Markets Data Volatility Heatmap Portfolio Calculator

MRK Deep Analytical Report

Merck & Co., Inc. | Category: Equity Mega Cap | Ann. Div Yield: 2.84% ($3.24) | 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 1.57% 1.20% 1.34% 2.05% 2.12% 2.17% 112.87 117.76 110.51 120.28
Weekly 3.56% 2.98% 3.47% 4.78% 4.66% 4.78% 110.04 120.79 105.03 126.56
Monthly 6.76% 5.63% 6.70% 10.23% 9.71% 9.96% 104.63 127.04 94.95 139.99
Quarterly 10.84% 9.01% 10.49% 17.68% 16.81% 17.25% 97.45 136.40 82.37 161.36
Annual — — — — 33.62% 34.50% 82.37 161.36 58.85 225.85
Option Time Horizon — — — — 12.69% 13.02% 101.55 130.89 89.45 148.60
Calculation Notes: Computed at 2026-03-23T16:31 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $115.29  |  Strike (K): $120.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.9750 (Bid $3.8000 / Ask $4.1500)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 2.84%  |  Binomial IV (Annual): 33.62% (CRR binomial tree, American, n=20 steps)  |  BS IV: 33.90% (European Black-Scholes)  |  Yahoo IV (Annual): 34.50% → 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
2026-03-16 $0.8500
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 10.49 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%1600.99%1.60%
-3.47% to -2.29%5303.28%4.88%
-2.29% to -1.12%206112.75%17.63%
-1.12% to 0.06%550434.06%51.69%
0.06% to 1.23%493530.54%82.22%
1.23% to 2.41%197212.20%94.42%
2.41% to 3.58%6173.82%98.24%
3.58% to 4.76%1801.11%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 Variance2.456%
Kurtosis10.49
Skewness-0.29
Range39.814%
Minimum-26.781%
Maximum13.033%
Count16161
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.194% 7918 48.99% 0.585%
Negative -1.116% 7619 47.14% -0.526%
Zero 0.000% 624 3.86% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.03%
20 1 Month 2.36%
60 1 Quarter 2.41%
250 1 Year 2.61%
750 3 Years 2.11%
1,250 5 Years 2.05%
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 0.17%00.00%0.00%
0.17% to 1.06%278117.21%17.21%
1.06% to 1.96%717044.36%61.57%
1.96% to 2.86%373323.10%84.67%
2.86% to 3.75%14599.03%93.70%
3.75% to 4.65%5443.37%97.06%
4.65% to 5.55%2341.45%98.51%
Greater than 5.55%2411.49%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.76%3.16% 83.73%68.27%
±2σ -0.43%4.35% 96.23%95.45%
±3σ -1.63%5.55% 98.51%99.73%
Descriptive Statistics
Mean1.960%
Standard Error0.009%
Median1.688%
Mode1.818%
Standard Deviation1.196%
Sample Variance1.431%
Kurtosis24.81
Skewness3.34
Range19.603%
Minimum0.194%
Maximum19.797%
Count16162
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.960% 16162 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 4.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.03%850.53%0.53%
-4.03% to -3.03%1941.20%1.73%
-3.03% to -2.03%6443.98%5.71%
-2.03% to -1.02%199612.35%18.06%
-1.02% to -0.02%478429.60%47.66%
-0.02% to 0.98%555834.39%82.05%
0.98% to 1.99%202012.50%94.55%
1.99% to 2.99%6093.77%98.32%
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% 75.77%68.27%
±2σ -2.70%2.66% 95.08%95.45%
±3σ -4.03%3.99% 98.84%99.73%
Descriptive Statistics
Mean-0.020%
Standard Error0.011%
Median0.000%
Mode0.000%
Standard Deviation1.338%
Sample Variance1.790%
Kurtosis4.98
Skewness0.13
Range22.255%
Minimum-10.380%
Maximum11.875%
Count16162
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 0.998% 7619 47.14% 0.470%
Negative -1.027% 7725 47.80% -0.491%
Zero 0.000% 818 5.06% 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 3.18 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%1173.49%5.13%
-5.05% to -2.38%46313.82%18.96%
-2.38% to 0.29%106631.82%50.78%
0.29% to 2.96%101430.27%81.04%
2.96% to 5.63%43913.10%94.15%
5.63% to 8.30%1374.09%98.24%
8.30% to 10.97%401.19%99.43%
Greater than 10.97%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%7.41% 94.90%95.45%
±3σ -10.39%10.97% 98.75%99.73%
Descriptive Statistics
Mean0.290%
Standard Error0.062%
Median0.241%
Mode0.000%
Standard Deviation3.561%
Sample Variance12.678%
Kurtosis3.18
Skewness0.02
Range47.878%
Minimum-23.009%
Maximum24.869%
Count3350
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.763% 1768 52.78% 1.458%
Negative -2.555% 1532 45.73% -1.168%
Zero 0.000% 50 1.49% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 4.73%
12 1 Quarter 5.25%
52 1 Year 5.95%
156 3 Years 4.89%
260 5 Years 4.78%
520 10 Years 4.49%
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 18.81 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%55816.65%16.65%
2.82% to 5.06%153845.90%62.55%
5.06% to 7.29%75022.38%84.93%
7.29% to 9.52%2848.48%93.40%
9.52% to 11.76%1193.55%96.96%
11.76% to 13.99%511.52%98.48%
Greater than 13.99%511.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.08%8.03% 83.20%68.27%
±2σ -0.90%11.01% 96.24%95.45%
±3σ -3.88%13.99% 98.48%99.73%
Descriptive Statistics
Mean5.056%
Standard Error0.051%
Median4.365%
Mode5.263%
Standard Deviation2.978%
Sample Variance8.868%
Kurtosis18.81
Skewness3.09
Range39.018%
Minimum0.662%
Maximum39.680%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.056% 3351 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 4.71 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 -7.88%381.13%1.46%
-7.88% to -5.28%1293.85%5.31%
-5.28% to -2.68%44413.25%18.56%
-2.68% to -0.08%108832.47%51.03%
-0.08% to 2.53%102830.68%81.71%
2.53% to 5.13%43112.86%94.57%
5.13% to 7.73%1153.43%98.00%
7.73% to 10.33%351.04%99.05%
Greater than 10.33%320.95%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.55%3.39% 74.90%68.27%
±2σ -7.02%6.86% 95.17%95.45%
±3σ -10.49%10.33% 98.72%99.73%
Descriptive Statistics
Mean-0.077%
Standard Error0.060%
Median-0.152%
Mode0.000%
Standard Deviation3.470%
Sample Variance12.043%
Kurtosis4.71
Skewness0.61
Range48.688%
Minimum-18.159%
Maximum30.529%
Count3351
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.610% 1573 46.94% 1.225%
Negative -2.528% 1726 51.51% -1.302%
Zero 0.000% 52 1.55% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.03. Further, an Excess Kurtosis of 0.96 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -19.05%40.52%0.52%
-19.05% to -13.99%81.04%1.56%
-13.99% to -8.92%354.55%6.10%
-8.92% to -3.85%11214.55%20.65%
-3.85% to 1.22%22429.09%49.74%
1.22% to 6.28%23029.87%79.61%
6.28% to 11.35%11014.29%93.90%
11.35% to 16.42%364.68%98.57%
16.42% to 21.48%81.04%99.61%
Greater than 21.48%30.39%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -5.54%7.97% 70.91%68.27%
±2σ -12.30%14.73% 94.55%95.45%
±3σ -19.05%21.48% 99.09%99.73%
Descriptive Statistics
Mean1.215%
Standard Error0.243%
Median1.276%
Mode-3.018%
Standard Deviation6.756%
Sample Variance45.639%
Kurtosis0.96
Skewness-0.03
Range57.335%
Minimum-25.992%
Maximum31.343%
Count770
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.650% 445 57.79% 3.265%
Negative -4.871% 324 42.08% -2.050%
Zero 0.000% 1 0.13% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 10.27%
12 1 Year 12.60%
36 3 Years 10.41%
60 5 Years 10.23%
120 10 Years 9.54%
240 20 Years 10.05%
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 6.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.46%00.00%0.00%
-5.46% to -1.24%00.00%0.00%
-1.24% to 2.98%00.00%0.00%
2.98% to 7.20%16221.01%21.01%
7.20% to 11.42%29638.39%59.40%
11.42% to 15.64%18724.25%83.66%
15.64% to 19.86%779.99%93.64%
19.86% to 24.09%253.24%96.89%
24.09% to 28.30%111.43%98.31%
Greater than 28.30%131.69%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 5.80%17.05% 79.64%68.27%
±2σ 0.17%22.68% 95.85%95.45%
±3σ -5.46%28.30% 98.31%99.73%
Descriptive Statistics
Mean11.424%
Standard Error0.203%
Median9.987%
Mode10.526%
Standard Deviation5.627%
Sample Variance31.665%
Kurtosis6.89
Skewness2.04
Range41.309%
Minimum3.256%
Maximum44.565%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.424% 771 100.00% 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 0.60. Further, an Excess Kurtosis of 1.70 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 -10.53%405.19%5.71%
-10.53% to -5.50%11915.43%21.14%
-5.50% to -0.48%24932.30%53.44%
-0.48% to 4.55%20626.72%80.16%
4.55% to 9.58%10413.49%93.64%
9.58% to 14.61%334.28%97.92%
14.61% to 19.63%121.56%99.48%
Greater than 19.63%40.52%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.18%6.23% 71.34%68.27%
±2σ -13.88%12.93% 94.94%95.45%
±3σ -20.59%19.63% 99.35%99.73%
Descriptive Statistics
Mean-0.477%
Standard Error0.241%
Median-0.844%
Mode-10.714%
Standard Deviation6.703%
Sample Variance44.925%
Kurtosis1.70
Skewness0.60
Range58.985%
Minimum-23.864%
Maximum35.121%
Count771
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.374% 336 43.58% 2.342%
Negative -5.019% 433 56.16% -2.819%
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 -0.09 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -28.97%10.39%0.39%
-28.97% to -20.84%10.39%0.78%
-20.84% to -12.71%166.23%7.00%
-12.71% to -4.57%4316.73%23.74%
-4.57% to 3.56%7428.79%52.53%
3.56% to 11.69%6826.46%78.99%
11.69% to 19.82%3312.84%91.83%
19.82% to 27.96%187.00%98.83%
27.96% to 36.09%31.17%100.00%
Greater than 36.09%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.28%14.40% 68.48%68.27%
±2σ -18.13%25.25% 95.72%95.45%
±3σ -28.97%36.09% 99.61%99.73%
Descriptive Statistics
Mean3.559%
Standard Error0.676%
Median3.028%
Mode-13.673%
Standard Deviation10.844%
Sample Variance117.588%
Kurtosis-0.09
Skewness0.11
Range62.509%
Minimum-30.371%
Maximum32.138%
Count257
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.042% 161 62.65% 6.291%
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 20.29%
12 3 Years 17.55%
20 5 Years 17.68%
40 10 Years 15.85%
80 20 Years 17.24%
200 50 Years 18.81%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.62. Further, an Excess Kurtosis of 3.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -6.50%00.00%0.00%
-6.50% to 0.26%00.00%0.00%
0.26% to 7.02%20.78%0.78%
7.02% to 13.78%5621.71%22.48%
13.78% to 20.54%10139.15%61.63%
20.54% to 27.30%5521.32%82.95%
27.30% to 34.06%2710.47%93.41%
34.06% to 40.82%72.71%96.12%
40.82% to 47.58%31.16%97.29%
Greater than 47.58%72.71%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 11.53%29.55% 76.74%68.27%
±2σ 2.51%38.56% 95.35%95.45%
±3σ -6.50%47.58% 97.29%99.73%
Descriptive Statistics
Mean20.538%
Standard Error0.561%
Median19.059%
Mode12.650%
Standard Deviation9.013%
Sample Variance81.232%
Kurtosis3.48
Skewness1.62
Range51.200%
Minimum6.783%
Maximum57.983%
Count258
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 20.538% 258 100.00% 20.538%
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 0.98 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -33.11%00.00%0.00%
-33.11% to -25.23%00.00%0.00%
-25.23% to -17.36%155.81%5.81%
-17.36% to -9.49%4517.44%23.26%
-9.49% to -1.62%7629.46%52.71%
-1.62% to 6.25%6023.26%75.97%
6.25% to 14.12%4316.67%92.64%
14.12% to 21.99%145.43%98.06%
21.99% to 29.86%31.16%99.22%
Greater than 29.86%20.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -12.12%8.87% 70.54%68.27%
±2σ -22.61%19.37% 96.12%95.45%
±3σ -33.11%29.86% 99.22%99.73%
Descriptive Statistics
Mean-1.621%
Standard Error0.653%
Median-1.940%
Mode-22.950%
Standard Deviation10.495%
Sample Variance110.149%
Kurtosis0.98
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 -8.483% 153 59.30% -5.031%
Zero 0.000% 0 0.00% 0.000%