PINS - 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	3.88%	2.64%	2.90%	4.34%	4.36%	4.33%	18.10	19.75	17.33	20.63
Weekly	8.43%	8.16%	8.48%	10.42%	9.59%	9.53%	17.18	20.81	15.60	22.90
Monthly	15.02%	14.94%	14.63%	21.58%	19.97%	19.85%	15.48	23.08	12.68	28.19
Quarterly	27.31%	31.62%	24.83%	36.17%	34.59%	34.38%	13.38	26.72	9.46	37.76
Annual	—	—	—	—	69.18%	68.75%	9.46	37.76	4.74	75.42
Option Time Horizon	—	—	—	—	26.11%	25.95%	14.56	24.55	11.21	31.87

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $18.91 | Strike (K): $19.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.9500 (Bid $1.8900 / Ask $2.0100) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 69.18% (CRR binomial tree, American, n=20 steps) | BS IV: 68.60% (European Black-Scholes) | Yahoo IV (Annual): 68.75% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.55. Further, an Excess Kurtosis of 10.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.58%	18	1.03%	1.03%
-11.58% to -8.67%	12	0.69%	1.72%
-8.67% to -5.76%	41	2.36%	4.08%
-5.76% to -2.85%	198	11.38%	15.46%
-2.85% to 0.06%	611	35.11%	50.57%
0.06% to 2.97%	613	35.23%	85.80%
2.97% to 5.88%	171	9.83%	95.63%
5.88% to 8.79%	39	2.24%	97.87%
8.79% to 11.70%	18	1.03%	98.91%
Greater than 11.70%	19	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.82%	3.94%	81.03%	68.27%
±2σ	-7.70%	7.82%	95.11%	95.45%
±3σ	-11.58%	11.70%	97.87%	99.73%

Descriptive Statistics

Mean	0.060%
Standard Error	0.093%
Median	0.011%
Mode	0.000%
Standard Deviation	3.880%
Sample Variance	15.053%
Kurtosis	10.46
Skewness	0.55
Range	59.764%
Minimum	-23.639%
Maximum	36.125%
Count	1740

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.601%	870	50.00%	1.301%
Negative	-2.503%	862	49.54%	-1.240%
Zero	0.000%	8	0.46%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.60%
20	1 Month	4.47%
60	1 Quarter	4.63%
250	1 Year	4.08%
750	3 Years	3.64%
1,250	5 Years	4.34%
2,500	10 Years	4.77%
5,000	20 Years	4.77%
12,500	50 Years	4.77%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.41. Further, an Excess Kurtosis of 27.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.52%	0	0.00%	0.00%
-3.52% to -1.53%	0	0.00%	0.00%
-1.53% to 0.45%	0	0.00%	0.00%
0.45% to 2.43%	312	17.92%	17.92%
2.43% to 4.42%	759	43.60%	61.52%
4.42% to 6.40%	404	23.21%	84.72%
6.40% to 8.38%	160	9.19%	93.91%
8.38% to 10.36%	59	3.39%	97.30%
10.36% to 12.35%	24	1.38%	98.68%
Greater than 12.35%	23	1.32%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.77%	7.06%	84.09%	68.27%
±2σ	-0.87%	9.70%	95.98%	95.45%
±3σ	-3.52%	12.35%	98.68%	99.73%

Descriptive Statistics

Mean	4.415%
Standard Error	0.063%
Median	3.817%
Mode	2.039%
Standard Deviation	2.644%
Sample Variance	6.989%
Kurtosis	27.16
Skewness	3.41
Range	39.506%
Minimum	0.795%
Maximum	40.301%
Count	1741

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.415%	1741	100.00%	4.415%
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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.62. Further, an Excess Kurtosis of 7.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.66%	12	0.69%	0.69%
-8.66% to -6.49%	18	1.03%	1.72%
-6.49% to -4.31%	51	2.93%	4.65%
-4.31% to -2.14%	229	13.15%	17.81%
-2.14% to 0.04%	561	32.22%	50.03%
0.04% to 2.21%	558	32.05%	82.08%
2.21% to 4.39%	197	11.32%	93.39%
4.39% to 6.56%	88	5.05%	98.45%
6.56% to 8.74%	18	1.03%	99.48%
Greater than 8.74%	9	0.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.86%	2.94%	75.47%	68.27%
±2σ	-5.76%	5.84%	95.23%	95.45%
±3σ	-8.66%	8.74%	98.79%	99.73%

Descriptive Statistics

Mean	0.036%
Standard Error	0.070%
Median	0.034%
Mode	0.000%
Standard Deviation	2.900%
Sample Variance	8.411%
Kurtosis	7.17
Skewness	-0.62
Range	41.910%
Minimum	-28.288%
Maximum	13.622%
Count	1741

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.086%	881	50.60%	1.056%
Negative	-2.090%	850	48.82%	-1.020%
Zero	0.000%	10	0.57%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.52. Further, an Excess Kurtosis of 4.46 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.02%	2	0.55%	0.55%
-25.02% to -18.70%	7	1.94%	2.49%
-18.70% to -12.37%	10	2.77%	5.26%
-12.37% to -6.05%	40	11.08%	16.34%
-6.05% to 0.27%	129	35.73%	52.08%
0.27% to 6.60%	115	31.86%	83.93%
6.60% to 12.92%	38	10.53%	94.46%
12.92% to 19.24%	12	3.32%	97.78%
19.24% to 25.57%	6	1.66%	99.45%
Greater than 25.57%	2	0.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.16%	8.70%	77.84%	68.27%
±2σ	-16.59%	17.14%	93.63%	95.45%
±3σ	-25.02%	25.57%	98.89%	99.73%

Descriptive Statistics

Mean	0.274%
Standard Error	0.444%
Median	0.000%
Mode	0.000%
Standard Deviation	8.431%
Sample Variance	71.089%
Kurtosis	4.46
Skewness	0.52
Range	76.853%
Minimum	-28.192%
Maximum	48.661%
Count	361

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.201%	179	49.58%	3.075%
Negative	-5.648%	179	49.58%	-2.801%
Zero	0.000%	3	0.83%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.77%
12	1 Quarter	12.10%
52	1 Year	10.06%
156	3 Years	8.81%
260	5 Years	10.42%
520	10 Years	11.47%
1,040	20 Years	11.47%
2,600	50 Years	11.47%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.08. Further, an Excess Kurtosis of 5.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.22%	0	0.00%	0.00%
-12.22% to -6.11%	0	0.00%	0.00%
-6.11% to 0.01%	0	0.00%	0.00%
0.01% to 6.13%	66	18.23%	18.23%
6.13% to 12.25%	171	47.24%	65.47%
12.25% to 18.37%	60	16.57%	82.04%
18.37% to 24.49%	41	11.33%	93.37%
24.49% to 30.61%	9	2.49%	95.86%
30.61% to 36.72%	8	2.21%	98.07%
Greater than 36.72%	7	1.93%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.09%	20.41%	81.49%	68.27%
±2σ	-4.07%	28.57%	95.58%	95.45%
±3σ	-12.22%	36.72%	98.07%	99.73%

Descriptive Statistics

Mean	12.250%
Standard Error	0.429%
Median	9.860%
Mode	3.299%
Standard Deviation	8.158%
Sample Variance	66.553%
Kurtosis	5.80
Skewness	2.08
Range	54.303%
Minimum	2.053%
Maximum	56.356%
Count	362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.250%	362	100.00%	12.250%
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 1.00. 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 -24.87%	2	0.55%	0.55%
-24.87% to -18.51%	0	0.00%	0.55%
-18.51% to -12.15%	14	3.87%	4.42%
-12.15% to -5.79%	47	12.98%	17.40%
-5.79% to 0.57%	136	37.57%	54.97%
0.57% to 6.92%	107	29.56%	84.53%
6.92% to 13.28%	35	9.67%	94.20%
13.28% to 19.64%	9	2.49%	96.69%
19.64% to 26.00%	6	1.66%	98.34%
Greater than 26.00%	6	1.66%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.91%	9.04%	79.28%	68.27%
±2σ	-16.39%	17.52%	94.20%	95.45%
±3σ	-24.87%	26.00%	97.79%	99.73%

Descriptive Statistics

Mean	0.566%
Standard Error	0.446%
Median	0.018%
Mode	6.865%
Standard Deviation	8.478%
Sample Variance	71.871%
Kurtosis	4.61
Skewness	1.00
Range	78.742%
Minimum	-33.038%
Maximum	45.704%
Count	362

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.391%	181	50.00%	3.196%
Negative	-5.318%	179	49.45%	-2.630%
Zero	0.000%	2	0.55%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.74. Further, an Excess Kurtosis of 1.41 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.59%	0	0.00%	0.00%
-44.59% to -33.32%	0	0.00%	0.00%
-33.32% to -22.06%	5	6.02%	6.02%
-22.06% to -10.79%	12	14.46%	20.48%
-10.79% to 0.48%	28	33.73%	54.22%
0.48% to 11.74%	21	25.30%	79.52%
11.74% to 23.01%	13	15.66%	95.18%
23.01% to 34.27%	2	2.41%	97.59%
34.27% to 45.54%	1	1.20%	98.80%
Greater than 45.54%	1	1.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.55%	15.50%	71.08%	68.27%
±2σ	-29.57%	30.52%	96.39%	95.45%
±3σ	-44.59%	45.54%	98.80%	99.73%

Descriptive Statistics

Mean	0.476%
Standard Error	1.649%
Median	-1.673%
Mode	-27.502%
Standard Deviation	15.021%
Sample Variance	225.618%
Kurtosis	1.41
Skewness	0.74
Range	82.170%
Minimum	-27.502%
Maximum	54.668%
Count	83

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.864%	39	46.99%	6.045%
Negative	-10.504%	44	53.01%	-5.568%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	27.36%
12	1 Year	21.98%
36	3 Years	19.20%
60	5 Years	21.58%
120	10 Years	24.13%
240	20 Years	24.13%
600	50 Years	24.13%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.91. Further, an Excess Kurtosis of 5.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.72%	0	0.00%	0.00%
-16.72% to -5.51%	0	0.00%	0.00%
-5.51% to 5.70%	0	0.00%	0.00%
5.70% to 16.91%	17	20.24%	20.24%
16.91% to 28.11%	37	44.05%	64.29%
28.11% to 39.32%	14	16.67%	80.95%
39.32% to 50.53%	8	9.52%	90.48%
50.53% to 61.74%	6	7.14%	97.62%
61.74% to 72.95%	1	1.19%	98.81%
Greater than 72.95%	1	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.17%	43.06%	80.95%	68.27%
±2σ	-1.77%	58.00%	95.24%	95.45%
±3σ	-16.72%	72.95%	98.81%	99.73%

Descriptive Statistics

Mean	28.115%
Standard Error	1.630%
Median	24.368%
Mode	35.670%
Standard Deviation	14.944%
Sample Variance	223.316%
Kurtosis	5.64
Skewness	1.91
Range	89.918%
Minimum	9.884%
Maximum	99.802%
Count	84

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.115%	84	100.00%	28.115%
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 0.01 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.49%	0	0.00%	0.00%
-42.49% to -31.52%	1	1.19%	1.19%
-31.52% to -20.55%	3	3.57%	4.76%
-20.55% to -9.58%	15	17.86%	22.62%
-9.58% to 1.39%	24	28.57%	51.19%
1.39% to 12.37%	25	29.76%	80.95%
12.37% to 23.34%	8	9.52%	90.48%
23.34% to 34.31%	6	7.14%	97.62%
34.31% to 45.28%	2	2.38%	100.00%
Greater than 45.28%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.23%	16.02%	69.05%	68.27%
±2σ	-27.86%	30.65%	94.05%	95.45%
±3σ	-42.49%	45.28%	100.00%	99.73%

Descriptive Statistics

Mean	1.394%
Standard Error	1.596%
Median	0.931%
Mode	-34.296%
Standard Deviation	14.629%
Sample Variance	214.006%
Kurtosis	0.01
Skewness	0.23
Range	71.072%
Minimum	-34.296%
Maximum	36.776%
Count	84

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.573%	43	51.19%	6.436%
Negative	-10.329%	41	48.81%	-5.042%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.24. Further, an Excess Kurtosis of 1.23 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -80.57%	0	0.00%	0.00%
-80.57% to -60.08%	0	0.00%	0.00%
-60.08% to -39.60%	0	0.00%	0.00%
-39.60% to -19.11%	5	17.86%	17.86%
-19.11% to 1.37%	13	46.43%	64.29%
1.37% to 21.86%	4	14.29%	78.57%
21.86% to 42.34%	3	10.71%	89.29%
42.34% to 62.83%	1	3.57%	92.86%
62.83% to 83.31%	2	7.14%	100.00%
Greater than 83.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.94%	28.68%	78.57%	68.27%
±2σ	-53.25%	56.00%	92.86%	95.45%
±3σ	-80.57%	83.31%	100.00%	99.73%

Descriptive Statistics

Mean	1.371%
Standard Error	5.162%
Median	-5.643%
Mode	-33.781%
Standard Deviation	27.313%
Sample Variance	746.000%
Kurtosis	1.23
Skewness	1.24
Range	105.697%
Minimum	-33.781%
Maximum	71.916%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.790%	10	35.71%	10.639%
Negative	-14.417%	18	64.29%	-9.268%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	39.44%
12	3 Years	35.05%
20	5 Years	36.17%
40	10 Years	42.74%
80	20 Years	42.74%
200	50 Years	42.74%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.20. Further, an Excess Kurtosis of 5.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.32%	0	0.00%	0.00%
-39.32% to -15.61%	0	0.00%	0.00%
-15.61% to 8.11%	0	0.00%	0.00%
8.11% to 31.82%	5	17.24%	17.24%
31.82% to 55.53%	15	51.72%	68.97%
55.53% to 79.25%	5	17.24%	86.21%
79.25% to 102.96%	1	3.45%	89.66%
102.96% to 126.67%	2	6.90%	96.55%
126.67% to 150.39%	0	0.00%	96.55%
Greater than 150.39%	1	3.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.91%	87.15%	86.21%	68.27%
±2σ	-7.70%	118.77%	96.55%	95.45%
±3σ	-39.32%	150.39%	96.55%	99.73%

Descriptive Statistics

Mean	55.532%
Standard Error	5.871%
Median	49.806%
Mode	24.060%
Standard Deviation	31.618%
Sample Variance	999.701%
Kurtosis	5.56
Skewness	2.20
Range	145.742%
Minimum	24.060%
Maximum	169.802%
Count	29

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	55.532%	29	100.00%	55.532%
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 0.07. Further, an Excess Kurtosis of -0.36 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -70.97%	0	0.00%	0.00%
-70.97% to -52.34%	0	0.00%	0.00%
-52.34% to -33.72%	2	6.90%	6.90%
-33.72% to -15.10%	5	17.24%	24.14%
-15.10% to 3.52%	6	20.69%	44.83%
3.52% to 22.15%	10	34.48%	79.31%
22.15% to 40.77%	3	10.34%	89.66%
40.77% to 59.40%	3	10.34%	100.00%
59.40% to 78.02%	0	0.00%	100.00%
Greater than 78.02%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.31%	28.36%	68.97%	68.27%
±2σ	-46.14%	53.19%	100.00%	95.45%
±3σ	-70.97%	78.02%	100.00%	99.73%

Descriptive Statistics

Mean	3.525%
Standard Error	4.611%
Median	5.544%
Mode	-41.761%
Standard Deviation	24.831%
Sample Variance	616.581%
Kurtosis	-0.36
Skewness	0.07
Range	92.371%
Minimum	-41.761%
Maximum	50.610%
Count	29

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.093%	17	58.62%	11.779%
Negative	-19.946%	12	41.38%	-8.253%
Zero	0.000%	0	0.00%	0.000%

PINS Deep Analytical Report