PFG - 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	2.70%	3.06%	2.25%	2.33%	2.31%	2.44%	84.07	88.04	82.15	90.10
Weekly	5.38%	8.37%	5.28%	5.51%	5.09%	5.36%	81.76	90.52	77.71	95.24
Monthly	11.46%	25.01%	13.39%	11.59%	10.59%	11.16%	77.39	95.64	69.61	106.32
Quarterly	13.84%	46.54%	17.73%	19.27%	18.34%	19.33%	71.62	103.34	59.62	124.14
Annual	—	—	—	—	36.67%	38.66%	59.62	124.14	41.32	179.13
Option Time Horizon	—	—	—	—	13.84%	14.59%	74.91	98.80	65.23	113.47

Calculation Notes: Computed at 2026-03-23T16:34 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $86.03 | Strike (K): $85.00 (first OTM call ≥ spot) | Observed Mid-Price: $5.2500 (Bid $4.9000 / Ask $5.6000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 3.62% | Binomial IV (Annual): 36.67% (CRR binomial tree, American, n=20 steps) | BS IV: 36.82% (European Black-Scholes) | Yahoo IV (Annual): 38.66% → 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
2026-03-11	$0.8000
2025-12-03	$0.7900
2025-09-04	$0.7800
2025-06-02	$0.7600
2025-03-12	$0.7500
2024-12-02	$0.7300
2024-09-05	$0.7200
2024-06-03	$0.7100
2024-03-11	$0.6900
2023-11-30	$0.6700
2023-09-06	$0.6500
2023-05-31	$0.6400
2023-03-14	$0.6400
2022-11-30	$0.6400
2022-09-07	$0.6400
2022-06-01	$0.6400
2022-03-09	$0.6400
2021-11-30	$0.6400
2021-08-31	$0.6300
2021-06-02	$0.6100
2021-02-26	$0.5600
2020-12-01	$0.5600
2020-08-31	$0.5600
2020-05-29	$0.5600
2020-02-28	$0.5600
2019-12-02	$0.5500
2019-09-04	$0.5500
2019-05-31	$0.5400
2019-03-01	$0.5400
2018-11-30	$0.5400
2018-09-05	$0.5300
2018-06-01	$0.5200
2018-03-02	$0.5100
2017-12-01	$0.4900
2017-08-30	$0.4700
2017-06-01	$0.4600
2017-03-02	$0.4500
2016-12-01	$0.4300
2016-08-31	$0.4100
2016-06-02	$0.3900
2016-03-03	$0.3800
2015-12-03	$0.3800
2015-09-02	$0.3800
2015-06-04	$0.3800
2015-03-05	$0.3600
2014-12-04	$0.3400
2014-09-04	$0.3400
2014-06-05	$0.3200
2014-03-06	$0.2800
2013-12-05	$0.2600
2013-09-03	$0.2600
2013-05-30	$0.2300
2013-03-07	$0.2300
2012-12-06	$0.2100
2012-09-04	$0.2100
2012-05-31	$0.1800
2012-03-08	$0.1800
2011-11-08	$0.7000
2010-11-17	$0.5500
2009-11-10	$0.5000
2008-11-12	$0.4500
2007-11-14	$0.9000
2006-11-20	$0.8000
2005-11-15	$0.6500
2004-11-09	$0.5500
2003-11-05	$0.4500
2002-11-06	$0.2500

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.81. Further, an Excess Kurtosis of 30.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.03%	49	0.80%	0.80%
-8.03% to -6.00%	45	0.73%	1.53%
-6.00% to -3.98%	127	2.07%	3.60%
-3.98% to -1.95%	492	8.01%	11.61%
-1.95% to 0.07%	2357	38.39%	50.01%
0.07% to 2.09%	2406	39.19%	89.20%
2.09% to 4.12%	468	7.62%	96.82%
4.12% to 6.14%	108	1.76%	98.58%
6.14% to 8.17%	37	0.60%	99.19%
Greater than 8.17%	50	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.63%	2.77%	85.63%	68.27%
±2σ	-5.33%	5.47%	96.35%	95.45%
±3σ	-8.03%	8.17%	98.39%	99.73%

Descriptive Statistics

Mean	0.070%
Standard Error	0.034%
Median	0.069%
Mode	0.000%
Standard Deviation	2.699%
Sample Variance	7.282%
Kurtosis	30.34
Skewness	0.81
Range	70.358%
Minimum	-29.595%
Maximum	40.763%
Count	6139

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.560%	3195	52.04%	0.812%
Negative	-1.569%	2903	47.29%	-0.742%
Zero	0.000%	41	0.67%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.18%
20	1 Month	2.88%
60	1 Quarter	2.56%
250	1 Year	2.40%
750	3 Years	2.13%
1,250	5 Years	2.33%
2,500	10 Years	2.46%
5,000	20 Years	2.98%
12,500	50 Years	2.84%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.28. Further, an Excess Kurtosis of 94.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.49%	0	0.00%	0.00%
-6.49% to -4.19%	0	0.00%	0.00%
-4.19% to -1.89%	0	0.00%	0.00%
-1.89% to 0.40%	1	0.02%	0.02%
0.40% to 2.70%	4372	71.21%	71.22%
2.70% to 5.00%	1263	20.57%	91.79%
5.00% to 7.30%	252	4.10%	95.90%
7.30% to 9.59%	88	1.43%	97.33%
9.59% to 11.89%	41	0.67%	98.00%
Greater than 11.89%	123	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-0.36%	5.76%	93.76%	68.27%
±2σ	-3.43%	8.83%	96.99%	95.45%
±3σ	-6.49%	11.89%	98.00%	99.73%

Descriptive Statistics

Mean	2.701%
Standard Error	0.039%
Median	1.950%
Mode	1.361%
Standard Deviation	3.063%
Sample Variance	9.384%
Kurtosis	94.34
Skewness	7.28
Range	69.340%
Minimum	0.340%
Maximum	69.680%
Count	6140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.701%	6140	100.00%	2.701%
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 1.53. Further, an Excess Kurtosis of 36.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.74%	47	0.77%	0.77%
-6.74% to -5.05%	39	0.64%	1.40%
-5.05% to -3.37%	95	1.55%	2.95%
-3.37% to -1.68%	538	8.76%	11.71%
-1.68% to 0.00%	2497	40.67%	52.38%
0.00% to 1.69%	2197	35.78%	88.16%
1.69% to 3.37%	502	8.18%	96.34%
3.37% to 5.06%	120	1.95%	98.29%
5.06% to 6.74%	47	0.77%	99.06%
Greater than 6.74%	58	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.24%	2.25%	85.55%	68.27%
±2σ	-4.49%	4.50%	95.83%	95.45%
±3σ	-6.74%	6.74%	98.29%	99.73%

Descriptive Statistics

Mean	0.003%
Standard Error	0.029%
Median	-0.053%
Mode	0.000%
Standard Deviation	2.247%
Sample Variance	5.050%
Kurtosis	36.72
Skewness	1.53
Range	68.043%
Minimum	-27.448%
Maximum	40.595%
Count	6140

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.384%	2924	47.62%	0.659%
Negative	-1.278%	3149	51.29%	-0.655%
Zero	0.000%	67	1.09%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.75. Further, an Excess Kurtosis of 16.12 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.85%	13	1.02%	1.02%
-15.85% to -11.81%	10	0.79%	1.81%
-11.81% to -7.77%	33	2.59%	4.40%
-7.77% to -3.73%	111	8.72%	13.12%
-3.73% to 0.30%	440	34.56%	47.68%
0.30% to 4.34%	508	39.91%	87.59%
4.34% to 8.38%	116	9.11%	96.70%
8.38% to 12.42%	21	1.65%	98.35%
12.42% to 16.46%	11	0.86%	99.21%
Greater than 16.46%	10	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.08%	5.69%	83.74%	68.27%
±2σ	-10.46%	11.07%	95.60%	95.45%
±3σ	-15.85%	16.46%	98.19%	99.73%

Descriptive Statistics

Mean	0.305%
Standard Error	0.151%
Median	0.478%
Mode	0.000%
Standard Deviation	5.384%
Sample Variance	28.986%
Kurtosis	16.12
Skewness	0.75
Range	87.135%
Minimum	-36.713%
Maximum	50.422%
Count	1273

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.234%	717	56.32%	1.822%
Negative	-3.502%	551	43.28%	-1.516%
Zero	0.000%	5	0.39%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.23%
12	1 Quarter	5.51%
52	1 Year	5.31%
156	3 Years	5.03%
260	5 Years	5.51%
520	10 Years	5.85%
1,040	20 Years	6.98%
2,600	50 Years	6.63%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 7.73. Further, an Excess Kurtosis of 98.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.13%	0	0.00%	0.00%
-18.13% to -11.85%	0	0.00%	0.00%
-11.85% to -5.58%	0	0.00%	0.00%
-5.58% to 0.70%	0	0.00%	0.00%
0.70% to 6.98%	914	71.74%	71.74%
6.98% to 13.25%	259	20.33%	92.07%
13.25% to 19.53%	50	3.92%	96.00%
19.53% to 25.80%	18	1.41%	97.41%
25.80% to 32.08%	11	0.86%	98.27%
Greater than 32.08%	22	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.39%	15.35%	94.82%	68.27%
±2σ	-9.76%	23.71%	96.94%	95.45%
±3σ	-18.13%	32.08%	98.27%	99.73%

Descriptive Statistics

Mean	6.977%
Standard Error	0.234%
Median	4.991%
Mode	2.058%
Standard Deviation	8.368%
Sample Variance	70.021%
Kurtosis	98.04
Skewness	7.73
Range	155.264%
Minimum	0.736%
Maximum	156.000%
Count	1274

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.977%	1274	100.00%	6.977%
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 1.61. Further, an Excess Kurtosis of 16.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.79%	9	0.71%	0.71%
-15.79% to -11.83%	9	0.71%	1.41%
-11.83% to -7.87%	13	1.02%	2.43%
-7.87% to -3.91%	121	9.50%	11.93%
-3.91% to 0.05%	564	44.27%	56.20%
0.05% to 4.01%	397	31.16%	87.36%
4.01% to 7.97%	101	7.93%	95.29%
7.97% to 11.93%	31	2.43%	97.72%
11.93% to 15.89%	12	0.94%	98.67%
Greater than 15.89%	17	1.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.23%	5.33%	85.24%	68.27%
±2σ	-10.51%	10.61%	95.76%	95.45%
±3σ	-15.79%	15.89%	97.96%	99.73%

Descriptive Statistics

Mean	0.051%
Standard Error	0.148%
Median	-0.365%
Mode	-3.846%
Standard Deviation	5.279%
Sample Variance	27.868%
Kurtosis	16.42
Skewness	1.61
Range	83.398%
Minimum	-32.265%
Maximum	51.133%
Count	1274

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.646%	571	44.82%	1.634%
Negative	-2.881%	700	54.95%	-1.583%
Zero	0.000%	3	0.23%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.93. Further, an Excess Kurtosis of 24.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.06%	2	0.68%	0.68%
-33.06% to -24.46%	3	1.02%	1.71%
-24.46% to -15.87%	3	1.02%	2.73%
-15.87% to -7.28%	29	9.90%	12.63%
-7.28% to 1.32%	108	36.86%	49.49%
1.32% to 9.91%	123	41.98%	91.47%
9.91% to 18.51%	16	5.46%	96.93%
18.51% to 27.11%	6	2.05%	98.98%
27.11% to 35.70%	0	0.00%	98.98%
Greater than 35.70%	3	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.14%	12.78%	86.35%	68.27%
±2σ	-21.60%	24.24%	95.90%	95.45%
±3σ	-33.06%	35.70%	98.29%	99.73%

Descriptive Statistics

Mean	1.320%
Standard Error	0.669%
Median	1.533%
Mode	-7.348%
Standard Deviation	11.460%
Sample Variance	131.321%
Kurtosis	24.26
Skewness	1.93
Range	156.090%
Minimum	-56.335%
Maximum	99.755%
Count	293

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.928%	172	58.70%	4.067%
Negative	-6.653%	121	41.30%	-2.747%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.56%
12	1 Year	10.14%
36	3 Years	10.66%
60	5 Years	11.59%
120	10 Years	12.63%
240	20 Years	15.01%
600	50 Years	14.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.78. Further, an Excess Kurtosis of 55.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.23%	0	0.00%	0.00%
-58.23% to -39.47%	0	0.00%	0.00%
-39.47% to -20.71%	0	0.00%	0.00%
-20.71% to -1.95%	0	0.00%	0.00%
-1.95% to 16.80%	227	77.21%	77.21%
16.80% to 35.56%	52	17.69%	94.90%
35.56% to 54.32%	5	1.70%	96.60%
54.32% to 73.08%	2	0.68%	97.28%
73.08% to 91.83%	1	0.34%	97.62%
Greater than 91.83%	7	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.21%	41.81%	95.92%	68.27%
±2σ	-33.22%	66.82%	97.28%	95.45%
±3σ	-58.23%	91.83%	97.62%	99.73%

Descriptive Statistics

Mean	16.803%
Standard Error	1.459%
Median	11.622%
Mode	11.644%
Standard Deviation	25.010%
Sample Variance	625.491%
Kurtosis	55.26
Skewness	6.78
Range	260.632%
Minimum	3.288%
Maximum	263.920%
Count	294

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.803%	294	100.00%	16.803%
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 4.79. Further, an Excess Kurtosis of 44.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.88%	1	0.34%	0.34%
-39.88% to -29.84%	1	0.34%	0.68%
-29.84% to -19.80%	2	0.68%	1.36%
-19.80% to -9.76%	17	5.78%	7.14%
-9.76% to 0.28%	153	52.04%	59.18%
0.28% to 10.32%	93	31.63%	90.82%
10.32% to 20.36%	19	6.46%	97.28%
20.36% to 30.40%	3	1.02%	98.30%
30.40% to 40.44%	2	0.68%	98.98%
Greater than 40.44%	3	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.10%	13.67%	91.16%	68.27%
±2σ	-26.49%	27.05%	96.94%	95.45%
±3σ	-39.88%	40.44%	98.64%	99.73%

Descriptive Statistics

Mean	0.283%
Standard Error	0.781%
Median	-1.054%
Mode	-8.154%
Standard Deviation	13.386%
Sample Variance	179.175%
Kurtosis	44.46
Skewness	4.79
Range	185.232%
Minimum	-51.530%
Maximum	133.702%
Count	294

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.406%	127	43.20%	3.631%
Negative	-5.894%	167	56.80%	-3.348%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Left Skewed (Negative Asymmetry) with a Skewness factor of -0.56. Further, an Excess Kurtosis of 3.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.45%	1	1.02%	1.02%
-38.45% to -28.06%	1	1.02%	2.04%
-28.06% to -17.68%	5	5.10%	7.14%
-17.68% to -7.30%	12	12.24%	19.39%
-7.30% to 3.09%	27	27.55%	46.94%
3.09% to 13.47%	37	37.76%	84.69%
13.47% to 23.85%	9	9.18%	93.88%
23.85% to 34.23%	5	5.10%	98.98%
34.23% to 44.62%	0	0.00%	98.98%
Greater than 44.62%	1	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.76%	16.93%	76.53%	68.27%
±2σ	-24.60%	30.77%	94.90%	95.45%
±3σ	-38.45%	44.62%	97.96%	99.73%

Descriptive Statistics

Mean	3.086%
Standard Error	1.398%
Median	3.634%
Mode	-55.328%
Standard Deviation	13.844%
Sample Variance	191.647%
Kurtosis	3.09
Skewness	-0.56
Range	100.371%
Minimum	-55.328%
Maximum	45.043%
Count	98

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.718%	63	64.29%	6.890%
Negative	-10.651%	35	35.71%	-3.804%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	14.72%
12	3 Years	18.42%
20	5 Years	19.27%
40	10 Years	21.29%
80	20 Years	24.77%
200	50 Years	23.36%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.90. Further, an Excess Kurtosis of 25.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -107.70%	0	0.00%	0.00%
-107.70% to -72.79%	0	0.00%	0.00%
-72.79% to -37.89%	0	0.00%	0.00%
-37.89% to -2.98%	0	0.00%	0.00%
-2.98% to 31.92%	77	77.78%	77.78%
31.92% to 66.82%	17	17.17%	94.95%
66.82% to 101.73%	1	1.01%	95.96%
101.73% to 136.63%	0	0.00%	95.96%
136.63% to 171.54%	1	1.01%	96.97%
Greater than 171.54%	3	3.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.62%	78.46%	95.96%	68.27%
±2σ	-61.16%	125.00%	95.96%	95.45%
±3σ	-107.70%	171.54%	96.97%	99.73%

Descriptive Statistics

Mean	31.919%
Standard Error	4.677%
Median	19.992%
Mode	8.058%
Standard Deviation	46.539%
Sample Variance	2165.911%
Kurtosis	25.59
Skewness	4.90
Range	326.182%
Minimum	8.058%
Maximum	334.240%
Count	99

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.919%	99	100.00%	31.919%
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 3.77. Further, an Excess Kurtosis of 24.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.38%	0	0.00%	0.00%
-53.38% to -40.08%	0	0.00%	0.00%
-40.08% to -26.78%	1	1.01%	1.01%
-26.78% to -13.48%	10	10.10%	11.11%
-13.48% to -0.19%	51	51.52%	62.63%
-0.19% to 13.11%	26	26.26%	88.89%
13.11% to 26.41%	8	8.08%	96.97%
26.41% to 39.71%	1	1.01%	97.98%
39.71% to 53.01%	1	1.01%	98.99%
Greater than 53.01%	1	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.92%	17.55%	86.87%	68.27%
±2σ	-35.65%	35.28%	97.98%	95.45%
±3σ	-53.38%	53.01%	98.99%	99.73%

Descriptive Statistics

Mean	-0.186%
Standard Error	1.782%
Median	-2.835%
Mode	-32.827%
Standard Deviation	17.732%
Sample Variance	314.407%
Kurtosis	24.06
Skewness	3.77
Range	156.682%
Minimum	-32.827%
Maximum	123.855%
Count	99

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.166%	35	35.35%	5.362%
Negative	-8.582%	64	64.65%	-5.548%
Zero	0.000%	0	0.00%	0.000%

PFG Deep Analytical Report