Markets Data Volatility Heatmap Portfolio Calculator

CVS Deep Analytical Report

CVS Health Corporation | Category: Equity Mega Cap | Ann. Div Yield: 3.72% ($2.66) | Last Updated: 2026-03-24 | Data Range: 1973-05-01 → 2026-03-01 (635 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 1.95% 1.61% 1.69% 2.41% 2.42% 2.46% 69.01 72.43 67.36 74.20
Weekly 4.38% 3.93% 4.30% 5.87% 5.32% 5.42% 67.03 74.56 63.56 78.64
Monthly 8.40% 8.33% 8.57% 12.82% 11.08% 11.28% 63.28 78.98 56.64 88.23
Quarterly 13.92% 16.53% 15.05% 21.47% 19.19% 19.54% 58.35 85.65 48.16 103.77
Annual — — — — 38.38% 39.09% 48.16 103.77 32.81 152.33
Option Time Horizon — — — — 14.49% 14.75% 61.16 81.72 52.91 94.46
Calculation Notes: Computed at 2026-03-23T16:43 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $70.69  |  Strike (K): $72.50 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.3250 (Bid $3.2000 / Ask $3.4500)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.72%  |  Binomial IV (Annual): 38.38% (CRR binomial tree, American, n=20 steps)  |  BS IV: 38.84% (European Black-Scholes)  |  Yahoo IV (Annual): 39.09% → 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
2026-01-22 $0.6650
2025-10-23 $0.6650
2025-07-22 $0.6650
2025-04-22 $0.6650
2025-01-23 $0.6650
2024-10-21 $0.6650
2024-07-22 $0.6650
2024-04-19 $0.6650
2024-01-19 $0.6650
2023-10-19 $0.6050
2023-07-20 $0.6050
2023-04-20 $0.6050
2023-01-19 $0.6050
2022-10-20 $0.5500
2022-07-21 $0.5500
2022-04-21 $0.5500
2022-01-20 $0.5500
2021-10-21 $0.5000
2021-07-22 $0.5000
2021-04-22 $0.5000
2021-01-21 $0.5000
2020-10-21 $0.5000
2020-07-22 $0.5000
2020-04-22 $0.5000
2020-01-22 $0.5000
2019-10-23 $0.5000
2019-07-24 $0.5000
2019-04-22 $0.5000
2019-01-24 $0.5000
2018-10-23 $0.5000
2018-07-24 $0.5000
2018-04-20 $0.5000
2018-01-23 $0.5000
2017-10-23 $0.5000
2017-07-20 $0.5000
2017-04-19 $0.5000
2017-01-20 $0.5000
2016-10-20 $0.4250
2016-07-19 $0.4250
2016-04-20 $0.4250
2016-01-20 $0.4250
2015-10-20 $0.3500
2015-07-21 $0.3500
2015-04-22 $0.3500
2015-01-20 $0.3500
2014-10-21 $0.2750
2014-07-17 $0.2750
2014-04-17 $0.2750
2014-01-21 $0.2750
2013-10-17 $0.2250
2013-07-18 $0.2250
2013-04-19 $0.2250
2013-01-22 $0.2250
2012-10-18 $0.1630
2012-07-19 $0.1630
2012-04-19 $0.1630
2012-01-19 $0.1630
2011-10-19 $0.1250
2011-07-20 $0.1250
2011-04-19 $0.1250
2011-01-19 $0.1250
2010-10-20 $0.0880
2010-07-20 $0.0880
2010-04-21 $0.0880
2010-01-20 $0.0880
2009-10-20 $0.0760
2009-07-21 $0.0760
2009-04-20 $0.0760
2009-01-21 $0.0760
2008-10-17 $0.0690
2008-07-17 $0.0690
2008-04-17 $0.0600
2008-01-17 $0.0600
2007-10-18 $0.0600
2007-07-19 $0.0600
2007-04-20 $0.0600
2007-01-18 $0.0490
2006-10-18 $0.0390
2006-07-19 $0.0390
2006-04-20 $0.0390
2006-01-19 $0.0390
2005-10-19 $0.0360
2005-07-19 $0.0360
2005-04-20 $0.0365
2005-01-20 $0.0365
2004-10-20 $0.0340
2004-07-20 $0.0330
2004-04-21 $0.0330
2004-01-20 $0.0335
2003-10-17 $0.0290
2003-07-17 $0.0290
2003-04-17 $0.0290
2003-01-21 $0.0290
2002-10-17 $0.0290
2002-07-18 $0.0290
2002-04-19 $0.0290
2002-01-18 $0.0290
2001-10-18 $0.0290
2001-07-19 $0.0290
2001-04-20 $0.0290
2001-01-19 $0.0290
2000-10-19 $0.0290
2000-07-20 $0.0290
2000-04-20 $0.0290
2000-01-20 $0.0290
1999-10-20 $0.0290
1999-07-20 $0.0290
1999-04-21 $0.0290
1999-01-20 $0.0290
1998-10-21 $0.0290
1998-07-21 $0.0290
1998-04-21 $0.0275
1998-01-21 $0.0275
1997-10-21 $0.0275
1997-07-21 $0.0070
1997-04-21 $0.0070
1997-01-21 $0.0070
1996-10-21 $0.0070
1996-10-16 $1.4750
1996-07-19 $0.0275
1996-04-18 $0.0275
1996-01-19 $0.0275
1995-10-20 $0.0950
1995-07-20 $0.0950
1995-04-18 $0.0950
1995-01-18 $0.0950
1994-10-18 $0.0950
1994-07-19 $0.0950
1994-04-19 $0.0950
1994-01-18 $0.0950
1993-10-19 $0.0950
1993-07-20 $0.0950
1993-04-19 $0.0950
1993-01-19 $0.0950
1992-10-20 $0.0925
1992-07-20 $0.0925
1992-04-20 $0.0925
1992-01-14 $0.0925
1991-10-16 $0.0900
1991-07-17 $0.0900
1991-04-19 $0.0900
1991-01-15 $0.0900
1990-10-18 $0.0887
1990-07-17 $0.0887
1990-04-20 $0.0887
1990-01-16 $0.0887
1989-10-18 $0.0813
1989-07-18 $0.0813
1989-04-18 $0.0813
1989-01-17 $0.0813
1988-10-18 $0.0656
1988-07-19 $0.0656
1988-04-19 $0.0656
1988-01-19 $0.0656
1987-10-20 $0.0550
1987-07-20 $0.0550
1987-04-20 $0.0550
1987-01-20 $0.0550
1986-10-15 $0.0488
1986-07-17 $0.0488
1986-04-15 $0.0488
1986-01-17 $0.0488
1985-10-21 $0.0450
1985-07-17 $0.0450
1985-04-16 $0.0450
1985-01-16 $0.0450
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.13. Further, an Excess Kurtosis of 9.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.78%960.72%0.72%
-5.78% to -4.32%1331.00%1.72%
-4.32% to -2.86%3962.98%4.70%
-2.86% to -1.41%151311.37%16.06%
-1.41% to 0.05%487436.62%52.69%
0.05% to 1.51%412030.96%83.64%
1.51% to 2.97%150411.30%94.94%
2.97% to 4.43%4243.19%98.13%
4.43% to 5.89%1381.04%99.17%
Greater than 5.89%1110.83%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.89%2.00% 78.74%68.27%
±2σ -3.84%3.94% 95.27%95.45%
±3σ -5.78%5.89% 98.44%99.73%
Descriptive Statistics
Mean0.054%
Standard Error0.017%
Median0.000%
Mode0.000%
Standard Deviation1.945%
Sample Variance3.783%
Kurtosis9.37
Skewness-0.13
Range41.205%
Minimum-22.992%
Maximum18.213%
Count13309
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.440% 6383 47.96% 0.691%
Negative -1.368% 6193 46.53% -0.637%
Zero 0.000% 733 5.51% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.72%
20 1 Month 2.75%
60 1 Quarter 2.87%
250 1 Year 2.70%
750 3 Years 2.60%
1,250 5 Years 2.41%
2,500 10 Years 2.35%
5,000 20 Years 2.29%
12,500 50 Years 2.32%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.10. Further, an Excess Kurtosis of 18.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.52%00.00%0.00%
-2.52% to -1.31%00.00%0.00%
-1.31% to -0.10%00.00%0.00%
-0.10% to 1.11%208715.68%15.68%
1.11% to 2.32%640748.14%63.82%
2.32% to 3.53%293422.04%85.86%
3.53% to 4.74%10187.65%93.51%
4.74% to 5.95%3892.92%96.43%
5.95% to 7.16%2121.59%98.02%
Greater than 7.16%2631.98%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 0.70%3.93% 86.12%68.27%
±2σ -0.91%5.55% 95.76%95.45%
±3σ -2.52%7.16% 98.02%99.73%
Descriptive Statistics
Mean2.319%
Standard Error0.014%
Median1.908%
Mode2.500%
Standard Deviation1.614%
Sample Variance2.605%
Kurtosis18.75
Skewness3.10
Range27.828%
Minimum0.241%
Maximum28.069%
Count13310
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.319% 13310 100.00% 2.319%
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 0.26. Further, an Excess Kurtosis of 6.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.07%900.68%0.68%
-5.07% to -3.80%1501.13%1.80%
-3.80% to -2.53%4383.29%5.09%
-2.53% to -1.27%157411.83%16.92%
-1.27% to 0.00%492436.99%53.91%
0.00% to 1.27%391629.42%83.34%
1.27% to 2.54%150711.32%94.66%
2.54% to 3.80%4503.38%98.04%
3.80% to 5.07%1501.13%99.17%
Greater than 5.07%1110.83%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.69%1.69% 77.49%68.27%
±2σ -3.38%3.38% 94.71%95.45%
±3σ -5.07%5.07% 98.49%99.73%
Descriptive Statistics
Mean0.001%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.690%
Sample Variance2.855%
Kurtosis6.15
Skewness0.26
Range30.153%
Minimum-11.940%
Maximum18.213%
Count13310
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.275% 6134 46.09% 0.588%
Negative -1.254% 6226 46.78% -0.587%
Zero 0.000% 950 7.14% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of 4.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.88%190.69%0.69%
-12.88% to -9.60%331.20%1.88%
-9.60% to -6.31%1053.81%5.69%
-6.31% to -3.02%32111.63%17.33%
-3.02% to 0.27%90932.95%50.27%
0.27% to 3.55%89032.26%82.53%
3.55% to 6.84%33212.03%94.56%
6.84% to 10.13%1013.66%98.22%
10.13% to 13.41%270.98%99.20%
Greater than 13.41%220.80%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.12%4.65% 77.20%68.27%
±2σ -8.50%9.03% 94.96%95.45%
±3σ -12.88%13.42% 98.51%99.73%
Descriptive Statistics
Mean0.266%
Standard Error0.083%
Median0.251%
Mode0.000%
Standard Deviation4.383%
Sample Variance19.206%
Kurtosis4.08
Skewness0.08
Range52.316%
Minimum-25.901%
Maximum26.415%
Count2759
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.255% 1436 52.05% 1.694%
Negative -3.100% 1271 46.07% -1.428%
Zero 0.000% 52 1.89% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 7.70%
12 1 Quarter 7.17%
52 1 Year 6.60%
156 3 Years 6.47%
260 5 Years 5.87%
520 10 Years 5.72%
1,040 20 Years 5.39%
2,600 50 Years 5.59%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.41. Further, an Excess Kurtosis of 8.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -5.72%00.00%0.00%
-5.72% to -2.77%00.00%0.00%
-2.77% to 0.17%00.00%0.00%
0.17% to 3.12%45116.34%16.34%
3.12% to 6.07%132247.90%64.24%
6.07% to 9.01%56620.51%84.75%
9.01% to 11.96%2177.86%92.61%
11.96% to 14.90%1033.73%96.34%
14.90% to 17.85%421.52%97.86%
Greater than 17.85%592.14%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.14%9.99% 84.53%68.27%
±2σ -1.79%13.92% 95.22%95.45%
±3σ -5.72%17.85% 97.86%99.73%
Descriptive Statistics
Mean6.065%
Standard Error0.075%
Median5.000%
Mode5.263%
Standard Deviation3.928%
Sample Variance15.427%
Kurtosis8.53
Skewness2.41
Range32.944%
Minimum0.949%
Maximum33.893%
Count2760
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.065% 2760 100.00% 6.065%
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 0.64. Further, an Excess Kurtosis of 4.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.90%150.54%0.54%
-12.90% to -9.67%220.80%1.34%
-9.67% to -6.45%923.33%4.67%
-6.45% to -3.23%37713.66%18.33%
-3.23% to -0.00%90232.68%51.01%
-0.00% to 3.22%89232.32%83.33%
3.22% to 6.44%28810.43%93.77%
6.44% to 9.67%1063.84%97.61%
9.67% to 12.89%371.34%98.95%
Greater than 12.89%291.05%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.30%4.29% 77.17%68.27%
±2σ -8.60%8.59% 95.00%95.45%
±3σ -12.90%12.89% 98.41%99.73%
Descriptive Statistics
Mean-0.003%
Standard Error0.082%
Median-0.133%
Mode0.000%
Standard Deviation4.298%
Sample Variance18.471%
Kurtosis4.56
Skewness0.64
Range50.389%
Minimum-19.403%
Maximum30.986%
Count2760
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.252% 1289 46.70% 1.519%
Negative -2.984% 1408 51.01% -1.522%
Zero 0.000% 63 2.28% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.35. Further, an Excess Kurtosis of 4.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -24.10%50.79%0.79%
-24.10% to -17.80%40.63%1.42%
-17.80% to -11.50%274.26%5.68%
-11.50% to -5.19%8613.56%19.24%
-5.19% to 1.11%21033.12%52.37%
1.11% to 7.41%17227.13%79.50%
7.41% to 13.71%10216.09%95.58%
13.71% to 20.02%203.15%98.74%
20.02% to 26.32%40.63%99.37%
Greater than 26.32%40.63%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.29%9.51% 75.55%68.27%
±2σ -15.70%17.92% 96.21%95.45%
±3σ -24.10%26.32% 98.58%99.73%
Descriptive Statistics
Mean1.109%
Standard Error0.334%
Median0.654%
Mode0.000%
Standard Deviation8.404%
Sample Variance70.633%
Kurtosis4.79
Skewness0.35
Range93.226%
Minimum-36.364%
Maximum56.862%
Count634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.926% 337 53.16% 3.682%
Negative -5.723% 285 44.95% -2.573%
Zero 0.000% 12 1.89% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 13.52%
12 1 Year 13.58%
36 3 Years 14.58%
60 5 Years 12.82%
120 10 Years 12.49%
240 20 Years 11.54%
600 50 Years 12.13%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.54. Further, an Excess Kurtosis of 9.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.04%00.00%0.00%
-11.04% to -4.80%00.00%0.00%
-4.80% to 1.45%00.00%0.00%
1.45% to 7.69%10115.91%15.91%
7.69% to 13.94%31249.13%65.04%
13.94% to 20.18%13220.79%85.83%
20.18% to 26.43%477.40%93.23%
26.43% to 32.68%213.31%96.54%
32.68% to 38.92%91.42%97.95%
Greater than 38.92%132.05%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 5.61%22.27% 83.46%68.27%
±2σ -2.72%30.59% 95.28%95.45%
±3σ -11.04%38.92% 97.95%99.73%
Descriptive Statistics
Mean13.939%
Standard Error0.330%
Median11.724%
Mode10.588%
Standard Deviation8.328%
Sample Variance69.359%
Kurtosis9.84
Skewness2.54
Range65.358%
Minimum3.743%
Maximum69.101%
Count635
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.939% 635 100.00% 13.939%
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 1.13. Further, an Excess Kurtosis of 5.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.96%20.31%0.31%
-25.96% to -19.54%40.63%0.94%
-19.54% to -13.11%162.52%3.46%
-13.11% to -6.69%11017.32%20.79%
-6.69% to -0.26%20231.81%52.60%
-0.26% to 6.16%19029.92%82.52%
6.16% to 12.59%7311.50%94.02%
12.59% to 19.02%264.09%98.11%
19.02% to 25.44%40.63%98.74%
Greater than 25.44%81.26%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.83%8.31% 76.06%68.27%
±2σ -17.39%16.87% 95.75%95.45%
±3σ -25.96%25.44% 98.43%99.73%
Descriptive Statistics
Mean-0.261%
Standard Error0.340%
Median-0.757%
Mode0.000%
Standard Deviation8.567%
Sample Variance73.392%
Kurtosis5.77
Skewness1.13
Range93.393%
Minimum-36.250%
Maximum57.143%
Count635
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.562% 289 45.51% 2.986%
Negative -6.138% 336 52.91% -3.248%
Zero 0.000% 10 1.57% 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 1.65 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -38.48%20.95%0.95%
-38.48% to -28.05%31.42%2.37%
-28.05% to -17.61%52.37%4.74%
-17.61% to -7.17%3416.11%20.85%
-7.17% to 3.27%6028.44%49.29%
3.27% to 13.71%6329.86%79.15%
13.71% to 24.14%3215.17%94.31%
24.14% to 34.58%73.32%97.63%
34.58% to 45.02%31.42%99.05%
Greater than 45.02%20.95%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -10.65%17.18% 74.88%68.27%
±2σ -24.57%31.10% 94.79%95.45%
±3σ -38.48%45.02% 98.10%99.73%
Descriptive Statistics
Mean3.268%
Standard Error0.958%
Median3.534%
Mode-48.485%
Standard Deviation13.917%
Sample Variance193.687%
Kurtosis1.65
Skewness0.02
Range97.235%
Minimum-48.485%
Maximum48.750%
Count211
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.219% 132 62.56% 7.018%
Negative -10.017% 79 37.44% -3.750%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 22.62%
12 3 Years 23.63%
20 5 Years 21.47%
40 10 Years 21.26%
80 20 Years 19.82%
200 50 Years 21.07%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.95. Further, an Excess Kurtosis of 12.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -23.66%00.00%0.00%
-23.66% to -11.26%00.00%0.00%
-11.26% to 1.13%00.00%0.00%
1.13% to 13.53%2712.74%12.74%
13.53% to 25.93%11453.77%66.51%
25.93% to 38.33%4219.81%86.32%
38.33% to 50.72%157.08%93.40%
50.72% to 63.12%62.83%96.23%
63.12% to 75.52%41.89%98.11%
Greater than 75.52%41.89%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 9.40%42.46% 88.21%68.27%
±2σ -7.13%58.99% 94.34%95.45%
±3σ -23.66%75.52% 98.11%99.73%
Descriptive Statistics
Mean25.929%
Standard Error1.135%
Median21.444%
Mode26.230%
Standard Deviation16.530%
Sample Variance273.226%
Kurtosis12.48
Skewness2.95
Range123.291%
Minimum8.654%
Maximum131.945%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 25.929% 212 100.00% 25.929%
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 1.91. Further, an Excess Kurtosis of 8.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -45.98%00.00%0.00%
-45.98% to -34.70%00.00%0.00%
-34.70% to -23.41%62.83%2.83%
-23.41% to -12.13%3416.04%18.87%
-12.13% to -0.84%8238.68%57.55%
-0.84% to 10.44%5525.94%83.49%
10.44% to 21.73%2612.26%95.75%
21.73% to 33.01%41.89%97.64%
33.01% to 44.29%00.00%97.64%
Greater than 44.29%52.36%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.89%14.20% 78.30%68.27%
±2σ -30.94%29.25% 96.70%95.45%
±3σ -45.98%44.29% 97.64%99.73%
Descriptive Statistics
Mean-0.844%
Standard Error1.033%
Median-3.022%
Mode-32.773%
Standard Deviation15.046%
Sample Variance226.372%
Kurtosis8.99
Skewness1.91
Range126.891%
Minimum-32.773%
Maximum94.118%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.848% 87 41.04% 4.862%
Negative -9.678% 125 58.96% -5.706%
Zero 0.000% 0 0.00% 0.000%