PRPL - 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	5.31%	4.97%	4.72%	7.95%	14.23%	14.17%	0.60	0.80	0.52	0.92
Weekly	11.15%	13.38%	11.35%	18.06%	31.33%	31.20%	0.51	0.95	0.37	1.30
Monthly	22.80%	34.53%	26.07%	38.14%	65.21%	64.95%	0.36	1.33	0.19	2.56
Quarterly	36.00%	64.62%	48.26%	59.48%	112.94%	112.50%	0.22	2.15	0.07	6.65
Annual	—	—	—	—	225.89%	225.00%	0.07	6.65	0.01	63.68
Option Time Horizon	—	—	—	—	81.06%	80.74%	0.31	1.56	0.14	3.52

Calculation Notes: Computed at 2026-03-01T12:17 UTC | Reference Contract: Call option expiring 2026-04-17 (47 days) | Spot Price (S): $0.69 | Strike (K): $2.50 (first OTM call ≥ spot) | Observed Mid-Price: $0.0250 (Bid $0.0000 / Ask $0.0500) | Risk-Free Rate (r): 3.74% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 225.89% (CRR binomial tree, American, n=20 steps) | BS IV: 226.22% (European Black-Scholes) | Yahoo IV (Annual): 225.00% → 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
2023-04-27	$0.0010

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.66. Further, an Excess Kurtosis of 8.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.92%	11	0.50%	0.50%
-15.92% to -11.93%	22	1.00%	1.50%
-11.93% to -7.95%	59	2.68%	4.17%
-7.95% to -3.96%	261	11.84%	16.02%
-3.96% to 0.02%	815	36.98%	52.99%
0.02% to 4.01%	707	32.08%	85.07%
4.01% to 7.99%	219	9.94%	95.01%
7.99% to 11.98%	61	2.77%	97.78%
11.98% to 15.96%	25	1.13%	98.91%
Greater than 15.96%	24	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.29%	5.33%	79.99%	68.27%
±2σ	-10.60%	10.65%	95.24%	95.45%
±3σ	-15.92%	15.96%	98.41%	99.73%

Descriptive Statistics

Mean	0.022%
Standard Error	0.113%
Median	0.000%
Mode	0.000%
Standard Deviation	5.313%
Sample Variance	28.224%
Kurtosis	8.45
Skewness	0.66
Range	72.013%
Minimum	-32.586%
Maximum	39.427%
Count	2204

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.761%	1037	47.05%	1.770%
Negative	-3.508%	1098	49.82%	-1.748%
Zero	0.000%	69	3.13%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.35%
20	1 Month	5.35%
60	1 Quarter	5.93%
250	1 Year	7.82%
750	3 Years	8.45%
1,250	5 Years	7.95%
2,500	10 Years	7.07%
5,000	20 Years	7.07%
12,500	50 Years	7.07%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.52. Further, an Excess Kurtosis of 13.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.82%	0	0.00%	0.00%
-7.82% to -4.10%	0	0.00%	0.00%
-4.10% to -0.37%	0	0.00%	0.00%
-0.37% to 3.35%	374	16.96%	16.96%
3.35% to 7.08%	964	43.72%	60.68%
7.08% to 10.80%	536	24.31%	84.99%
10.80% to 14.53%	183	8.30%	93.29%
14.53% to 18.25%	81	3.67%	96.96%
18.25% to 21.98%	34	1.54%	98.50%
Greater than 21.98%	33	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.11%	12.04%	79.68%	68.27%
±2σ	-2.85%	17.01%	96.37%	95.45%
±3σ	-7.82%	21.98%	98.50%	99.73%

Descriptive Statistics

Mean	7.078%
Standard Error	0.106%
Median	6.109%
Mode	0.500%
Standard Deviation	4.966%
Sample Variance	24.665%
Kurtosis	13.69
Skewness	2.52
Range	57.925%
Minimum	0.030%
Maximum	57.955%
Count	2205

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.078%	2205	100.00%	7.078%
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 0.27. Further, an Excess Kurtosis of 5.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.76%	13	0.59%	0.59%
-13.76% to -10.22%	28	1.27%	1.86%
-10.22% to -6.68%	65	2.95%	4.81%
-6.68% to -3.13%	266	12.06%	16.87%
-3.13% to 0.41%	807	36.60%	53.47%
0.41% to 3.95%	650	29.48%	82.95%
3.95% to 7.49%	267	12.11%	95.06%
7.49% to 11.03%	62	2.81%	97.87%
11.03% to 14.57%	24	1.09%	98.96%
Greater than 14.57%	23	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.32%	5.13%	76.87%	68.27%
±2σ	-9.04%	9.85%	94.69%	95.45%
±3σ	-13.76%	14.57%	98.37%	99.73%

Descriptive Statistics

Mean	0.406%
Standard Error	0.101%
Median	0.157%
Mode	0.000%
Standard Deviation	4.721%
Sample Variance	22.285%
Kurtosis	5.11
Skewness	0.27
Range	62.586%
Minimum	-27.886%
Maximum	34.700%
Count	2205

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.526%	1153	52.29%	1.844%
Negative	-3.225%	983	44.58%	-1.438%
Zero	0.000%	69	3.13%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.88. Further, an Excess Kurtosis of 3.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.36%	2	0.41%	0.41%
-33.36% to -25.00%	4	0.81%	1.22%
-25.00% to -16.64%	17	3.45%	4.67%
-16.64% to -8.29%	57	11.56%	16.23%
-8.29% to 0.07%	187	37.93%	54.16%
0.07% to 8.43%	154	31.24%	85.40%
8.43% to 16.79%	41	8.32%	93.71%
16.79% to 25.15%	14	2.84%	96.55%
25.15% to 33.51%	10	2.03%	98.58%
Greater than 33.51%	7	1.42%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.07%	11.22%	78.90%	68.27%
±2σ	-22.22%	22.37%	93.91%	95.45%
±3σ	-33.36%	33.51%	98.17%	99.73%

Descriptive Statistics

Mean	0.075%
Standard Error	0.502%
Median	-0.100%
Mode	0.000%
Standard Deviation	11.146%
Sample Variance	124.234%
Kurtosis	3.92
Skewness	0.88
Range	97.899%
Minimum	-40.323%
Maximum	57.576%
Count	493

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.015%	228	46.25%	3.707%
Negative	-7.105%	252	51.12%	-3.632%
Zero	0.000%	13	2.64%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.80%
12	1 Quarter	11.03%
52	1 Year	15.85%
156	3 Years	18.59%
260	5 Years	18.06%
520	10 Years	15.05%
1,040	20 Years	15.05%
2,600	50 Years	15.05%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.84. 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 -23.34%	0	0.00%	0.00%
-23.34% to -13.31%	0	0.00%	0.00%
-13.31% to -3.27%	0	0.00%	0.00%
-3.27% to 6.77%	84	17.00%	17.00%
6.77% to 16.80%	225	45.55%	62.55%
16.80% to 26.84%	107	21.66%	84.21%
26.84% to 36.88%	38	7.69%	91.90%
36.88% to 46.92%	22	4.45%	96.36%
46.92% to 56.95%	7	1.42%	97.77%
Greater than 56.95%	11	2.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.42%	30.19%	76.92%	68.27%
±2σ	-9.96%	43.57%	94.74%	95.45%
±3σ	-23.35%	56.95%	97.77%	99.73%

Descriptive Statistics

Mean	16.804%
Standard Error	0.602%
Median	14.122%
Mode	0.899%
Standard Deviation	13.383%
Sample Variance	179.112%
Kurtosis	4.94
Skewness	1.84
Range	88.920%
Minimum	0.071%
Maximum	88.991%
Count	494

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.804%	494	100.00%	16.804%
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 0.96. Further, an Excess Kurtosis of 5.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.54%	1	0.20%	0.20%
-32.54% to -24.03%	7	1.42%	1.62%
-24.03% to -15.52%	23	4.66%	6.28%
-15.52% to -7.01%	40	8.10%	14.37%
-7.01% to 1.50%	211	42.71%	57.09%
1.50% to 10.01%	140	28.34%	85.43%
10.01% to 18.52%	41	8.30%	93.72%
18.52% to 27.02%	16	3.24%	96.96%
27.02% to 35.53%	10	2.02%	98.99%
Greater than 35.53%	5	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.85%	12.84%	77.73%	68.27%
±2σ	-21.20%	24.19%	93.93%	95.45%
±3σ	-32.54%	35.53%	98.79%	99.73%

Descriptive Statistics

Mean	1.496%
Standard Error	0.510%
Median	0.492%
Mode	0.000%
Standard Deviation	11.346%
Sample Variance	128.724%
Kurtosis	5.29
Skewness	0.96
Range	107.127%
Minimum	-35.577%
Maximum	71.550%
Count	494

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.201%	271	54.86%	4.499%
Negative	-7.030%	211	42.71%	-3.003%
Zero	0.000%	12	2.43%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.77. Further, an Excess Kurtosis of 2.02 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -67.97%	0	0.00%	0.00%
-67.97% to -50.87%	1	0.81%	0.81%
-50.87% to -33.77%	6	4.88%	5.69%
-33.77% to -16.67%	19	15.45%	21.14%
-16.67% to 0.43%	43	34.96%	56.10%
0.43% to 17.53%	33	26.83%	82.93%
17.53% to 34.62%	11	8.94%	91.87%
34.62% to 51.73%	7	5.69%	97.56%
51.73% to 68.82%	1	0.81%	98.37%
Greater than 68.82%	2	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.37%	23.23%	73.98%	68.27%
±2σ	-45.17%	46.02%	95.93%	95.45%
±3σ	-67.97%	68.82%	98.37%	99.73%

Descriptive Statistics

Mean	0.427%
Standard Error	2.056%
Median	0.000%
Mode	0.000%
Standard Deviation	22.799%
Sample Variance	519.780%
Kurtosis	2.02
Skewness	0.77
Range	140.527%
Minimum	-58.174%
Maximum	82.353%
Count	123

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.605%	60	48.78%	8.100%
Negative	-15.471%	61	49.59%	-7.673%
Zero	0.000%	2	1.63%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.00%
12	1 Year	30.39%
36	3 Years	38.85%
60	5 Years	38.14%
120	10 Years	31.28%
240	20 Years	30.64%
600	50 Years	30.64%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.96. Further, an Excess Kurtosis of 7.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.61%	0	0.00%	0.00%
-64.61% to -38.71%	0	0.00%	0.00%
-38.71% to -12.80%	0	0.00%	0.00%
-12.80% to 13.10%	29	23.39%	23.39%
13.10% to 39.00%	42	33.87%	57.26%
39.00% to 64.90%	31	25.00%	82.26%
64.90% to 90.80%	17	13.71%	95.97%
90.80% to 116.70%	2	1.61%	97.58%
116.70% to 142.60%	1	0.81%	98.39%
Greater than 142.60%	2	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.46%	73.53%	72.58%	68.27%
±2σ	-30.07%	108.07%	97.58%	95.45%
±3σ	-64.61%	142.60%	98.39%	99.73%

Descriptive Statistics

Mean	38.998%
Standard Error	3.101%
Median	34.081%
Mode	0.101%
Standard Deviation	34.535%
Sample Variance	1192.659%
Kurtosis	7.24
Skewness	1.96
Range	225.238%
Minimum	0.101%
Maximum	225.339%
Count	124

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.998%	124	100.00%	38.998%
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 1.73. Further, an Excess Kurtosis of 6.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -72.89%	0	0.00%	0.00%
-72.89% to -53.33%	0	0.00%	0.00%
-53.33% to -33.78%	3	2.42%	2.42%
-33.78% to -14.23%	18	14.52%	16.94%
-14.23% to 5.32%	58	46.77%	63.71%
5.32% to 24.88%	27	21.77%	85.48%
24.88% to 44.43%	10	8.06%	93.55%
44.43% to 63.98%	3	2.42%	95.97%
63.98% to 83.53%	3	2.42%	98.39%
Greater than 83.53%	2	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.75%	31.39%	80.65%	68.27%
±2σ	-46.82%	57.46%	95.16%	95.45%
±3σ	-72.89%	83.53%	98.39%	99.73%

Descriptive Statistics

Mean	5.323%
Standard Error	2.341%
Median	0.152%
Mode	0.000%
Standard Deviation	26.070%
Sample Variance	679.627%
Kurtosis	6.22
Skewness	1.73
Range	188.070%
Minimum	-46.521%
Maximum	141.549%
Count	124

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.562%	67	54.03%	11.110%
Negative	-13.047%	55	44.35%	-5.787%
Zero	0.000%	2	1.61%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.54. Further, an Excess Kurtosis of 5.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -108.10%	0	0.00%	0.00%
-108.10% to -81.10%	0	0.00%	0.00%
-81.10% to -54.10%	2	4.76%	4.76%
-54.10% to -27.11%	4	9.52%	14.29%
-27.11% to -0.11%	14	33.33%	47.62%
-0.11% to 26.89%	18	42.86%	90.48%
26.89% to 53.89%	1	2.38%	92.86%
53.89% to 80.89%	2	4.76%	97.62%
80.89% to 107.88%	0	0.00%	97.62%
Greater than 107.88%	1	2.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-36.10%	35.89%	78.57%	68.27%
±2σ	-72.10%	71.89%	95.24%	95.45%
±3σ	-108.10%	107.88%	97.62%	99.73%

Descriptive Statistics

Mean	-0.107%
Standard Error	5.554%
Median	0.259%
Mode	-68.910%
Standard Deviation	35.997%
Sample Variance	1295.798%
Kurtosis	5.43
Skewness	1.54
Range	211.157%
Minimum	-68.910%
Maximum	142.247%
Count	42

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.945%	22	52.38%	10.971%
Negative	-23.264%	20	47.62%	-11.078%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	42.67%
12	3 Years	59.98%
20	5 Years	59.48%
40	10 Years	51.70%
80	20 Years	49.54%
200	50 Years	49.54%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 1.39 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -118.48%	0	0.00%	0.00%
-118.48% to -70.01%	0	0.00%	0.00%
-70.01% to -21.54%	0	0.00%	0.00%
-21.54% to 26.93%	11	25.58%	25.58%
26.93% to 75.40%	16	37.21%	62.79%
75.40% to 123.86%	9	20.93%	83.72%
123.86% to 172.33%	3	6.98%	90.70%
172.33% to 220.80%	2	4.65%	95.35%
220.80% to 269.27%	2	4.65%	100.00%
Greater than 269.27%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.77%	140.02%	65.12%	68.27%
±2σ	-53.85%	204.64%	93.02%	95.45%
±3σ	-118.48%	269.27%	100.00%	99.73%

Descriptive Statistics

Mean	75.396%
Standard Error	9.855%
Median	69.472%
Mode	1.712%
Standard Deviation	64.624%
Sample Variance	4176.318%
Kurtosis	1.39
Skewness	1.20
Range	259.374%
Minimum	1.712%
Maximum	261.086%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	75.396%	43	100.00%	75.396%
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 2.37. Further, an Excess Kurtosis of 7.50 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -130.75%	0	0.00%	0.00%
-130.75% to -94.56%	0	0.00%	0.00%
-94.56% to -58.37%	1	2.33%	2.33%
-58.37% to -22.18%	3	6.98%	9.30%
-22.18% to 14.01%	26	60.47%	69.77%
14.01% to 50.21%	7	16.28%	86.05%
50.21% to 86.40%	2	4.65%	90.70%
86.40% to 122.59%	2	4.65%	95.35%
122.59% to 158.78%	1	2.33%	97.67%
Greater than 158.78%	1	2.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.24%	62.27%	81.40%	68.27%
±2σ	-82.50%	110.53%	95.35%	95.45%
±3σ	-130.75%	158.78%	97.67%	99.73%

Descriptive Statistics

Mean	14.014%
Standard Error	7.359%
Median	0.704%
Mode	-58.966%
Standard Deviation	48.256%
Sample Variance	2328.677%
Kurtosis	7.50
Skewness	2.37
Range	277.523%
Minimum	-58.966%
Maximum	218.557%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.659%	24	55.81%	20.461%
Negative	-14.591%	19	44.19%	-6.447%
Zero	0.000%	0	0.00%	0.000%

PRPL Deep Analytical Report