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%	3.07%	2.25%	2.33%	1.16%	1.44%	94.66	96.88	93.56	98.01
Weekly	5.39%	8.38%	5.29%	5.52%	2.55%	3.17%	93.35	98.24	90.99	100.78
Monthly	11.46%	25.05%	13.40%	11.57%	5.31%	6.60%	90.80	100.99	86.10	106.50
Quarterly	13.79%	46.56%	17.70%	19.05%	9.21%	11.43%	87.34	104.99	79.66	115.12
Annual	—	—	—	—	18.41%	22.86%	79.66	115.12	66.26	138.39
Option Time Horizon	—	—	—	—	7.08%	8.79%	89.21	102.79	83.11	110.33

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $95.76 | Strike (K): $100.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.1750 (Bid $0.6000 / Ask $1.7500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 3.34% | Binomial IV (Annual): 18.41% (CRR binomial tree, American, n=20 steps) | BS IV: 18.57% (European Black-Scholes) | Yahoo IV (Annual): 22.86% → 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
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 30.31 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%	44	0.72%	1.52%
-6.00% to -3.98%	128	2.09%	3.61%
-3.98% to -1.95%	488	7.98%	11.59%
-1.95% to 0.07%	2348	38.38%	49.97%
0.07% to 2.10%	2402	39.26%	89.23%
2.10% to 4.12%	466	7.62%	96.85%
4.12% to 6.15%	107	1.75%	98.59%
6.15% to 8.18%	36	0.59%	99.18%
Greater than 8.18%	50	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.63%	2.77%	85.67%	68.27%
±2σ	-5.33%	5.47%	96.34%	95.45%
±3σ	-8.03%	8.17%	98.38%	99.73%

Descriptive Statistics

Mean	0.072%
Standard Error	0.035%
Median	0.074%
Mode	0.000%
Standard Deviation	2.701%
Sample Variance	7.297%
Kurtosis	30.31
Skewness	0.81
Range	70.358%
Minimum	-29.595%
Maximum	40.763%
Count	6118

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.560%	3189	52.12%	0.813%
Negative	-1.570%	2889	47.22%	-0.741%
Zero	0.000%	40	0.65%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.71%
20	1 Month	2.70%
60	1 Quarter	2.19%
250	1 Year	2.34%
750	3 Years	2.16%
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 94.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.50%	0	0.00%	0.00%
-6.50% to -4.20%	0	0.00%	0.00%
-4.20% to -1.90%	0	0.00%	0.00%
-1.90% to 0.40%	1	0.02%	0.02%
0.40% to 2.70%	4360	71.25%	71.27%
2.70% to 5.00%	1255	20.51%	91.78%
5.00% to 7.30%	252	4.12%	95.90%
7.30% to 9.60%	87	1.42%	97.32%
9.60% to 11.90%	41	0.67%	97.99%
Greater than 11.90%	123	2.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-0.37%	5.77%	93.77%	68.27%
±2σ	-3.44%	8.84%	96.98%	95.45%
±3σ	-6.50%	11.91%	97.99%	99.73%

Descriptive Statistics

Mean	2.701%
Standard Error	0.039%
Median	1.947%
Mode	1.361%
Standard Deviation	3.068%
Sample Variance	9.412%
Kurtosis	94.10
Skewness	7.28
Range	69.340%
Minimum	0.340%
Maximum	69.680%
Count	6119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.701%	6119	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 36.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.75%	47	0.77%	0.77%
-6.75% to -5.06%	39	0.64%	1.41%
-5.06% to -3.37%	94	1.54%	2.94%
-3.37% to -1.68%	533	8.71%	11.65%
-1.68% to 0.00%	2496	40.79%	52.44%
0.00% to 1.69%	2185	35.71%	88.15%
1.69% to 3.38%	500	8.17%	96.32%
3.38% to 5.07%	123	2.01%	98.33%
5.07% to 6.75%	44	0.72%	99.05%
Greater than 6.75%	58	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.25%	2.25%	85.62%	68.27%
±2σ	-4.50%	4.50%	95.82%	95.45%
±3σ	-6.75%	6.75%	98.28%	99.73%

Descriptive Statistics

Mean	0.003%
Standard Error	0.029%
Median	-0.057%
Mode	0.000%
Standard Deviation	2.250%
Sample Variance	5.062%
Kurtosis	36.67
Skewness	1.53
Range	68.043%
Minimum	-27.448%
Maximum	40.595%
Count	6119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.386%	2910	47.56%	0.659%
Negative	-1.278%	3142	51.35%	-0.656%
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 16.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.86%	13	1.02%	1.02%
-15.86% to -11.81%	10	0.79%	1.81%
-11.81% to -7.77%	33	2.60%	4.41%
-7.77% to -3.73%	110	8.67%	13.08%
-3.73% to 0.31%	440	34.67%	47.75%
0.31% to 4.36%	505	39.80%	87.55%
4.36% to 8.40%	116	9.14%	96.69%
8.40% to 12.44%	21	1.65%	98.35%
12.44% to 16.48%	11	0.87%	99.21%
Greater than 16.48%	10	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.08%	5.70%	83.77%	68.27%
±2σ	-10.47%	11.09%	95.59%	95.45%
±3σ	-15.86%	16.48%	98.19%	99.73%

Descriptive Statistics

Mean	0.314%
Standard Error	0.151%
Median	0.481%
Mode	0.000%
Standard Deviation	5.390%
Sample Variance	29.056%
Kurtosis	16.09
Skewness	0.75
Range	87.135%
Minimum	-36.713%
Maximum	50.422%
Count	1269

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.239%	716	56.42%	1.828%
Negative	-3.504%	548	43.18%	-1.513%
Zero	0.000%	5	0.39%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	5.44%
12	1 Quarter	4.83%
52	1 Year	5.21%
156	3 Years	5.16%
260	5 Years	5.52%
520	10 Years	5.85%
1,040	20 Years	6.97%
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 7.72. Further, an Excess Kurtosis of 97.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.16%	0	0.00%	0.00%
-18.16% to -11.88%	0	0.00%	0.00%
-11.88% to -5.59%	0	0.00%	0.00%
-5.59% to 0.69%	0	0.00%	0.00%
0.69% to 6.98%	912	71.81%	71.81%
6.98% to 13.27%	257	20.24%	92.05%
13.27% to 19.55%	50	3.94%	95.98%
19.55% to 25.84%	18	1.42%	97.40%
25.84% to 32.12%	11	0.87%	98.27%
Greater than 32.12%	22	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.40%	15.36%	94.80%	68.27%
±2σ	-9.78%	23.74%	96.93%	95.45%
±3σ	-18.16%	32.12%	98.27%	99.73%

Descriptive Statistics

Mean	6.980%
Standard Error	0.235%
Median	4.986%
Mode	2.058%
Standard Deviation	8.381%
Sample Variance	70.236%
Kurtosis	97.73
Skewness	7.72
Range	155.264%
Minimum	0.736%
Maximum	156.000%
Count	1270

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.980%	1270	100.00%	6.980%
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 16.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.81%	8	0.63%	0.63%
-15.81% to -11.85%	10	0.79%	1.42%
-11.85% to -7.88%	13	1.02%	2.44%
-7.88% to -3.92%	121	9.53%	11.97%
-3.92% to 0.04%	560	44.09%	56.06%
0.04% to 4.01%	398	31.34%	87.40%
4.01% to 7.97%	100	7.87%	95.28%
7.97% to 11.94%	31	2.44%	97.72%
11.94% to 15.90%	12	0.94%	98.66%
Greater than 15.90%	17	1.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.24%	5.33%	85.12%	68.27%
±2σ	-10.53%	10.62%	95.75%	95.45%
±3σ	-15.81%	15.90%	98.03%	99.73%

Descriptive Statistics

Mean	0.045%
Standard Error	0.148%
Median	-0.383%
Mode	-3.846%
Standard Deviation	5.286%
Sample Variance	27.943%
Kurtosis	16.39
Skewness	1.61
Range	83.398%
Minimum	-32.265%
Maximum	51.133%
Count	1270

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.650%	568	44.72%	1.632%
Negative	-2.885%	699	55.04%	-1.588%
Zero	0.000%	3	0.24%	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 24.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.03%	2	0.68%	0.68%
-33.03% to -24.44%	3	1.03%	1.71%
-24.44% to -15.84%	3	1.03%	2.74%
-15.84% to -7.24%	28	9.59%	12.33%
-7.24% to 1.36%	108	36.99%	49.32%
1.36% to 9.96%	123	42.12%	91.44%
9.96% to 18.55%	16	5.48%	96.92%
18.55% to 27.15%	6	2.05%	98.97%
27.15% to 35.75%	0	0.00%	98.97%
Greater than 35.75%	3	1.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.11%	12.82%	86.30%	68.27%
±2σ	-21.57%	24.29%	95.89%	95.45%
±3σ	-33.03%	35.75%	98.29%	99.73%

Descriptive Statistics

Mean	1.358%
Standard Error	0.671%
Median	1.538%
Mode	-7.348%
Standard Deviation	11.464%
Sample Variance	131.422%
Kurtosis	24.28
Skewness	1.93
Range	156.090%
Minimum	-56.335%
Maximum	99.755%
Count	292

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.895%	173	59.25%	4.085%
Negative	-6.691%	119	40.75%	-2.727%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	9.58%
12	1 Year	9.96%
36	3 Years	11.04%
60	5 Years	11.57%
120	10 Years	12.61%
240	20 Years	14.99%
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 6.77. Further, an Excess Kurtosis of 55.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.34%	0	0.00%	0.00%
-58.34% to -39.56%	0	0.00%	0.00%
-39.56% to -20.77%	0	0.00%	0.00%
-20.77% to -1.98%	0	0.00%	0.00%
-1.98% to 16.81%	226	77.13%	77.13%
16.81% to 35.60%	52	17.75%	94.88%
35.60% to 54.39%	5	1.71%	96.59%
54.39% to 73.18%	2	0.68%	97.27%
73.18% to 91.97%	1	0.34%	97.61%
Greater than 91.97%	7	2.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.24%	41.86%	95.90%	68.27%
±2σ	-33.29%	66.91%	97.27%	95.45%
±3σ	-58.35%	91.97%	97.61%	99.73%

Descriptive Statistics

Mean	16.811%
Standard Error	1.464%
Median	11.599%
Mode	11.644%
Standard Deviation	25.052%
Sample Variance	627.615%
Kurtosis	55.06
Skewness	6.77
Range	260.632%
Minimum	3.288%
Maximum	263.920%
Count	293

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.811%	293	100.00%	16.811%
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 4.80. Further, an Excess Kurtosis of 44.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.95%	1	0.34%	0.34%
-39.95% to -29.90%	1	0.34%	0.68%
-29.90% to -19.85%	2	0.68%	1.37%
-19.85% to -9.80%	16	5.46%	6.83%
-9.80% to 0.25%	152	51.88%	58.70%
0.25% to 10.30%	94	32.08%	90.78%
10.30% to 20.35%	19	6.48%	97.27%
20.35% to 30.40%	3	1.02%	98.29%
30.40% to 40.45%	2	0.68%	98.98%
Greater than 40.45%	3	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.15%	13.65%	91.13%	68.27%
±2σ	-26.55%	27.05%	96.93%	95.45%
±3σ	-39.94%	40.45%	98.63%	99.73%

Descriptive Statistics

Mean	0.252%
Standard Error	0.783%
Median	-1.074%
Mode	-8.154%
Standard Deviation	13.399%
Sample Variance	179.532%
Kurtosis	44.48
Skewness	4.80
Range	185.232%
Minimum	-51.530%
Maximum	133.702%
Count	293

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.402%	126	43.00%	3.613%
Negative	-5.896%	167	57.00%	-3.361%
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 -0.58. Further, an Excess Kurtosis of 3.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.19%	1	1.02%	1.02%
-38.19% to -27.84%	1	1.02%	2.04%
-27.84% to -17.50%	5	5.10%	7.14%
-17.50% to -7.16%	11	11.22%	18.37%
-7.16% to 3.19%	28	28.57%	46.94%
3.19% to 13.53%	37	37.76%	84.69%
13.53% to 23.88%	9	9.18%	93.88%
23.88% to 34.22%	5	5.10%	98.98%
34.22% to 44.56%	0	0.00%	98.98%
Greater than 44.56%	1	1.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.61%	16.98%	74.49%	68.27%
±2σ	-24.40%	30.77%	94.90%	95.45%
±3σ	-38.19%	44.56%	97.96%	99.73%

Descriptive Statistics

Mean	3.187%
Standard Error	1.393%
Median	3.634%
Mode	-55.328%
Standard Deviation	13.792%
Sample Variance	190.221%
Kurtosis	3.20
Skewness	-0.58
Range	100.371%
Minimum	-55.328%
Maximum	45.043%
Count	98

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.568%	64	65.31%	6.902%
Negative	-10.706%	34	34.69%	-3.714%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	13.58%
12	3 Years	18.04%
20	5 Years	19.05%
40	10 Years	21.18%
80	20 Years	24.71%
200	50 Years	23.32%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.89. Further, an Excess Kurtosis of 25.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -107.83%	0	0.00%	0.00%
-107.83% to -72.90%	0	0.00%	0.00%
-72.90% to -37.98%	0	0.00%	0.00%
-37.98% to -3.06%	0	0.00%	0.00%
-3.06% to 31.86%	77	77.78%	77.78%
31.86% to 66.78%	17	17.17%	94.95%
66.78% to 101.71%	1	1.01%	95.96%
101.71% to 136.63%	0	0.00%	95.96%
136.63% to 171.55%	1	1.01%	96.97%
Greater than 171.55%	3	3.03%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.70%	78.43%	95.96%	68.27%
±2σ	-61.26%	124.99%	95.96%	95.45%
±3σ	-107.83%	171.55%	96.97%	99.73%

Descriptive Statistics

Mean	31.863%
Standard Error	4.680%
Median	19.992%
Mode	8.058%
Standard Deviation	46.563%
Sample Variance	2168.109%
Kurtosis	25.56
Skewness	4.89
Range	326.182%
Minimum	8.058%
Maximum	334.240%
Count	99

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.863%	99	100.00%	31.863%
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 3.80. Further, an Excess Kurtosis of 24.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.41%	0	0.00%	0.00%
-53.41% to -40.13%	0	0.00%	0.00%
-40.13% to -26.85%	1	1.01%	1.01%
-26.85% to -13.57%	10	10.10%	11.11%
-13.57% to -0.29%	52	52.53%	63.64%
-0.29% to 12.98%	25	25.25%	88.89%
12.98% to 26.26%	8	8.08%	96.97%
26.26% to 39.54%	1	1.01%	97.98%
39.54% to 52.82%	1	1.01%	98.99%
Greater than 52.82%	1	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.00%	17.41%	86.87%	68.27%
±2σ	-35.70%	35.11%	97.98%	95.45%
±3σ	-53.41%	52.82%	98.99%	99.73%

Descriptive Statistics

Mean	-0.295%
Standard Error	1.779%
Median	-2.835%
Mode	-32.827%
Standard Deviation	17.705%
Sample Variance	313.454%
Kurtosis	24.32
Skewness	3.80
Range	156.682%
Minimum	-32.827%
Maximum	123.855%
Count	99

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.333%	34	34.34%	5.266%
Negative	-8.469%	65	65.66%	-5.560%
Zero	0.000%	0	0.00%	0.000%

PFG Deep Analytical Report