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%	4.22%	3.71%	3.73%	5.96	6.42	5.74	6.66
Weekly	7.31%	6.61%	7.19%	9.88%	8.17%	8.21%	5.70	6.71	5.25	7.28
Monthly	13.37%	14.30%	13.78%	21.53%	17.00%	17.08%	5.22	7.33	4.40	8.69
Quarterly	20.83%	29.85%	23.46%	39.64%	29.44%	29.59%	4.61	8.30	3.43	11.15
Annual	—	—	—	—	58.89%	59.18%	3.43	11.15	1.90	20.08
Option Time Horizon	—	—	—	—	22.23%	22.34%	4.95	7.72	3.97	9.65

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $6.18 | Strike (K): $7.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.2750 (Bid $0.2500 / Ask $0.3000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 58.89% (CRR binomial tree, American, n=20 steps) | BS IV: 59.12% (European Black-Scholes) | Yahoo IV (Annual): 59.18% → 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 10.19 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	0.72%	1.58%
-7.16% to -4.75%	137	2.68%	4.26%
-4.75% to -2.34%	608	11.89%	16.15%
-2.34% to 0.07%	1740	34.02%	50.18%
0.07% to 2.47%	1736	33.95%	84.12%
2.47% to 4.88%	578	11.30%	95.42%
4.88% to 7.29%	152	2.97%	98.40%
7.29% to 9.70%	43	0.84%	99.24%
Greater than 9.70%	39	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.15%	3.28%	78.88%	68.27%
±2σ	-6.36%	6.49%	95.60%	95.45%
±3σ	-9.57%	9.70%	98.38%	99.73%

Descriptive Statistics

Mean	0.065%
Standard Error	0.045%
Median	0.056%
Mode	0.000%
Standard Deviation	3.212%
Sample Variance	10.314%
Kurtosis	10.19
Skewness	0.12
Range	53.451%
Minimum	-25.743%
Maximum	27.708%
Count	5114

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.219%	2583	50.51%	1.121%
Negative	-2.176%	2481	48.51%	-1.056%
Zero	0.000%	50	0.98%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.88%
20	1 Month	4.84%
60	1 Quarter	5.50%
250	1 Year	4.69%
750	3 Years	4.13%
1,250	5 Years	4.22%
2,500	10 Years	4.08%
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 3.01. Further, an Excess Kurtosis of 17.40 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.72%	0	0.00%	0.00%
-3.72% to -1.81%	0	0.00%	0.00%
-1.81% to 0.11%	0	0.00%	0.00%
0.11% to 2.02%	799	15.62%	15.62%
2.02% to 3.94%	2444	47.78%	63.40%
3.94% to 5.86%	1148	22.44%	85.85%
5.86% to 7.77%	383	7.49%	93.33%
7.77% to 9.69%	164	3.21%	96.54%
9.69% to 11.61%	75	1.47%	98.01%
Greater than 11.61%	102	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.39%	6.50%	85.81%	68.27%
±2σ	-1.17%	9.05%	95.82%	95.45%
±3σ	-3.72%	11.61%	98.01%	99.73%

Descriptive Statistics

Mean	3.941%
Standard Error	0.036%
Median	3.276%
Mode	1.868%
Standard Deviation	2.555%
Sample Variance	6.529%
Kurtosis	17.40
Skewness	3.01
Range	38.469%
Minimum	0.666%
Maximum	39.135%
Count	5115

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.941%	5115	100.00%	3.941%
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 9.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.02%	28	0.55%	0.55%
-8.02% to -5.99%	43	0.84%	1.39%
-5.99% to -3.96%	167	3.26%	4.65%
-3.96% to -1.93%	655	12.81%	17.46%
-1.93% to 0.10%	1777	34.74%	52.20%
0.10% to 2.13%	1563	30.56%	82.76%
2.13% to 4.16%	602	11.77%	94.53%
4.16% to 6.19%	175	3.42%	97.95%
6.19% to 8.22%	58	1.13%	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%	77.01%	68.27%
±2σ	-5.32%	5.51%	95.35%	95.45%
±3σ	-8.02%	8.22%	98.53%	99.73%

Descriptive Statistics

Mean	0.097%
Standard Error	0.038%
Median	0.000%
Mode	0.000%
Standard Deviation	2.707%
Sample Variance	7.329%
Kurtosis	9.19
Skewness	0.68
Range	52.404%
Minimum	-17.737%
Maximum	34.667%
Count	5115

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.036%	2519	49.25%	1.003%
Negative	-1.824%	2540	49.66%	-0.906%
Zero	0.000%	56	1.09%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.09. Further, an Excess Kurtosis of 3.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.59%	10	0.94%	0.94%
-21.59% to -16.11%	10	0.94%	1.89%
-16.11% to -10.63%	42	3.96%	5.84%
-10.63% to -5.15%	118	11.12%	16.97%
-5.15% to 0.33%	350	32.99%	49.95%
0.33% to 5.81%	363	34.21%	84.17%
5.81% to 11.29%	113	10.65%	94.82%
11.29% to 16.77%	32	3.02%	97.83%
16.77% to 22.25%	10	0.94%	98.77%
Greater than 22.25%	13	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.98%	7.64%	78.51%	68.27%
±2σ	-14.28%	14.94%	94.44%	95.45%
±3σ	-21.59%	22.25%	97.83%	99.73%

Descriptive Statistics

Mean	0.330%
Standard Error	0.224%
Median	0.333%
Mode	-1.280%
Standard Deviation	7.307%
Sample Variance	53.394%
Kurtosis	3.77
Skewness	0.09
Range	75.248%
Minimum	-37.976%
Maximum	37.272%
Count	1061

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.230%	553	52.12%	2.726%
Negative	-5.035%	505	47.60%	-2.397%
Zero	0.000%	3	0.28%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.07%
12	1 Quarter	13.37%
52	1 Year	10.51%
156	3 Years	9.47%
260	5 Years	9.88%
520	10 Years	9.74%
1,040	20 Years	9.69%
2,600	50 Years	9.77%

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 -9.63%	0	0.00%	0.00%
-9.63% to -4.68%	0	0.00%	0.00%
-4.68% to 0.28%	0	0.00%	0.00%
0.28% to 5.23%	178	16.76%	16.76%
5.23% to 10.19%	511	48.12%	64.88%
10.19% to 15.14%	209	19.68%	84.56%
15.14% to 20.10%	93	8.76%	93.31%
20.10% to 25.05%	26	2.45%	95.76%
25.05% to 30.01%	20	1.88%	97.65%
Greater than 30.01%	25	2.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.58%	16.79%	85.69%	68.27%
±2σ	-3.02%	23.40%	95.01%	95.45%
±3σ	-9.63%	30.01%	97.65%	99.73%

Descriptive Statistics

Mean	10.188%
Standard Error	0.203%
Median	8.319%
Mode	6.686%
Standard Deviation	6.606%
Sample Variance	43.633%
Kurtosis	12.08
Skewness	2.68
Range	67.128%
Minimum	1.804%
Maximum	68.932%
Count	1062

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.188%	1062	100.00%	10.188%
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 9.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.25%	3	0.28%	0.28%
-21.25% to -15.86%	8	0.75%	1.04%
-15.86% to -10.47%	34	3.20%	4.24%
-10.47% to -5.08%	129	12.15%	16.38%
-5.08% to 0.32%	396	37.29%	53.67%
0.32% to 5.71%	329	30.98%	84.65%
5.71% to 11.10%	103	9.70%	94.35%
11.10% to 16.49%	35	3.30%	97.65%
16.49% to 21.88%	12	1.13%	98.78%
Greater than 21.88%	13	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.87%	7.50%	79.47%	68.27%
±2σ	-14.06%	14.69%	95.20%	95.45%
±3σ	-21.25%	21.88%	98.49%	99.73%

Descriptive Statistics

Mean	0.315%
Standard Error	0.221%
Median	-0.184%
Mode	0.000%
Standard Deviation	7.187%
Sample Variance	51.648%
Kurtosis	9.24
Skewness	1.48
Range	86.116%
Minimum	-26.352%
Maximum	59.764%
Count	1062

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.353%	516	48.59%	2.601%
Negative	-4.486%	541	50.94%	-2.285%
Zero	0.000%	5	0.47%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.47. Further, an Excess Kurtosis of 2.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.91%	0	0.00%	0.00%
-38.91% to -28.88%	4	1.64%	1.64%
-28.88% to -18.85%	14	5.74%	7.38%
-18.85% to -8.83%	26	10.66%	18.03%
-8.83% to 1.20%	78	31.97%	50.00%
1.20% to 11.23%	71	29.10%	79.10%
11.23% to 21.25%	39	15.98%	95.08%
21.25% to 31.28%	8	3.28%	98.36%
31.28% to 41.31%	2	0.82%	99.18%
Greater than 41.31%	2	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.17%	14.57%	74.59%	68.27%
±2σ	-25.54%	27.94%	95.49%	95.45%
±3σ	-38.91%	41.31%	99.18%	99.73%

Descriptive Statistics

Mean	1.199%
Standard Error	0.856%
Median	1.169%
Mode	-35.095%
Standard Deviation	13.369%
Sample Variance	178.742%
Kurtosis	2.69
Skewness	0.47
Range	105.286%
Minimum	-35.095%
Maximum	70.191%
Count	244

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.693%	130	53.28%	5.697%
Negative	-9.712%	113	46.31%	-4.498%
Zero	0.000%	1	0.41%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	29.31%
12	1 Year	22.12%
36	3 Years	20.61%
60	5 Years	21.53%
120	10 Years	21.50%
240	20 Years	20.74%
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 2.08. Further, an Excess Kurtosis of 6.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.63%	0	0.00%	0.00%
-18.63% to -7.90%	0	0.00%	0.00%
-7.90% to 2.83%	0	0.00%	0.00%
2.83% to 13.55%	43	17.55%	17.55%
13.55% to 24.28%	107	43.67%	61.22%
24.28% to 35.00%	50	20.41%	81.63%
35.00% to 45.73%	28	11.43%	93.06%
45.73% to 56.45%	8	3.27%	96.33%
56.45% to 67.18%	4	1.63%	97.96%
Greater than 67.18%	5	2.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.97%	38.58%	81.63%	68.27%
±2σ	-4.33%	52.88%	95.92%	95.45%
±3σ	-18.63%	67.18%	97.96%	99.73%

Descriptive Statistics

Mean	24.276%
Standard Error	0.914%
Median	19.956%
Mode	4.649%
Standard Deviation	14.301%
Sample Variance	204.508%
Kurtosis	6.09
Skewness	2.08
Range	94.354%
Minimum	4.649%
Maximum	99.003%
Count	245

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	24.276%	245	100.00%	24.276%
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 0.88. Further, an Excess Kurtosis of 1.76 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.56%	0	0.00%	0.00%
-40.56% to -30.22%	2	0.82%	0.82%
-30.22% to -19.88%	3	1.22%	2.04%
-19.88% to -9.55%	47	19.18%	21.22%
-9.55% to 0.79%	85	34.69%	55.92%
0.79% to 11.13%	65	26.53%	82.45%
11.13% to 21.46%	25	10.20%	92.65%
21.46% to 31.80%	10	4.08%	96.73%
31.80% to 42.14%	5	2.04%	98.78%
Greater than 42.14%	3	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.99%	14.57%	73.88%	68.27%
±2σ	-26.78%	28.36%	94.29%	95.45%
±3σ	-40.56%	42.14%	98.78%	99.73%

Descriptive Statistics

Mean	0.790%
Standard Error	0.881%
Median	-0.765%
Mode	-40.355%
Standard Deviation	13.783%
Sample Variance	189.980%
Kurtosis	1.76
Skewness	0.88
Range	96.272%
Minimum	-40.355%
Maximum	55.917%
Count	245

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.812%	115	46.94%	5.544%
Negative	-8.961%	130	53.06%	-4.755%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.03. Further, an Excess Kurtosis of 0.30 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.01%	0	0.00%	0.00%
-60.01% to -44.39%	1	1.23%	1.23%
-44.39% to -28.77%	7	8.64%	9.88%
-28.77% to -13.15%	8	9.88%	19.75%
-13.15% to 2.47%	25	30.86%	50.62%
2.47% to 18.09%	23	28.40%	79.01%
18.09% to 33.71%	13	16.05%	95.06%
33.71% to 49.33%	3	3.70%	98.77%
49.33% to 64.95%	0	0.00%	98.77%
Greater than 64.95%	1	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.36%	23.29%	69.14%	68.27%
±2σ	-39.19%	44.12%	96.30%	95.45%
±3σ	-60.01%	64.95%	98.77%	99.73%

Descriptive Statistics

Mean	2.467%
Standard Error	2.314%
Median	1.368%
Mode	-48.365%
Standard Deviation	20.827%
Sample Variance	433.750%
Kurtosis	0.30
Skewness	0.03
Range	114.674%
Minimum	-48.365%
Maximum	66.309%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.840%	43	53.09%	9.471%
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	40.12%
12	3 Years	37.09%
20	5 Years	39.64%
40	10 Years	38.16%
80	20 Years	36.81%
200	50 Years	36.82%

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 -41.19%	0	0.00%	0.00%
-41.19% to -18.80%	0	0.00%	0.00%
-18.80% to 3.59%	0	0.00%	0.00%
3.59% to 25.98%	13	15.85%	15.85%
25.98% to 48.37%	36	43.90%	59.76%
48.37% to 70.76%	24	29.27%	89.02%
70.76% to 93.15%	3	3.66%	92.68%
93.15% to 115.53%	3	3.66%	96.34%
115.53% to 137.93%	1	1.22%	97.56%
Greater than 137.93%	2	2.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.51%	78.22%	87.80%	68.27%
±2σ	-11.34%	108.07%	95.12%	95.45%
±3σ	-41.19%	137.93%	97.56%	99.73%

Descriptive Statistics

Mean	48.366%
Standard Error	3.297%
Median	41.645%
Mode	15.742%
Standard Deviation	29.853%
Sample Variance	891.173%
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	48.366%	82	100.00%	48.366%
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 1.37. Further, an Excess Kurtosis of 2.61 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.81%	0	0.00%	0.00%
-68.81% to -51.21%	0	0.00%	0.00%
-51.21% to -33.61%	1	1.22%	1.22%
-33.61% to -16.02%	17	20.73%	21.95%
-16.02% to 1.58%	29	35.37%	57.32%
1.58% to 19.17%	21	25.61%	82.93%
19.17% to 36.77%	5	6.10%	89.02%
36.77% to 54.36%	7	8.54%	97.56%
54.36% to 71.96%	1	1.22%	98.78%
Greater than 71.96%	1	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.88%	25.04%	74.39%	68.27%
±2σ	-45.34%	48.50%	95.12%	95.45%
±3σ	-68.81%	71.96%	98.78%	99.73%

Descriptive Statistics

Mean	1.577%
Standard Error	2.591%
Median	-3.551%
Mode	-38.418%
Standard Deviation	23.461%
Sample Variance	550.396%
Kurtosis	2.61
Skewness	1.37
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	-14.350%	45	54.88%	-7.875%
Zero	0.000%	0	0.00%	0.000%

UAA Deep Analytical Report