MSFT - Detail Report

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	2.09%	1.65%	1.80%	2.16%	2.19%	2.23%	374.38	391.16	366.27	399.83
Weekly	4.56%	4.30%	4.52%	5.15%	4.82%	4.91%	364.66	401.59	347.48	421.44
Monthly	9.35%	9.27%	8.75%	10.93%	10.04%	10.23%	346.11	423.11	313.04	467.81
Quarterly	16.00%	16.03%	13.05%	18.84%	17.39%	17.72%	321.58	455.39	270.24	541.91
Annual	—	—	—	—	34.79%	35.43%	270.24	541.91	190.83	767.39
Option Time Horizon	—	—	—	—	13.13%	13.37%	335.59	436.38	294.29	497.61

Calculation Notes: Computed at 2026-03-23T16:30 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $382.68 | Strike (K): $385.00 (first OTM call ≥ spot) | Observed Mid-Price: $19.5750 (Bid $19.4500 / Ask $19.7000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.91% | Binomial IV (Annual): 34.79% (CRR binomial tree, American, n=20 steps) | BS IV: 34.67% (European Black-Scholes) | Yahoo IV (Annual): 35.43% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2026-02-19	$0.9100
2025-11-20	$0.9100
2025-08-21	$0.8300
2025-05-15	$0.8300
2025-02-20	$0.8300
2024-11-21	$0.8300
2024-08-15	$0.7500
2024-05-15	$0.7500
2024-02-14	$0.7500
2023-11-15	$0.7500
2023-08-16	$0.6800
2023-05-17	$0.6800
2023-02-15	$0.6800
2022-11-16	$0.6800
2022-08-17	$0.6200
2022-05-18	$0.6200
2022-02-16	$0.6200
2021-11-17	$0.6200
2021-08-18	$0.5600
2021-05-19	$0.5600
2021-02-17	$0.5600
2020-11-18	$0.5600
2020-08-19	$0.5100
2020-05-20	$0.5100
2020-02-19	$0.5100
2019-11-20	$0.5100
2019-08-14	$0.4600
2019-05-15	$0.4600
2019-02-20	$0.4600
2018-11-14	$0.4600
2018-08-15	$0.4200
2018-05-16	$0.4200
2018-02-14	$0.4200
2017-11-15	$0.4200
2017-08-15	$0.3900
2017-05-16	$0.3900
2017-02-14	$0.3900
2016-11-15	$0.3900
2016-08-16	$0.3600
2016-05-17	$0.3600
2016-02-16	$0.3600
2015-11-17	$0.3600
2015-08-18	$0.3100
2015-05-19	$0.3100
2015-02-17	$0.3100
2014-11-18	$0.3100
2014-08-19	$0.2800
2014-05-13	$0.2800
2014-02-18	$0.2800
2013-11-19	$0.2800
2013-08-13	$0.2300
2013-05-14	$0.2300
2013-02-19	$0.2300
2012-11-13	$0.2300
2012-08-14	$0.2000
2012-05-15	$0.2000
2012-02-14	$0.2000
2011-11-15	$0.2000
2011-08-16	$0.1600
2011-05-17	$0.1600
2011-02-15	$0.1600
2010-11-16	$0.1600
2010-08-17	$0.1300
2010-05-18	$0.1300
2010-02-16	$0.1300
2009-11-17	$0.1300
2009-08-18	$0.1300
2009-05-19	$0.1300
2009-02-17	$0.1300
2008-11-18	$0.1300
2008-08-19	$0.1100
2008-05-13	$0.1100
2008-02-19	$0.1100
2007-11-13	$0.1100
2007-08-14	$0.1000
2007-05-15	$0.1000
2007-02-13	$0.1000
2006-11-14	$0.1000
2006-08-15	$0.0900
2006-05-15	$0.0900
2006-02-15	$0.0900
2005-11-15	$0.0800
2005-08-15	$0.0800
2005-05-16	$0.0800
2005-02-15	$0.0800
2004-11-15	$3.0800
2004-08-23	$0.0800
2003-10-15	$0.1600
2003-02-19	$0.0800

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.10. Further, an Excess Kurtosis of 10.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.16%	70	0.69%	0.69%
-6.16% to -4.60%	79	0.78%	1.48%
-4.60% to -3.03%	339	3.36%	4.84%
-3.03% to -1.46%	1152	11.43%	16.27%
-1.46% to 0.11%	3585	35.55%	51.82%
0.11% to 1.68%	3150	31.24%	83.06%
1.68% to 3.25%	1167	11.57%	94.63%
3.25% to 4.81%	345	3.42%	98.06%
4.81% to 6.38%	120	1.19%	99.25%
Greater than 6.38%	76	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.98%	2.20%	77.70%	68.27%
±2σ	-4.07%	4.29%	95.18%	95.45%
±3σ	-6.16%	6.38%	98.55%	99.73%

Descriptive Statistics

Mean	0.109%
Standard Error	0.021%
Median	0.038%
Mode	0.000%
Standard Deviation	2.091%
Sample Variance	4.371%
Kurtosis	10.85
Skewness	-0.10
Range	49.681%
Minimum	-30.116%
Maximum	19.565%
Count	10083

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.527%	5112	50.70%	0.774%
Negative	-1.409%	4759	47.20%	-0.665%
Zero	0.000%	212	2.10%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.77%
20	1 Month	2.08%
60	1 Quarter	2.37%
250	1 Year	2.04%
750	3 Years	1.95%
1,250	5 Years	2.16%
2,500	10 Years	2.09%
5,000	20 Years	2.16%
12,500	50 Years	2.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.82. Further, an Excess Kurtosis of 45.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.45%	0	0.00%	0.00%
-2.45% to -1.21%	0	0.00%	0.00%
-1.21% to 0.03%	0	0.00%	0.00%
0.03% to 1.27%	1811	17.96%	17.96%
1.27% to 2.51%	4419	43.82%	61.78%
2.51% to 3.75%	2290	22.71%	84.49%
3.75% to 4.99%	894	8.87%	93.36%
4.99% to 6.23%	361	3.58%	96.94%
6.23% to 7.47%	140	1.39%	98.32%
Greater than 7.47%	169	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.86%	4.17%	84.39%	68.27%
±2σ	-0.79%	5.82%	96.26%	95.45%
±3σ	-2.45%	7.47%	98.32%	99.73%

Descriptive Statistics

Mean	2.512%
Standard Error	0.016%
Median	2.096%
Mode	1.786%
Standard Deviation	1.653%
Sample Variance	2.731%
Kurtosis	45.34
Skewness	3.82
Range	40.735%
Minimum	0.376%
Maximum	41.111%
Count	10084

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.512%	10084	100.00%	2.512%
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 0.83. Further, an Excess Kurtosis of 19.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.43%	70	0.69%	0.69%
-5.43% to -4.08%	119	1.18%	1.87%
-4.08% to -2.73%	358	3.55%	5.42%
-2.73% to -1.38%	1164	11.54%	16.97%
-1.38% to -0.03%	3269	32.42%	49.39%
-0.03% to 1.32%	3388	33.60%	82.98%
1.32% to 2.67%	1151	11.41%	94.40%
2.67% to 4.02%	397	3.94%	98.33%
4.02% to 5.37%	99	0.98%	99.32%
Greater than 5.37%	69	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.83%	1.77%	77.10%	68.27%
±2σ	-3.63%	3.57%	94.97%	95.45%
±3σ	-5.43%	5.37%	98.62%	99.73%

Descriptive Statistics

Mean	-0.031%
Standard Error	0.018%
Median	0.000%
Mode	0.000%
Standard Deviation	1.800%
Sample Variance	3.241%
Kurtosis	19.80
Skewness	0.83
Range	49.525%
Minimum	-13.613%
Maximum	35.912%
Count	10084

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.285%	4813	47.73%	0.613%
Negative	-1.295%	5016	49.74%	-0.644%
Zero	0.000%	255	2.53%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.10. Further, an Excess Kurtosis of 4.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.17%	10	0.48%	0.48%
-13.17% to -9.75%	28	1.34%	1.82%
-9.75% to -6.32%	67	3.21%	5.03%
-6.32% to -2.90%	283	13.55%	18.58%
-2.90% to 0.52%	679	32.52%	51.10%
0.52% to 3.95%	660	31.61%	82.71%
3.95% to 7.37%	237	11.35%	94.06%
7.37% to 10.79%	85	4.07%	98.13%
10.79% to 14.21%	23	1.10%	99.23%
Greater than 14.21%	16	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.04%	5.09%	75.24%	68.27%
±2σ	-8.61%	9.65%	94.78%	95.45%
±3σ	-13.17%	14.21%	98.75%	99.73%

Descriptive Statistics

Mean	0.523%
Standard Error	0.100%
Median	0.460%
Mode	0.000%
Standard Deviation	4.564%
Sample Variance	20.826%
Kurtosis	4.61
Skewness	0.10
Range	64.739%
Minimum	-36.713%
Maximum	28.026%
Count	2088

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.444%	1155	55.32%	1.905%
Negative	-3.144%	918	43.97%	-1.382%
Zero	0.000%	15	0.72%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	5.46%
12	1 Quarter	6.22%
52	1 Year	5.06%
156	3 Years	4.62%
260	5 Years	5.15%
520	10 Years	4.89%
1,040	20 Years	5.02%
2,600	50 Years	6.19%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.77. Further, an Excess Kurtosis of 34.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.53%	0	0.00%	0.00%
-6.53% to -3.30%	0	0.00%	0.00%
-3.30% to -0.07%	0	0.00%	0.00%
-0.07% to 3.16%	374	17.90%	17.90%
3.16% to 6.38%	916	43.85%	61.75%
6.38% to 9.61%	478	22.88%	84.63%
9.61% to 12.84%	183	8.76%	93.39%
12.84% to 16.07%	76	3.64%	97.03%
16.07% to 19.30%	31	1.48%	98.52%
Greater than 19.30%	31	1.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.08%	10.69%	84.63%	68.27%
±2σ	-2.22%	14.99%	95.88%	95.45%
±3σ	-6.53%	19.30%	98.52%	99.73%

Descriptive Statistics

Mean	6.385%
Standard Error	0.094%
Median	5.358%
Mode	4.762%
Standard Deviation	4.304%
Sample Variance	18.522%
Kurtosis	34.92
Skewness	3.77
Range	65.149%
Minimum	0.962%
Maximum	66.111%
Count	2089

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.385%	2089	100.00%	6.385%
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 1.33. Further, an Excess Kurtosis of 16.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.80%	10	0.48%	0.48%
-13.80% to -10.41%	19	0.91%	1.39%
-10.41% to -7.02%	75	3.59%	4.98%
-7.02% to -3.63%	259	12.40%	17.38%
-3.63% to -0.23%	730	34.94%	52.32%
-0.23% to 3.16%	630	30.16%	82.48%
3.16% to 6.55%	247	11.82%	94.30%
6.55% to 9.94%	75	3.59%	97.89%
9.94% to 13.33%	27	1.29%	99.19%
Greater than 13.33%	17	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.76%	4.29%	76.50%	68.27%
±2σ	-9.28%	8.81%	95.02%	95.45%
±3σ	-13.80%	13.33%	98.71%	99.73%

Descriptive Statistics

Mean	-0.235%
Standard Error	0.099%
Median	-0.435%
Mode	0.000%
Standard Deviation	4.523%
Sample Variance	20.456%
Kurtosis	16.28
Skewness	1.33
Range	78.574%
Minimum	-18.905%
Maximum	59.669%
Count	2089

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.286%	937	44.85%	1.474%
Negative	-3.143%	1136	54.38%	-1.709%
Zero	0.000%	16	0.77%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.70. Further, an Excess Kurtosis of 3.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.79%	1	0.21%	0.21%
-25.79% to -18.78%	2	0.42%	0.62%
-18.78% to -11.76%	22	4.58%	5.21%
-11.76% to -4.75%	72	15.00%	20.21%
-4.75% to 2.27%	151	31.46%	51.67%
2.27% to 9.28%	153	31.87%	83.54%
9.28% to 16.30%	52	10.83%	94.38%
16.30% to 23.31%	11	2.29%	96.67%
23.31% to 30.32%	11	2.29%	98.96%
Greater than 30.32%	5	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.09%	11.62%	74.58%	68.27%
±2σ	-16.44%	20.97%	95.42%	95.45%
±3σ	-25.79%	30.32%	98.75%	99.73%

Descriptive Statistics

Mean	2.266%
Standard Error	0.427%
Median	2.099%
Mode	0.000%
Standard Deviation	9.353%
Sample Variance	87.487%
Kurtosis	3.01
Skewness	0.70
Range	85.907%
Minimum	-34.353%
Maximum	51.554%
Count	480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.747%	288	60.00%	4.648%
Negative	-6.049%	189	39.38%	-2.382%
Zero	0.000%	3	0.62%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	11.32%
12	1 Year	10.39%
36	3 Years	9.80%
60	5 Years	10.93%
120	10 Years	10.44%
240	20 Years	10.73%
600	50 Years	13.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.68. Further, an Excess Kurtosis of 28.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.32%	0	0.00%	0.00%
-13.32% to -6.37%	0	0.00%	0.00%
-6.37% to 0.58%	0	0.00%	0.00%
0.58% to 7.53%	76	15.80%	15.80%
7.53% to 14.48%	221	45.95%	61.75%
14.48% to 21.43%	110	22.87%	84.62%
21.43% to 28.38%	44	9.15%	93.76%
28.38% to 35.33%	17	3.53%	97.30%
35.33% to 42.28%	6	1.25%	98.54%
Greater than 42.28%	7	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.21%	23.75%	83.99%	68.27%
±2σ	-4.05%	33.02%	96.67%	95.45%
±3σ	-13.32%	42.28%	98.54%	99.73%

Descriptive Statistics

Mean	14.482%
Standard Error	0.423%
Median	12.187%
Mode	6.392%
Standard Deviation	9.267%
Sample Variance	85.871%
Kurtosis	28.43
Skewness	3.68
Range	109.902%
Minimum	2.849%
Maximum	112.751%
Count	481

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.482%	481	100.00%	14.482%
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 0.23. Further, an Excess Kurtosis of 1.78 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.51%	2	0.42%	0.42%
-27.51% to -20.95%	6	1.25%	1.66%
-20.95% to -14.39%	18	3.74%	5.41%
-14.39% to -7.83%	58	12.06%	17.46%
-7.83% to -1.27%	173	35.97%	53.43%
-1.27% to 5.29%	127	26.40%	79.83%
5.29% to 11.85%	65	13.51%	93.35%
11.85% to 18.41%	23	4.78%	98.13%
18.41% to 24.97%	6	1.25%	99.38%
Greater than 24.97%	3	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.02%	7.48%	73.60%	68.27%
±2σ	-18.77%	16.22%	94.18%	95.45%
±3σ	-27.51%	24.97%	98.96%	99.73%

Descriptive Statistics

Mean	-1.271%
Standard Error	0.399%
Median	-1.892%
Mode	-6.750%
Standard Deviation	8.747%
Sample Variance	76.517%
Kurtosis	1.78
Skewness	0.23
Range	69.411%
Minimum	-34.017%
Maximum	35.394%
Count	481

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.669%	195	40.54%	2.704%
Negative	-6.731%	284	59.04%	-3.974%
Zero	0.000%	2	0.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.49. Further, an Excess Kurtosis of 4.94 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.38%	0	0.00%	0.00%
-41.38% to -29.38%	0	0.00%	0.00%
-29.38% to -17.38%	4	2.50%	2.50%
-17.38% to -5.37%	29	18.12%	20.62%
-5.37% to 6.63%	53	33.12%	53.75%
6.63% to 18.63%	47	29.38%	83.12%
18.63% to 30.64%	18	11.25%	94.38%
30.64% to 42.64%	4	2.50%	96.88%
42.64% to 54.64%	3	1.88%	98.75%
Greater than 54.64%	2	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.37%	22.64%	77.50%	68.27%
±2σ	-25.38%	38.64%	95.62%	95.45%
±3σ	-41.38%	54.64%	98.75%	99.73%

Descriptive Statistics

Mean	6.631%
Standard Error	1.265%
Median	5.758%
Mode	-28.736%
Standard Deviation	16.004%
Sample Variance	256.125%
Kurtosis	4.94
Skewness	1.49
Range	117.445%
Minimum	-28.736%
Maximum	88.709%
Count	160

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.923%	101	63.12%	9.420%
Negative	-7.563%	59	36.88%	-2.789%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	20.10%
12	3 Years	17.45%
20	5 Years	18.84%
40	10 Years	18.44%
80	20 Years	18.64%
200	50 Years	23.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.27. Further, an Excess Kurtosis of 7.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.30%	0	0.00%	0.00%
-21.30% to -9.28%	0	0.00%	0.00%
-9.28% to 2.75%	0	0.00%	0.00%
2.75% to 14.77%	26	16.15%	16.15%
14.77% to 26.79%	80	49.69%	65.84%
26.79% to 38.81%	30	18.63%	84.47%
38.81% to 50.84%	13	8.07%	92.55%
50.84% to 62.86%	6	3.73%	96.27%
62.86% to 74.88%	2	1.24%	97.52%
Greater than 74.88%	4	2.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.76%	42.82%	85.71%	68.27%
±2σ	-5.27%	58.85%	95.65%	95.45%
±3σ	-21.30%	74.88%	97.52%	99.73%

Descriptive Statistics

Mean	26.792%
Standard Error	1.263%
Median	21.847%
Mode	8.040%
Standard Deviation	16.030%
Sample Variance	256.956%
Kurtosis	7.46
Skewness	2.27
Range	104.711%
Minimum	8.040%
Maximum	112.751%
Count	161

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.792%	161	100.00%	26.792%
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 -0.02. Further, an Excess Kurtosis of 1.12 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.11%	1	0.62%	0.62%
-43.11% to -33.32%	2	1.24%	1.86%
-33.32% to -23.54%	5	3.11%	4.97%
-23.54% to -13.75%	25	15.53%	20.50%
-13.75% to -3.96%	55	34.16%	54.66%
-3.96% to 5.82%	41	25.47%	80.12%
5.82% to 15.61%	22	13.66%	93.79%
15.61% to 25.39%	8	4.97%	98.76%
25.39% to 35.18%	1	0.62%	99.38%
Greater than 35.18%	1	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.01%	9.08%	73.91%	68.27%
±2σ	-30.06%	22.13%	95.03%	95.45%
±3σ	-43.11%	35.18%	98.76%	99.73%

Descriptive Statistics

Mean	-3.965%
Standard Error	1.028%
Median	-5.098%
Mode	-46.666%
Standard Deviation	13.047%
Sample Variance	170.218%
Kurtosis	1.12
Skewness	-0.02
Range	87.885%
Minimum	-46.666%
Maximum	41.219%
Count	161

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.512%	63	39.13%	3.331%
Negative	-12.110%	97	60.25%	-7.296%
Zero	0.000%	1	0.62%	0.000%

MSFT Deep Analytical Report