UAA - 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	3.21%	2.56%	2.71%	4.21%	2.99%	3.32%	7.90	8.39	7.67	8.64
Weekly	7.32%	6.61%	7.20%	9.86%	6.59%	7.31%	7.62	8.69	7.14	9.29
Monthly	13.44%	14.33%	13.81%	21.44%	13.71%	15.22%	7.10	9.34	6.19	10.71
Quarterly	21.08%	29.86%	23.64%	39.56%	23.74%	26.37%	6.42	10.32	5.06	13.09
Annual	—	—	—	—	47.49%	52.73%	5.06	13.09	3.15	21.04
Option Time Horizon	—	—	—	—	18.27%	20.28%	6.78	9.77	5.65	11.73

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $8.14 | Strike (K): $9.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.3000 (Bid $0.2500 / Ask $0.3500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 47.49% (CRR binomial tree, American, n=20 steps) | BS IV: 47.63% (European Black-Scholes) | Yahoo IV (Annual): 52.73% → 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 Fairly Symmetrical with a Skewness factor of 0.12. Further, an Excess Kurtosis of 10.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.57%	44	0.86%	0.86%
-9.57% to -7.16%	37	0.73%	1.59%
-7.16% to -4.75%	136	2.67%	4.26%
-4.75% to -2.34%	604	11.86%	16.12%
-2.34% to 0.07%	1731	33.99%	50.11%
0.07% to 2.48%	1739	34.14%	84.25%
2.48% to 4.89%	571	11.21%	95.46%
4.89% to 7.30%	149	2.93%	98.39%
7.30% to 9.71%	43	0.84%	99.23%
Greater than 9.71%	39	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.14%	3.28%	78.83%	68.27%
±2σ	-6.36%	6.50%	95.60%	95.45%
±3σ	-9.57%	9.71%	98.37%	99.73%

Descriptive Statistics

Mean	0.070%
Standard Error	0.045%
Median	0.059%
Mode	0.000%
Standard Deviation	3.213%
Sample Variance	10.322%
Kurtosis	10.22
Skewness	0.12
Range	53.451%
Minimum	-25.743%
Maximum	27.708%
Count	5093

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.219%	2578	50.62%	1.123%
Negative	-2.175%	2465	48.40%	-1.053%
Zero	0.000%	50	0.98%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.71%
20	1 Month	6.17%
60	1 Quarter	4.97%
250	1 Year	4.64%
750	3 Years	4.11%
1,250	5 Years	4.21%
2,500	10 Years	4.06%
5,000	20 Years	4.08%
12,500	50 Years	4.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.02. Further, an Excess Kurtosis of 17.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.74%	0	0.00%	0.00%
-3.74% to -1.82%	0	0.00%	0.00%
-1.82% to 0.10%	0	0.00%	0.00%
0.10% to 2.02%	790	15.51%	15.51%
2.02% to 3.94%	2448	48.06%	63.56%
3.94% to 5.86%	1136	22.30%	85.87%
5.86% to 7.78%	379	7.44%	93.31%
7.78% to 9.70%	164	3.22%	96.53%
9.70% to 11.62%	75	1.47%	98.00%
Greater than 11.62%	102	2.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.38%	6.50%	85.92%	68.27%
±2σ	-1.18%	9.06%	95.80%	95.45%
±3σ	-3.74%	11.62%	98.00%	99.73%

Descriptive Statistics

Mean	3.938%
Standard Error	0.036%
Median	3.271%
Mode	1.868%
Standard Deviation	2.559%
Sample Variance	6.547%
Kurtosis	17.38
Skewness	3.02
Range	38.469%
Minimum	0.666%
Maximum	39.135%
Count	5094

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.938%	5094	100.00%	3.938%
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 0.68. Further, an Excess Kurtosis of 9.22 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%	28	0.55%	0.55%
-8.03% to -6.00%	43	0.84%	1.39%
-6.00% to -3.97%	164	3.22%	4.61%
-3.97% to -1.94%	649	12.74%	17.35%
-1.94% to 0.10%	1777	34.88%	52.24%
0.10% to 2.13%	1554	30.51%	82.74%
2.13% to 4.16%	600	11.78%	94.52%
4.16% to 6.19%	174	3.42%	97.94%
6.19% to 8.22%	58	1.14%	99.08%
Greater than 8.22%	47	0.92%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.61%	2.80%	77.03%	68.27%
±2σ	-5.32%	5.51%	95.37%	95.45%
±3σ	-8.03%	8.22%	98.53%	99.73%

Descriptive Statistics

Mean	0.096%
Standard Error	0.038%
Median	0.000%
Mode	0.000%
Standard Deviation	2.708%
Sample Variance	7.333%
Kurtosis	9.22
Skewness	0.68
Range	52.404%
Minimum	-17.737%
Maximum	34.667%
Count	5094

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.036%	2506	49.20%	1.002%
Negative	-1.823%	2532	49.71%	-0.906%
Zero	0.000%	56	1.10%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of 3.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.60%	10	0.95%	0.95%
-21.60% to -16.11%	10	0.95%	1.89%
-16.11% to -10.62%	42	3.97%	5.87%
-10.62% to -5.13%	117	11.07%	16.93%
-5.13% to 0.36%	349	33.02%	49.95%
0.36% to 5.85%	363	34.34%	84.30%
5.85% to 11.34%	111	10.50%	94.80%
11.34% to 16.82%	32	3.03%	97.82%
16.82% to 22.31%	10	0.95%	98.77%
Greater than 22.31%	13	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.96%	7.68%	78.24%	68.27%
±2σ	-14.28%	14.99%	94.42%	95.45%
±3σ	-21.60%	22.31%	97.82%	99.73%

Descriptive Statistics

Mean	0.357%
Standard Error	0.225%
Median	0.386%
Mode	-1.280%
Standard Deviation	7.319%
Sample Variance	53.573%
Kurtosis	3.76
Skewness	0.08
Range	75.248%
Minimum	-37.976%
Maximum	37.272%
Count	1057

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.243%	553	52.32%	2.743%
Negative	-5.035%	501	47.40%	-2.386%
Zero	0.000%	3	0.28%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	16.62%
12	1 Quarter	12.12%
52	1 Year	10.51%
156	3 Years	9.44%
260	5 Years	9.86%
520	10 Years	9.70%
1,040	20 Years	9.69%
2,600	50 Years	9.76%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.68. Further, an Excess Kurtosis of 12.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.66%	0	0.00%	0.00%
-9.66% to -4.70%	0	0.00%	0.00%
-4.70% to 0.26%	0	0.00%	0.00%
0.26% to 5.22%	176	16.64%	16.64%
5.22% to 10.18%	511	48.30%	64.93%
10.18% to 15.14%	208	19.66%	84.59%
15.14% to 20.10%	92	8.70%	93.29%
20.10% to 25.06%	27	2.55%	95.84%
25.06% to 30.02%	19	1.80%	97.64%
Greater than 30.02%	25	2.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.57%	16.80%	85.73%	68.27%
±2σ	-3.04%	23.41%	94.99%	95.45%
±3σ	-9.66%	30.02%	97.64%	99.73%

Descriptive Statistics

Mean	10.182%
Standard Error	0.203%
Median	8.305%
Mode	6.686%
Standard Deviation	6.613%
Sample Variance	43.735%
Kurtosis	12.08
Skewness	2.68
Range	67.128%
Minimum	1.804%
Maximum	68.932%
Count	1058

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.182%	1058	100.00%	10.182%
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 1.48. Further, an Excess Kurtosis of 9.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.31%	3	0.28%	0.28%
-21.31% to -15.91%	8	0.76%	1.04%
-15.91% to -10.51%	34	3.21%	4.25%
-10.51% to -5.11%	128	12.10%	16.35%
-5.11% to 0.30%	396	37.43%	53.78%
0.30% to 5.70%	327	30.91%	84.69%
5.70% to 11.10%	102	9.64%	94.33%
11.10% to 16.50%	35	3.31%	97.64%
16.50% to 21.90%	12	1.13%	98.77%
Greater than 21.90%	13	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.91%	7.50%	79.30%	68.27%
±2σ	-14.11%	14.70%	95.18%	95.45%
±3σ	-21.31%	21.90%	98.49%	99.73%

Descriptive Statistics

Mean	0.297%
Standard Error	0.221%
Median	-0.198%
Mode	0.000%
Standard Deviation	7.202%
Sample Variance	51.870%
Kurtosis	9.20
Skewness	1.48
Range	86.116%
Minimum	-26.352%
Maximum	59.764%
Count	1058

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.365%	512	48.39%	2.596%
Negative	-4.497%	541	51.13%	-2.299%
Zero	0.000%	5	0.47%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.49. Further, an Excess Kurtosis of 2.67 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.99%	0	0.00%	0.00%
-38.99% to -28.91%	4	1.65%	1.65%
-28.91% to -18.84%	14	5.76%	7.41%
-18.84% to -8.76%	27	11.11%	18.52%
-8.76% to 1.32%	80	32.92%	51.44%
1.32% to 11.40%	68	27.98%	79.42%
11.40% to 21.48%	37	15.23%	94.65%
21.48% to 31.55%	8	3.29%	97.94%
31.55% to 41.63%	3	1.23%	99.18%
Greater than 41.63%	2	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.12%	14.76%	75.31%	68.27%
±2σ	-25.55%	28.19%	95.06%	95.45%
±3σ	-38.99%	41.63%	99.18%	99.73%

Descriptive Statistics

Mean	1.320%
Standard Error	0.862%
Median	1.230%
Mode	-35.095%
Standard Deviation	13.437%
Sample Variance	180.561%
Kurtosis	2.67
Skewness	0.49
Range	105.286%
Minimum	-35.095%
Maximum	70.191%
Count	243

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.782%	130	53.50%	5.768%
Negative	-9.650%	112	46.09%	-4.448%
Zero	0.000%	1	0.41%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	28.91%
12	1 Year	21.97%
36	3 Years	20.62%
60	5 Years	21.44%
120	10 Years	21.39%
240	20 Years	20.79%
600	50 Years	21.11%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.07. Further, an Excess Kurtosis of 6.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.72%	0	0.00%	0.00%
-18.72% to -7.97%	0	0.00%	0.00%
-7.97% to 2.77%	0	0.00%	0.00%
2.77% to 13.52%	43	17.62%	17.62%
13.52% to 24.27%	107	43.85%	61.48%
24.27% to 35.02%	49	20.08%	81.56%
35.02% to 45.76%	28	11.48%	93.03%
45.76% to 56.51%	8	3.28%	96.31%
56.51% to 67.25%	4	1.64%	97.95%
Greater than 67.25%	5	2.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.94%	38.60%	81.56%	68.27%
±2σ	-4.39%	52.93%	95.90%	95.45%
±3σ	-18.72%	67.25%	97.95%	99.73%

Descriptive Statistics

Mean	24.268%
Standard Error	0.917%
Median	19.901%
Mode	4.649%
Standard Deviation	14.329%
Sample Variance	205.334%
Kurtosis	6.06
Skewness	2.07
Range	94.354%
Minimum	4.649%
Maximum	99.003%
Count	244

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.268%	244	100.00%	24.268%
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 0.87. Further, an Excess Kurtosis of 1.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.76%	0	0.00%	0.00%
-40.76% to -30.39%	2	0.82%	0.82%
-30.39% to -20.03%	4	1.64%	2.46%
-20.03% to -9.67%	44	18.03%	20.49%
-9.67% to 0.69%	86	35.25%	55.74%
0.69% to 11.05%	66	27.05%	82.79%
11.05% to 21.41%	23	9.43%	92.21%
21.41% to 31.77%	11	4.51%	96.72%
31.77% to 42.13%	5	2.05%	98.77%
Greater than 42.13%	3	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.12%	14.50%	73.77%	68.27%
±2σ	-26.94%	28.32%	94.26%	95.45%
±3σ	-40.76%	42.13%	98.77%	99.73%

Descriptive Statistics

Mean	0.690%
Standard Error	0.884%
Median	-0.773%
Mode	-40.355%
Standard Deviation	13.815%
Sample Variance	190.867%
Kurtosis	1.79
Skewness	0.87
Range	96.272%
Minimum	-40.355%
Maximum	55.917%
Count	244

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.759%	114	46.72%	5.494%
Negative	-9.017%	130	53.28%	-4.804%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.01. Further, an Excess Kurtosis of 0.19 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.39%	0	0.00%	0.00%
-60.39% to -44.58%	1	1.23%	1.23%
-44.58% to -28.76%	7	8.64%	9.88%
-28.76% to -12.95%	8	9.88%	19.75%
-12.95% to 2.86%	24	29.63%	49.38%
2.86% to 18.67%	23	28.40%	77.78%
18.67% to 34.48%	15	18.52%	96.30%
34.48% to 50.29%	2	2.47%	98.77%
50.29% to 66.10%	0	0.00%	98.77%
Greater than 66.10%	1	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.22%	23.94%	67.90%	68.27%
±2σ	-39.30%	45.02%	96.30%	95.45%
±3σ	-60.39%	66.10%	98.77%	99.73%

Descriptive Statistics

Mean	2.857%
Standard Error	2.342%
Median	2.868%
Mode	-48.365%
Standard Deviation	21.081%
Sample Variance	444.388%
Kurtosis	0.19
Skewness	0.01
Range	114.674%
Minimum	-48.365%
Maximum	66.309%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.575%	43	53.09%	9.861%
Negative	-15.332%	37	45.68%	-7.004%
Zero	0.000%	1	1.24%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	39.75%
12	3 Years	36.96%
20	5 Years	39.56%
40	10 Years	38.13%
80	20 Years	36.79%
200	50 Years	36.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.58. Further, an Excess Kurtosis of 8.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.24%	0	0.00%	0.00%
-41.24% to -18.85%	0	0.00%	0.00%
-18.85% to 3.55%	0	0.00%	0.00%
3.55% to 25.94%	13	15.85%	15.85%
25.94% to 48.34%	36	43.90%	59.76%
48.34% to 70.74%	24	29.27%	89.02%
70.74% to 93.13%	3	3.66%	92.68%
93.13% to 115.53%	3	3.66%	96.34%
115.53% to 137.92%	1	1.22%	97.56%
Greater than 137.92%	2	2.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.48%	78.20%	87.80%	68.27%
±2σ	-11.38%	108.06%	95.12%	95.45%
±3σ	-41.24%	137.92%	97.56%	99.73%

Descriptive Statistics

Mean	48.340%
Standard Error	3.298%
Median	41.644%
Mode	15.742%
Standard Deviation	29.861%
Sample Variance	891.678%
Kurtosis	8.51
Skewness	2.58
Range	170.591%
Minimum	15.742%
Maximum	186.333%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	48.340%	82	100.00%	48.340%
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 1.35. Further, an Excess Kurtosis of 2.53 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -69.63%	0	0.00%	0.00%
-69.63% to -51.90%	0	0.00%	0.00%
-51.90% to -34.17%	1	1.22%	1.22%
-34.17% to -16.44%	17	20.73%	21.95%
-16.44% to 1.29%	29	35.37%	57.32%
1.29% to 19.02%	21	25.61%	82.93%
19.02% to 36.75%	5	6.10%	89.02%
36.75% to 54.48%	7	8.54%	97.56%
54.48% to 72.21%	1	1.22%	98.78%
Greater than 72.21%	1	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.35%	24.93%	73.17%	68.27%
±2σ	-45.99%	48.57%	95.12%	95.45%
±3σ	-69.63%	72.21%	98.78%	99.73%

Descriptive Statistics

Mean	1.289%
Standard Error	2.611%
Median	-3.610%
Mode	-38.418%
Standard Deviation	23.641%
Sample Variance	558.891%
Kurtosis	2.53
Skewness	1.35
Range	133.524%
Minimum	-38.418%
Maximum	95.106%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.948%	37	45.12%	9.452%
Negative	-14.876%	45	54.88%	-8.164%
Zero	0.000%	0	0.00%	0.000%

UAA Deep Analytical Report