NTRA - 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	3.87%	3.47%	3.37%	4.95%	3.24%	3.34%	205.35	219.11	198.80	226.33
Weekly	8.44%	8.87%	8.54%	11.35%	7.14%	7.35%	197.51	227.81	183.90	244.67
Monthly	18.14%	20.43%	17.40%	23.61%	14.86%	15.31%	182.83	246.10	157.59	285.51
Quarterly	32.29%	34.63%	34.80%	42.90%	25.73%	26.51%	163.99	274.37	126.78	354.89
Annual	—	—	—	—	51.47%	53.03%	126.78	354.89	75.78	593.76
Option Time Horizon	—	—	—	—	19.80%	20.40%	174.02	258.56	142.77	315.16

Calculation Notes: Computed at 2026-02-22T14:23 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $212.12 | Strike (K): $220.00 (first OTM call ≥ spot) | Observed Mid-Price: $14.0500 (Bid $12.5000 / Ask $15.6000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 51.47% (CRR binomial tree, American, n=20 steps) | BS IV: 52.06% (European Black-Scholes) | Yahoo IV (Annual): 53.03% → 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 0.47. Further, an Excess Kurtosis of 11.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.46%	15	0.56%	0.56%
-11.46% to -8.55%	22	0.82%	1.38%
-8.55% to -5.65%	83	3.11%	4.49%
-5.65% to -2.75%	322	12.05%	16.54%
-2.75% to 0.16%	924	34.57%	51.10%
0.16% to 3.06%	870	32.55%	83.65%
3.06% to 5.97%	322	12.05%	95.70%
5.97% to 8.87%	71	2.66%	98.35%
8.87% to 11.78%	17	0.64%	98.99%
Greater than 11.78%	27	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.71%	4.03%	79.12%	68.27%
±2σ	-7.58%	7.90%	95.77%	95.45%
±3σ	-11.46%	11.78%	98.43%	99.73%

Descriptive Statistics

Mean	0.159%
Standard Error	0.075%
Median	0.075%
Mode	0.000%
Standard Deviation	3.872%
Sample Variance	14.989%
Kurtosis	11.41
Skewness	0.47
Range	72.739%
Minimum	-32.785%
Maximum	39.954%
Count	2673

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.752%	1362	50.95%	1.402%
Negative	-2.562%	1297	48.52%	-1.243%
Zero	0.000%	14	0.52%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.93%
20	1 Month	4.15%
60	1 Quarter	3.46%
250	1 Year	3.98%
750	3 Years	4.07%
1,250	5 Years	4.95%
2,500	10 Years	5.14%
5,000	20 Years	5.31%
12,500	50 Years	5.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 5.33. Further, an Excess Kurtosis of 69.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.14%	0	0.00%	0.00%
-5.14% to -2.53%	0	0.00%	0.00%
-2.53% to 0.07%	0	0.00%	0.00%
0.07% to 2.68%	349	13.05%	13.05%
2.68% to 5.29%	1345	50.30%	63.35%
5.29% to 7.89%	637	23.82%	87.17%
7.89% to 10.50%	196	7.33%	94.50%
10.50% to 13.10%	77	2.88%	97.38%
13.10% to 15.71%	25	0.93%	98.32%
Greater than 15.71%	45	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.81%	8.76%	88.59%	68.27%
±2σ	-1.66%	12.23%	96.56%	95.45%
±3σ	-5.14%	15.71%	98.32%	99.73%

Descriptive Statistics

Mean	5.285%
Standard Error	0.067%
Median	4.517%
Mode	2.564%
Standard Deviation	3.474%
Sample Variance	12.069%
Kurtosis	69.95
Skewness	5.33
Range	73.171%
Minimum	1.273%
Maximum	74.444%
Count	2674

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.285%	2674	100.00%	5.285%
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 0.18. Further, an Excess Kurtosis of 5.07 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.15%	20	0.75%	0.75%
-10.15% to -7.62%	26	0.97%	1.72%
-7.62% to -5.09%	71	2.66%	4.38%
-5.09% to -2.56%	374	13.99%	18.36%
-2.56% to -0.03%	860	32.16%	50.52%
-0.03% to 2.49%	849	31.75%	82.27%
2.49% to 5.02%	321	12.00%	94.28%
5.02% to 7.55%	105	3.93%	98.20%
7.55% to 10.08%	31	1.16%	99.36%
Greater than 10.08%	17	0.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.40%	3.34%	76.29%	68.27%
±2σ	-6.78%	6.71%	95.14%	95.45%
±3σ	-10.15%	10.08%	98.62%	99.73%

Descriptive Statistics

Mean	-0.034%
Standard Error	0.065%
Median	-0.076%
Mode	0.000%
Standard Deviation	3.371%
Sample Variance	11.363%
Kurtosis	5.07
Skewness	0.18
Range	48.950%
Minimum	-25.445%
Maximum	23.505%
Count	2674

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.467%	1296	48.47%	1.196%
Negative	-2.422%	1357	50.75%	-1.229%
Zero	0.000%	21	0.79%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.25. Further, an Excess Kurtosis of 3.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.54%	3	0.54%	0.54%
-24.54% to -18.22%	6	1.08%	1.62%
-18.22% to -11.89%	24	4.32%	5.95%
-11.89% to -5.56%	60	10.81%	16.76%
-5.56% to 0.76%	187	33.69%	50.45%
0.76% to 7.09%	171	30.81%	81.26%
7.09% to 13.42%	72	12.97%	94.23%
13.42% to 19.74%	24	4.32%	98.56%
19.74% to 26.07%	3	0.54%	99.10%
Greater than 26.07%	5	0.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.67%	9.20%	74.95%	68.27%
±2σ	-16.11%	17.63%	95.32%	95.45%
±3σ	-24.54%	26.07%	98.56%	99.73%

Descriptive Statistics

Mean	0.763%
Standard Error	0.358%
Median	0.711%
Mode	0.000%
Standard Deviation	8.435%
Sample Variance	71.156%
Kurtosis	3.06
Skewness	0.25
Range	78.044%
Minimum	-33.303%
Maximum	44.741%
Count	555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.393%	297	53.51%	3.421%
Negative	-5.831%	253	45.59%	-2.658%
Zero	0.000%	5	0.90%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.70%
12	1 Quarter	7.84%
52	1 Year	8.84%
156	3 Years	9.32%
260	5 Years	11.35%
520	10 Years	11.79%
1,040	20 Years	12.12%
2,600	50 Years	12.12%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.39. Further, an Excess Kurtosis of 39.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.52%	0	0.00%	0.00%
-13.52% to -6.87%	0	0.00%	0.00%
-6.87% to -0.21%	0	0.00%	0.00%
-0.21% to 6.44%	78	14.03%	14.03%
6.44% to 13.10%	267	48.02%	62.05%
13.10% to 19.75%	132	23.74%	85.79%
19.75% to 26.41%	48	8.63%	94.42%
26.41% to 33.07%	17	3.06%	97.48%
33.07% to 39.72%	5	0.90%	98.38%
Greater than 39.72%	9	1.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.23%	21.97%	88.13%	68.27%
±2σ	-4.65%	30.85%	96.22%	95.45%
±3σ	-13.52%	39.72%	98.38%	99.73%

Descriptive Statistics

Mean	13.100%
Standard Error	0.376%
Median	11.032%
Mode	5.488%
Standard Deviation	8.874%
Sample Variance	78.740%
Kurtosis	39.43
Skewness	4.39
Range	115.967%
Minimum	2.999%
Maximum	118.966%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.100%	556	100.00%	13.100%
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 1.01. Further, an Excess Kurtosis of 4.89 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.68%	2	0.36%	0.36%
-25.68% to -19.28%	4	0.72%	1.08%
-19.28% to -12.88%	20	3.60%	4.68%
-12.88% to -6.47%	75	13.49%	18.17%
-6.47% to -0.07%	198	35.61%	53.78%
-0.07% to 6.33%	169	30.40%	84.17%
6.33% to 12.73%	54	9.71%	93.88%
12.73% to 19.14%	22	3.96%	97.84%
19.14% to 25.54%	6	1.08%	98.92%
Greater than 25.54%	6	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.61%	8.46%	75.72%	68.27%
±2σ	-17.14%	17.00%	94.96%	95.45%
±3σ	-25.68%	25.54%	98.56%	99.73%

Descriptive Statistics

Mean	-0.071%
Standard Error	0.362%
Median	-0.556%
Mode	0.000%
Standard Deviation	8.536%
Sample Variance	72.856%
Kurtosis	4.89
Skewness	1.01
Range	80.942%
Minimum	-30.604%
Maximum	50.338%
Count	556

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.585%	250	44.96%	2.961%
Negative	-5.563%	303	54.50%	-3.032%
Zero	0.000%	3	0.54%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.48. Further, an Excess Kurtosis of 0.33 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -50.92%	0	0.00%	0.00%
-50.92% to -37.32%	1	0.79%	0.79%
-37.32% to -23.71%	6	4.72%	5.51%
-23.71% to -10.10%	22	17.32%	22.83%
-10.10% to 3.51%	37	29.13%	51.97%
3.51% to 17.12%	34	26.77%	78.74%
17.12% to 30.72%	16	12.60%	91.34%
30.72% to 44.33%	9	7.09%	98.43%
44.33% to 57.94%	1	0.79%	99.21%
Greater than 57.94%	1	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.64%	21.65%	73.23%	68.27%
±2σ	-32.78%	39.80%	94.49%	95.45%
±3σ	-50.92%	57.94%	99.21%	99.73%

Descriptive Statistics

Mean	3.508%
Standard Error	1.610%
Median	3.151%
Mode	-38.129%
Standard Deviation	18.144%
Sample Variance	329.201%
Kurtosis	0.33
Skewness	0.48
Range	99.536%
Minimum	-38.129%
Maximum	61.407%
Count	127

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.795%	72	56.69%	8.955%
Negative	-12.809%	54	42.52%	-5.446%
Zero	0.000%	1	0.79%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	14.14%
12	1 Year	18.85%
36	3 Years	20.96%
60	5 Years	23.61%
120	10 Years	26.11%
240	20 Years	26.47%
600	50 Years	26.47%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.56. Further, an Excess Kurtosis of 18.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.87%	0	0.00%	0.00%
-29.87% to -14.55%	0	0.00%	0.00%
-14.55% to 0.77%	0	0.00%	0.00%
0.77% to 16.09%	23	17.97%	17.97%
16.09% to 31.41%	55	42.97%	60.94%
31.41% to 46.73%	35	27.34%	88.28%
46.73% to 62.05%	9	7.03%	95.31%
62.05% to 77.38%	4	3.12%	98.44%
77.38% to 92.70%	0	0.00%	98.44%
Greater than 92.70%	2	1.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.98%	51.84%	90.62%	68.27%
±2σ	-9.44%	72.27%	97.66%	95.45%
±3σ	-29.87%	92.70%	98.44%	99.73%

Descriptive Statistics

Mean	31.412%
Standard Error	1.806%
Median	27.089%
Mode	9.858%
Standard Deviation	20.428%
Sample Variance	417.294%
Kurtosis	18.75
Skewness	3.56
Range	148.954%
Minimum	9.858%
Maximum	158.812%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.412%	128	100.00%	31.412%
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 0.54. Further, an Excess Kurtosis of 0.55 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -52.56%	0	0.00%	0.00%
-52.56% to -39.51%	0	0.00%	0.00%
-39.51% to -26.46%	7	5.47%	5.47%
-26.46% to -13.41%	20	15.62%	21.09%
-13.41% to -0.35%	46	35.94%	57.03%
-0.35% to 12.70%	29	22.66%	79.69%
12.70% to 25.75%	16	12.50%	92.19%
25.75% to 38.80%	8	6.25%	98.44%
38.80% to 51.85%	1	0.78%	99.22%
Greater than 51.85%	1	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.76%	17.05%	71.88%	68.27%
±2σ	-35.16%	34.45%	96.88%	95.45%
±3σ	-52.56%	51.85%	99.22%	99.73%

Descriptive Statistics

Mean	-0.355%
Standard Error	1.538%
Median	-2.962%
Mode	15.807%
Standard Deviation	17.403%
Sample Variance	302.854%
Kurtosis	0.55
Skewness	0.54
Range	98.825%
Minimum	-37.566%
Maximum	61.259%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.520%	55	42.97%	6.669%
Negative	-12.316%	73	57.03%	-7.024%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.39. Further, an Excess Kurtosis of 0.76 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -86.14%	0	0.00%	0.00%
-86.14% to -61.93%	0	0.00%	0.00%
-61.93% to -37.71%	4	9.30%	9.30%
-37.71% to -13.50%	2	4.65%	13.95%
-13.50% to 10.72%	19	44.19%	58.14%
10.72% to 34.94%	7	16.28%	74.42%
34.94% to 59.15%	9	20.93%	95.35%
59.15% to 83.37%	1	2.33%	97.67%
83.37% to 107.58%	1	2.33%	100.00%
Greater than 107.58%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.57%	43.01%	74.42%	68.27%
±2σ	-53.86%	75.29%	95.35%	95.45%
±3σ	-86.14%	107.58%	100.00%	99.73%

Descriptive Statistics

Mean	10.719%
Standard Error	4.924%
Median	5.660%
Mode	-54.395%
Standard Deviation	32.288%
Sample Variance	1042.535%
Kurtosis	0.76
Skewness	0.39
Range	160.684%
Minimum	-54.395%
Maximum	106.289%
Count	43

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.647%	27	62.79%	17.988%
Negative	-19.535%	16	37.21%	-7.269%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	33.35%
12	3 Years	41.14%
20	5 Years	42.90%
40	10 Years	48.47%
80	20 Years	48.87%
200	50 Years	48.87%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.78. Further, an Excess Kurtosis of 3.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.61%	0	0.00%	0.00%
-41.61% to -15.63%	0	0.00%	0.00%
-15.63% to 10.34%	0	0.00%	0.00%
10.34% to 36.32%	8	18.18%	18.18%
36.32% to 62.29%	22	50.00%	68.18%
62.29% to 88.27%	6	13.64%	81.82%
88.27% to 114.25%	4	9.09%	90.91%
114.25% to 140.22%	2	4.55%	95.45%
140.22% to 166.20%	1	2.27%	97.73%
Greater than 166.20%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	27.66%	96.93%	79.55%	68.27%
±2σ	-6.97%	131.56%	93.18%	95.45%
±3σ	-41.61%	166.20%	97.73%	99.73%

Descriptive Statistics

Mean	62.294%
Standard Error	5.221%
Median	51.723%
Mode	21.936%
Standard Deviation	34.634%
Sample Variance	1199.497%
Kurtosis	3.47
Skewness	1.78
Range	164.731%
Minimum	21.936%
Maximum	186.667%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	62.294%	44	100.00%	62.294%
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 1.63. Further, an Excess Kurtosis of 3.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -104.42%	0	0.00%	0.00%
-104.42% to -78.33%	0	0.00%	0.00%
-78.33% to -52.23%	0	0.00%	0.00%
-52.23% to -26.13%	9	20.45%	20.45%
-26.13% to -0.03%	18	40.91%	61.36%
-0.03% to 26.07%	12	27.27%	88.64%
26.07% to 52.17%	0	0.00%	88.64%
52.17% to 78.26%	3	6.82%	95.45%
78.26% to 104.36%	1	2.27%	97.73%
Greater than 104.36%	1	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.83%	34.77%	81.82%	68.27%
±2σ	-69.63%	69.56%	95.45%	95.45%
±3σ	-104.43%	104.36%	97.73%	99.73%

Descriptive Statistics

Mean	-0.031%
Standard Error	5.246%
Median	-3.919%
Mode	-51.611%
Standard Deviation	34.798%
Sample Variance	1210.916%
Kurtosis	3.25
Skewness	1.63
Range	168.702%
Minimum	-51.611%
Maximum	117.091%
Count	44

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	31.180%	17	38.64%	12.047%
Negative	-19.683%	27	61.36%	-12.078%
Zero	0.000%	0	0.00%	0.000%

NTRA Deep Analytical Report