52.53%
3.58% to 11.72%6826.46%78.99%
11.72% to 19.86%3312.84%91.83%
19.86% to 28.00%187.00%98.83%
28.00% to 36.14%31.17%100.00%
Greater than 36.14%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.27%14.43% 68.48%68.27%
±2σ -18.12%25.29% 95.72%95.45%
±3σ -28.98%36.14% 99.61%99.73%
Descriptive Statistics
Mean3.582%
Standard Error0.677%
Median3.028%
Mode-13.673%
Standard Deviation10.853%
Sample Variance117.790%
Kurtosis-0.10
Skewness0.11
Range62.509%
Minimum-30.371%
Maximum32.138%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.079% 161 62.65% 6.314%
Negative -7.314% 96 37.35% -2.732%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 19.88%
12 3 Years 17.41%
20 5 Years 17.60%
40 10 Years 15.81%
80 20 Years 17.22%
200 50 Years 18.80%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.61. Further, an Excess Kurtosis of 3.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.52%00.00%0.00%
-6.52% to 0.24%00.00%0.00%
0.24% to 7.00%20.78%0.78%
7.00% to 13.77%5521.32%22.09%
13.77% to 20.53%10239.53%61.63%
20.53% to 27.29%5521.32%82.95%
27.29% to 34.06%2710.47%93.41%
34.06% to 40.82%72.71%96.12%
40.82% to 47.59%31.16%97.29%
Greater than 47.59%72.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 11.51%29.55% 76.74%68.27%
±2σ 2.49%38.57% 95.35%95.45%
±3σ -6.52%47.59% 97.29%99.73%
Descriptive Statistics
Mean20.531%
Standard Error0.561%
Median19.060%
Mode12.650%
Standard Deviation9.018%
Sample Variance81.329%
Kurtosis3.47
Skewness1.61
Range51.200%
Minimum6.783%
Maximum57.983%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 20.531% 258 100.00% 20.531%
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 0.58. Further, an Excess Kurtosis of 0.97 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -33.16%00.00%0.00%
-33.16% to -25.28%00.00%0.00%
-25.28% to -17.40%155.81%5.81%
-17.40% to -9.52%4517.44%23.26%
-9.52% to -1.64%7529.07%52.33%
-1.64% to 6.24%6123.64%75.97%
6.24% to 14.12%4316.67%92.64%
14.12% to 22.00%145.43%98.06%
22.00% to 29.88%31.16%99.22%
Greater than 29.88%20.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -12.15%8.87% 70.93%68.27%
±2σ -22.65%19.37% 96.12%95.45%
±3σ -33.16%29.88% 99.22%99.73%
Descriptive Statistics
Mean-1.641%
Standard Error0.654%
Median-1.940%
Mode-22.950%
Standard Deviation10.506%
Sample Variance110.379%
Kurtosis0.97
Skewness0.58
Range67.632%
Minimum-22.950%
Maximum44.682%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 8.377% 105 40.70% 3.409%
Negative -8.516% 153 59.30% -5.050%
Zero 0.000% 0 0.00% 0.000%