Markets Data Volatility Heatmap Portfolio Calculator

CVS Deep Analytical Report

CVS Health Corporation | Category: Equity Mega Cap | Ann. Div Yield: 3.44% ($2.66) | Last Updated: 2026-02-22 | Data Range: 1973-05-01 → 2026-02-01 (634 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% 2.40% 2.06% 2.08% 75.13 78.28 73.60 79.91
Weekly 4.38% 3.93% 4.30% 5.84% 4.53% 4.58% 73.30 80.24 70.05 83.96
Monthly 8.39% 8.34% 8.55% 12.79% 9.42% 9.54% 69.79 84.27 63.52 92.59
Quarterly 13.90% 16.56% 15.04% 21.16% 16.32% 16.52% 65.14 90.28 55.33 106.29
Annual — — — — 32.64% 33.03% 55.33 106.29 39.92 147.31
Option Time Horizon — — — — 12.55% 12.71% 67.64 86.95 59.66 98.58
Calculation Notes: Computed at 2026-02-22T14:25 UTC  |  Reference Contract: Call option expiring 2026-04-17 (54 days)  |  Spot Price (S): $76.69  |  Strike (K): $77.50 (first OTM call ≥ spot)  |  Observed Mid-Price: $3.4750 (Bid $3.4000 / Ask $3.5500)  |  Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 3.44%  |  Binomial IV (Annual): 32.64% (CRR binomial tree, American, n=20 steps)  |  BS IV: 32.74% (European Black-Scholes)  |  Yahoo IV (Annual): 33.03% → 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 -0.14. Further, an Excess Kurtosis of 9.38 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%3952.97%4.70%
-2.86% to -1.40%151311.39%16.08%
-1.40% to 0.06%486536.61%52.69%
0.06% to 1.51%411330.95%83.65%
1.51% to 2.97%150011.29%94.94%
2.97% to 4.43%4253.20%98.13%
4.43% to 5.89%1371.03%99.16%
Greater than 5.89%1110.84%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.89%2.00% 78.85%68.27%
±2σ -3.83%3.95% 95.27%95.45%
±3σ -5.78%5.89% 98.44%99.73%
Descriptive Statistics
Mean0.055%
Standard Error0.017%
Median0.000%
Mode0.000%
Standard Deviation1.945%
Sample Variance3.784%
Kurtosis9.38
Skewness-0.14
Range41.205%
Minimum-22.992%
Maximum18.213%
Count13288
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.441% 6374 47.97% 0.691%
Negative -1.367% 6181 46.52% -0.636%
Zero 0.000% 733 5.52% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.09%
20 1 Month 3.60%
60 1 Quarter 2.74%
250 1 Year 2.69%
750 3 Years 2.58%
1,250 5 Years 2.40%
2,500 10 Years 2.34%
5,000 20 Years 2.28%
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 18.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -2.53%00.00%0.00%
-2.53% to -1.31%00.00%0.00%
-1.31% to -0.10%00.00%0.00%
-0.10% to 1.11%208715.70%15.70%
1.11% to 2.32%639948.15%63.86%
2.32% to 3.53%292221.99%85.85%
3.53% to 4.74%10197.67%93.51%
4.74% to 5.95%3872.91%96.43%
5.95% to 7.16%2131.60%98.03%
Greater than 7.16%2621.97%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 -2.53%7.16% 98.03%99.73%
Descriptive Statistics
Mean2.319%
Standard Error0.014%
Median1.907%
Mode2.500%
Standard Deviation1.615%
Sample Variance2.607%
Kurtosis18.74
Skewness3.10
Range27.828%
Minimum0.241%
Maximum28.069%
Count13289
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.319% 13289 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 6.16 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%1.81%
-3.80% to -2.53%4383.30%5.10%
-2.53% to -1.27%156911.81%16.91%
-1.27% to 0.00%397229.89%46.80%
0.00% to 1.27%485936.56%83.36%
1.27% to 2.53%150211.30%94.66%
2.53% to 3.80%4483.37%98.04%
3.80% to 5.07%1501.13%99.16%
Greater than 5.07%1110.84%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -1.69%1.69% 77.52%68.27%
±2σ -3.38%3.38% 94.70%95.45%
±3σ -5.07%5.07% 98.49%99.73%
Descriptive Statistics
Mean0.000%
Standard Error0.015%
Median0.000%
Mode0.000%
Standard Deviation1.689%
Sample Variance2.854%
Kurtosis6.16
Skewness0.26
Range30.153%
Minimum-11.940%
Maximum18.213%
Count13289
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.274% 6120 46.05% 0.587%
Negative -1.254% 6219 46.80% -0.587%
Zero 0.000% 950 7.15% 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 4.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.87%190.69%0.69%
-12.87% to -9.59%331.20%1.89%
-9.59% to -6.30%1053.81%5.70%
-6.30% to -3.02%31911.58%17.28%
-3.02% to 0.27%90932.99%50.27%
0.27% to 3.56%88932.27%82.54%
3.56% to 6.84%33112.01%94.56%
6.84% to 10.13%1013.67%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 -4.11%4.65% 77.28%68.27%
±2σ -8.49%9.03% 94.95%95.45%
±3σ -12.87%13.41% 98.51%99.73%
Descriptive Statistics
Mean0.269%
Standard Error0.083%
Median0.251%
Mode0.000%
Standard Deviation4.381%
Sample Variance19.193%
Kurtosis4.09
Skewness0.08
Range52.316%
Minimum-25.901%
Maximum26.415%
Count2755
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.253% 1435 52.09% 1.694%
Negative -3.097% 1268 46.02% -1.425%
Zero 0.000% 52 1.89% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 9.01%
12 1 Quarter 6.19%
52 1 Year 6.38%
156 3 Years 6.42%
260 5 Years 5.84%
520 10 Years 5.68%
1,040 20 Years 5.38%
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 8.55 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 -2.78%00.00%0.00%
-2.78% to 0.17%00.00%0.00%
0.17% to 3.12%45116.36%16.36%
3.12% to 6.06%132147.93%64.30%
6.06% to 9.01%56520.50%84.80%
9.01% to 11.95%2167.84%92.63%
11.95% to 14.90%1023.70%96.34%
14.90% to 17.84%421.52%97.86%
Greater than 17.84%592.14%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.13%9.99% 84.54%68.27%
±2σ -1.79%13.92% 95.21%95.45%
±3σ -5.72%17.84% 97.86%99.73%
Descriptive Statistics
Mean6.061%
Standard Error0.075%
Median4.998%
Mode5.263%
Standard Deviation3.928%
Sample Variance15.432%
Kurtosis8.55
Skewness2.41
Range32.944%
Minimum0.949%
Maximum33.893%
Count2756
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.061% 2756 100.00% 6.061%
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 4.58 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.89%150.54%0.54%
-12.89% to -9.67%220.80%1.34%
-9.67% to -6.45%923.34%4.68%
-6.45% to -3.23%37613.64%18.32%
-3.23% to -0.01%90232.73%51.05%
-0.01% to 3.21%89132.33%83.38%
3.21% to 6.44%28710.41%93.80%
6.44% to 9.66%1053.81%97.61%
9.66% to 12.88%371.34%98.95%
Greater than 12.88%291.05%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -4.30%4.29% 77.25%68.27%
±2σ -8.60%8.59% 94.99%95.45%
±3σ -12.90%12.88% 98.40%99.73%
Descriptive Statistics
Mean-0.007%
Standard Error0.082%
Median-0.135%
Mode0.000%
Standard Deviation4.296%
Sample Variance18.453%
Kurtosis4.58
Skewness0.64
Range50.389%
Minimum-19.403%
Maximum30.986%
Count2756
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.248% 1286 46.66% 1.516%
Negative -2.982% 1407 51.05% -1.522%
Zero 0.000% 63 2.29% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.36. Further, an Excess Kurtosis of 4.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -24.06%50.79%0.79%
-24.06% to -17.76%40.63%1.42%
-17.76% to -11.47%264.11%5.53%
-11.47% to -5.17%8613.59%19.12%
-5.17% to 1.12%21033.18%52.29%
1.12% to 7.42%17227.17%79.46%
7.42% to 13.71%10216.11%95.58%
13.71% to 20.01%203.16%98.74%
20.01% to 26.30%40.63%99.37%
Greater than 26.30%40.63%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -7.27%9.52% 75.51%68.27%
±2σ -15.66%17.91% 96.21%95.45%
±3σ -24.06%26.30% 98.58%99.73%
Descriptive Statistics
Mean1.122%
Standard Error0.334%
Median0.663%
Mode0.000%
Standard Deviation8.393%
Sample Variance70.435%
Kurtosis4.84
Skewness0.36
Range93.226%
Minimum-36.364%
Maximum56.862%
Count633
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.913% 337 53.24% 3.680%
Negative -5.702% 284 44.87% -2.558%
Zero 0.000% 12 1.90% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 11.51%
12 1 Year 12.98%
36 3 Years 14.56%
60 5 Years 12.79%
120 10 Years 12.42%
240 20 Years 11.52%
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 9.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -11.07%00.00%0.00%
-11.07% to -4.82%00.00%0.00%
-4.82% to 1.43%00.00%0.00%
1.43% to 7.68%10015.77%15.77%
7.68% to 13.94%31349.37%65.14%
13.94% to 20.19%13120.66%85.80%
20.19% to 26.44%477.41%93.22%
26.44% to 32.69%213.31%96.53%
32.69% to 38.94%91.42%97.95%
Greater than 38.94%132.05%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 5.60%22.27% 83.75%68.27%
±2σ -2.74%30.61% 95.27%95.45%
±3σ -11.07%38.94% 97.95%99.73%
Descriptive Statistics
Mean13.935%
Standard Error0.331%
Median11.721%
Mode10.588%
Standard Deviation8.335%
Sample Variance69.464%
Kurtosis9.82
Skewness2.54
Range65.358%
Minimum3.743%
Maximum69.101%
Count634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 13.935% 634 100.00% 13.935%
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 1.14. Further, an Excess Kurtosis of 5.84 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -25.94%20.32%0.32%
-25.94% to -19.52%40.63%0.95%
-19.52% to -13.11%162.52%3.47%
-13.11% to -6.69%10917.19%20.66%
-6.69% to -0.28%20231.86%52.52%
-0.28% to 6.14%19130.13%82.65%
6.14% to 12.55%7311.51%94.16%
12.55% to 18.97%253.94%98.11%
18.97% to 25.39%40.63%98.74%
Greater than 25.39%81.26%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -8.83%8.28% 76.18%68.27%
±2σ -17.38%16.83% 95.74%95.45%
±3σ -25.94%25.39% 98.42%99.73%
Descriptive Statistics
Mean-0.276%
Standard Error0.340%
Median-0.767%
Mode0.000%
Standard Deviation8.554%
Sample Variance73.167%
Kurtosis5.84
Skewness1.14
Range93.393%
Minimum-36.250%
Maximum57.143%
Count634
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 6.539% 288 45.43% 2.970%
Negative -6.126% 336 53.00% -3.247%
Zero 0.000% 10 1.58% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.01. Further, an Excess Kurtosis of 1.66 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -38.41%20.95%0.95%
-38.41% to -27.98%31.42%2.37%
-27.98% to -17.55%52.37%4.74%
-17.55% to -7.12%3416.11%20.85%
-7.12% to 3.31%6028.44%49.29%
3.31% to 13.73%6329.86%79.15%
13.73% to 24.16%3215.17%94.31%
24.16% to 34.59%73.32%97.63%
34.59% 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 -10.60%17.21% 74.88%68.27%
±2σ -24.50%31.12% 94.79%95.45%
±3σ -38.41%45.02% 98.10%99.73%
Descriptive Statistics
Mean3.306%
Standard Error0.957%
Median3.534%
Mode-48.485%
Standard Deviation13.905%
Sample Variance193.343%
Kurtosis1.66
Skewness0.01
Range97.235%
Minimum-48.485%
Maximum48.750%
Count211
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.156% 133 63.03% 7.032%
Negative -10.079% 78 36.97% -3.726%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 21.03%
12 3 Years 23.10%
20 5 Years 21.16%
40 10 Years 21.10%
80 20 Years 19.74%
200 50 Years 21.04%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.94. Further, an Excess Kurtosis of 12.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -23.77%00.00%0.00%
-23.77% to -11.36%00.00%0.00%
-11.36% to 1.06%00.00%0.00%
1.06% to 13.48%2813.21%13.21%
13.48% to 25.89%11152.36%65.57%
25.89% to 38.31%4420.75%86.32%
38.31% to 50.73%157.08%93.40%
50.73% to 63.15%62.83%96.23%
63.15% to 75.56%41.89%98.11%
Greater than 75.56%41.89%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 9.34%42.45% 87.74%68.27%
±2σ -7.22%59.01% 94.34%95.45%
±3σ -23.77%75.56% 98.11%99.73%
Descriptive Statistics
Mean25.895%
Standard Error1.137%
Median21.444%
Mode26.230%
Standard Deviation16.556%
Sample Variance274.109%
Kurtosis12.41
Skewness2.94
Range123.291%
Minimum8.654%
Maximum131.945%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 25.895% 212 100.00% 25.895%
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 1.92. Further, an Excess Kurtosis of 9.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -46.00%00.00%0.00%
-46.00% to -34.72%00.00%0.00%
-34.72% to -23.44%62.83%2.83%
-23.44% to -12.16%3215.09%17.92%
-12.16% to -0.88%8540.09%58.02%
-0.88% to 10.40%5425.47%83.49%
10.40% to 21.68%2612.26%95.75%
21.68% to 32.96%41.89%97.64%
32.96% to 44.24%00.00%97.64%
Greater than 44.24%52.36%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -15.92%14.16% 78.30%68.27%
±2σ -30.96%29.20% 96.70%95.45%
±3σ -46.00%44.24% 97.64%99.73%
Descriptive Statistics
Mean-0.883%
Standard Error1.033%
Median-3.132%
Mode-32.773%
Standard Deviation15.040%
Sample Variance226.216%
Kurtosis9.02
Skewness1.92
Range126.891%
Minimum-32.773%
Maximum94.118%
Count212
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 11.924% 86 40.57% 4.837%
Negative -9.625% 126 59.43% -5.721%
Zero 0.000% 0 0.00% 0.000%