ENVA - 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	3.27%	3.13%	3.01%	3.45%	2.70%	3.24%	141.45	149.31	137.68	153.41
Weekly	7.25%	7.81%	7.23%	8.27%	5.95%	7.13%	136.93	154.25	129.02	163.71
Monthly	14.46%	17.71%	14.95%	18.95%	12.39%	14.85%	128.39	164.51	113.42	186.21
Quarterly	25.38%	38.90%	30.27%	34.09%	21.47%	25.72%	117.25	180.13	94.60	223.26
Annual	—	—	—	—	42.93%	51.44%	94.60	223.26	61.58	342.98
Option Time Horizon	—	—	—	—	20.35%	24.38%	118.57	178.13	96.74	218.33

Calculation Notes: Computed at 2026-02-22T14:24 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $145.33 | Strike (K): $150.00 (first OTM call ≥ spot) | Observed Mid-Price: $10.4000 (Bid $8.6000 / Ask $12.2000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 42.93% (CRR binomial tree, American, n=20 steps) | BS IV: 43.36% (European Black-Scholes) | Yahoo IV (Annual): 51.44% → 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 -0.41. Further, an Excess Kurtosis of 16.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.71%	18	0.64%	0.64%
-9.71% to -7.25%	20	0.71%	1.34%
-7.25% to -4.80%	79	2.79%	4.13%
-4.80% to -2.34%	308	10.88%	15.01%
-2.34% to 0.11%	1009	35.63%	50.64%
0.11% to 2.57%	979	34.57%	85.20%
2.57% to 5.03%	301	10.63%	95.83%
5.03% to 7.48%	70	2.47%	98.31%
7.48% to 9.94%	21	0.74%	99.05%
Greater than 9.94%	27	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.16%	3.39%	81.32%	68.27%
±2σ	-6.44%	6.66%	95.80%	95.45%
±3σ	-9.71%	9.94%	98.41%	99.73%

Descriptive Statistics

Mean	0.114%
Standard Error	0.062%
Median	0.068%
Mode	0.000%
Standard Deviation	3.275%
Sample Variance	10.728%
Kurtosis	16.52
Skewness	-0.41
Range	65.146%
Minimum	-37.934%
Maximum	27.212%
Count	2832

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.219%	1440	50.85%	1.128%
Negative	-2.146%	1338	47.25%	-1.014%
Zero	0.000%	54	1.91%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.37%
20	1 Month	4.42%
60	1 Quarter	3.57%
250	1 Year	3.58%
750	3 Years	3.20%
1,250	5 Years	3.45%
2,500	10 Years	4.03%
5,000	20 Years	4.13%
12,500	50 Years	4.13%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.66. Further, an Excess Kurtosis of 86.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.37%	0	0.00%	0.00%
-5.37% to -3.02%	0	0.00%	0.00%
-3.02% to -0.68%	0	0.00%	0.00%
-0.68% to 1.67%	180	6.35%	6.35%
1.67% to 4.02%	1684	59.44%	65.80%
4.02% to 6.37%	645	22.77%	88.56%
6.37% to 8.72%	191	6.74%	95.31%
8.72% to 11.06%	63	2.22%	97.53%
11.06% to 13.41%	28	0.99%	98.52%
Greater than 13.41%	42	1.48%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.89%	7.15%	91.49%	68.27%
±2σ	-2.24%	10.28%	96.96%	95.45%
±3σ	-5.37%	13.41%	98.52%	99.73%

Descriptive Statistics

Mean	4.020%
Standard Error	0.059%
Median	3.279%
Mode	3.571%
Standard Deviation	3.131%
Sample Variance	9.804%
Kurtosis	86.92
Skewness	6.66
Range	64.839%
Minimum	0.722%
Maximum	65.561%
Count	2833

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.020%	2833	100.00%	4.020%
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 2.78. Further, an Excess Kurtosis of 39.90 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.99%	17	0.60%	0.60%
-8.99% to -6.74%	14	0.49%	1.09%
-6.74% to -4.48%	83	2.93%	4.02%
-4.48% to -2.22%	299	10.55%	14.58%
-2.22% to 0.03%	1066	37.63%	52.21%
0.03% to 2.29%	955	33.71%	85.92%
2.29% to 4.54%	279	9.85%	95.76%
4.54% to 6.80%	75	2.65%	98.41%
6.80% to 9.05%	25	0.88%	99.29%
Greater than 9.05%	20	0.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.98%	3.04%	81.12%	68.27%
±2σ	-5.98%	6.04%	96.26%	95.45%
±3σ	-8.99%	9.05%	98.69%	99.73%

Descriptive Statistics

Mean	0.031%
Standard Error	0.056%
Median	0.000%
Mode	0.000%
Standard Deviation	3.007%
Sample Variance	9.044%
Kurtosis	39.90
Skewness	2.78
Range	64.655%
Minimum	-17.391%
Maximum	47.264%
Count	2833

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.037%	1364	48.15%	0.981%
Negative	-1.910%	1408	49.70%	-0.949%
Zero	0.000%	61	2.15%	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 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 -21.20%	3	0.51%	0.51%
-21.20% to -15.76%	5	0.85%	1.36%
-15.76% to -10.32%	24	4.08%	5.44%
-10.32% to -4.88%	65	11.05%	16.50%
-4.88% to 0.56%	211	35.88%	52.38%
0.56% to 6.00%	192	32.65%	85.03%
6.00% to 11.44%	56	9.52%	94.56%
11.44% to 16.89%	20	3.40%	97.96%
16.89% to 22.33%	4	0.68%	98.64%
Greater than 22.33%	8	1.36%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.69%	7.82%	77.89%	68.27%
±2σ	-13.95%	15.07%	95.24%	95.45%
±3σ	-21.20%	22.33%	98.13%	99.73%

Descriptive Statistics

Mean	0.562%
Standard Error	0.299%
Median	0.312%
Mode	0.000%
Standard Deviation	7.255%
Sample Variance	52.634%
Kurtosis	5.43
Skewness	0.74
Range	79.205%
Minimum	-32.219%
Maximum	46.986%
Count	588

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.350%	308	52.38%	2.802%
Negative	-4.756%	277	47.11%	-2.241%
Zero	0.000%	3	0.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.77%
12	1 Quarter	8.95%
52	1 Year	8.75%
156	3 Years	7.76%
260	5 Years	8.27%
520	10 Years	9.60%
1,040	20 Years	9.82%
2,600	50 Years	9.82%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.30. Further, an Excess Kurtosis of 16.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.96%	0	0.00%	0.00%
-12.96% to -7.10%	0	0.00%	0.00%
-7.10% to -1.24%	0	0.00%	0.00%
-1.24% to 4.61%	56	9.51%	9.51%
4.61% to 10.47%	340	57.72%	67.23%
10.47% to 16.33%	122	20.71%	87.95%
16.33% to 22.18%	31	5.26%	93.21%
22.18% to 28.04%	19	3.23%	96.43%
28.04% to 33.90%	9	1.53%	97.96%
Greater than 33.90%	12	2.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.66%	18.28%	89.47%	68.27%
±2σ	-5.15%	26.09%	95.59%	95.45%
±3σ	-12.96%	33.90%	97.96%	99.73%

Descriptive Statistics

Mean	10.470%
Standard Error	0.322%
Median	8.462%
Mode	3.717%
Standard Deviation	7.809%
Sample Variance	60.987%
Kurtosis	16.77
Skewness	3.30
Range	78.133%
Minimum	1.841%
Maximum	79.974%
Count	589

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.470%	589	100.00%	10.470%
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 0.81. Further, an Excess Kurtosis of 5.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.67%	4	0.68%	0.68%
-21.67% to -16.25%	6	1.02%	1.70%
-16.25% to -10.83%	17	2.89%	4.58%
-10.83% to -5.40%	71	12.05%	16.64%
-5.40% to 0.02%	211	35.82%	52.46%
0.02% to 5.44%	187	31.75%	84.21%
5.44% to 10.86%	53	9.00%	93.21%
10.86% to 16.28%	28	4.75%	97.96%
16.28% to 21.70%	5	0.85%	98.81%
Greater than 21.70%	7	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.21%	7.25%	77.25%	68.27%
±2σ	-14.44%	14.48%	95.59%	95.45%
±3σ	-21.67%	21.71%	98.13%	99.73%

Descriptive Statistics

Mean	0.018%
Standard Error	0.298%
Median	-0.351%
Mode	-4.693%
Standard Deviation	7.229%
Sample Variance	52.262%
Kurtosis	5.25
Skewness	0.81
Range	75.460%
Minimum	-28.711%
Maximum	46.749%
Count	589

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.326%	280	47.54%	2.532%
Negative	-4.823%	307	52.12%	-2.514%
Zero	0.000%	2	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.20. 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 -40.98%	1	0.74%	0.74%
-40.98% to -30.13%	0	0.00%	0.74%
-30.13% to -19.29%	6	4.44%	5.19%
-19.29% to -8.45%	22	16.30%	21.48%
-8.45% to 2.40%	44	32.59%	54.07%
2.40% to 13.24%	33	24.44%	78.52%
13.24% to 24.09%	21	15.56%	94.07%
24.09% to 34.93%	4	2.96%	97.04%
34.93% to 45.78%	4	2.96%	100.00%
Greater than 45.78%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.06%	16.86%	67.41%	68.27%
±2σ	-26.52%	31.32%	94.07%	95.45%
±3σ	-40.98%	45.78%	99.26%	99.73%

Descriptive Statistics

Mean	2.399%
Standard Error	1.244%
Median	1.099%
Mode	-42.154%
Standard Deviation	14.459%
Sample Variance	209.076%
Kurtosis	0.36
Skewness	0.20
Range	81.774%
Minimum	-42.154%
Maximum	39.620%
Count	135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.627%	73	54.07%	6.828%
Negative	-9.802%	61	45.19%	-4.429%
Zero	0.000%	1	0.74%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.24%
12	1 Year	18.71%
36	3 Years	18.41%
60	5 Years	18.95%
120	10 Years	21.74%
240	20 Years	22.04%
600	50 Years	22.04%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.21. Further, an Excess Kurtosis of 27.41 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.45%	0	0.00%	0.00%
-27.45% to -14.17%	0	0.00%	0.00%
-14.17% to -0.88%	0	0.00%	0.00%
-0.88% to 12.40%	12	8.82%	8.82%
12.40% to 25.68%	75	55.15%	63.97%
25.68% to 38.97%	34	25.00%	88.97%
38.97% to 52.25%	9	6.62%	95.59%
52.25% to 65.53%	1	0.74%	96.32%
65.53% to 78.82%	3	2.21%	98.53%
Greater than 78.82%	2	1.47%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.97%	43.39%	91.91%	68.27%
±2σ	-9.74%	61.10%	95.59%	95.45%
±3σ	-27.45%	78.82%	98.53%	99.73%

Descriptive Statistics

Mean	25.683%
Standard Error	1.519%
Median	21.846%
Mode	8.571%
Standard Deviation	17.711%
Sample Variance	313.663%
Kurtosis	27.41
Skewness	4.21
Range	154.694%
Minimum	8.571%
Maximum	163.265%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.683%	136	100.00%	25.683%
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 1.09. Further, an Excess Kurtosis of 3.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.84%	0	0.00%	0.00%
-44.84% to -33.63%	0	0.00%	0.00%
-33.63% to -22.42%	6	4.41%	4.41%
-22.42% to -11.21%	25	18.38%	22.79%
-11.21% to 0.01%	41	30.15%	52.94%
0.01% to 11.22%	39	28.68%	81.62%
11.22% to 22.43%	16	11.76%	93.38%
22.43% to 33.65%	6	4.41%	97.79%
33.65% to 44.86%	2	1.47%	99.26%
Greater than 44.86%	1	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.94%	14.96%	71.32%	68.27%
±2σ	-29.89%	29.91%	96.32%	95.45%
±3σ	-44.84%	44.86%	99.26%	99.73%

Descriptive Statistics

Mean	0.008%
Standard Error	1.282%
Median	-0.890%
Mode	0.000%
Standard Deviation	14.951%
Sample Variance	223.520%
Kurtosis	3.54
Skewness	1.09
Range	101.628%
Minimum	-28.490%
Maximum	73.138%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.805%	64	47.06%	5.555%
Negative	-10.778%	70	51.47%	-5.548%
Zero	0.000%	2	1.47%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.17. Further, an Excess Kurtosis of 0.28 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.43%	0	0.00%	0.00%
-68.43% to -49.40%	1	2.22%	2.22%
-49.40% to -30.36%	1	2.22%	4.44%
-30.36% to -11.33%	6	13.33%	17.78%
-11.33% to 7.71%	19	42.22%	60.00%
7.71% to 26.74%	9	20.00%	80.00%
26.74% to 45.77%	4	8.89%	88.89%
45.77% to 64.81%	5	11.11%	100.00%
64.81% to 83.84%	0	0.00%	100.00%
Greater than 83.84%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.67%	33.08%	68.89%	68.27%
±2σ	-43.05%	58.46%	95.56%	95.45%
±3σ	-68.43%	83.84%	100.00%	99.73%

Descriptive Statistics

Mean	7.705%
Standard Error	3.783%
Median	2.414%
Mode	-57.154%
Standard Deviation	25.378%
Sample Variance	644.036%
Kurtosis	0.28
Skewness	0.17
Range	120.841%
Minimum	-57.154%
Maximum	63.687%
Count	45

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.276%	27	60.00%	13.366%
Negative	-14.152%	18	40.00%	-5.661%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.39%
12	3 Years	36.05%
20	5 Years	34.09%
40	10 Years	38.75%
80	20 Years	39.88%
200	50 Years	39.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.95. Further, an Excess Kurtosis of 10.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.94%	0	0.00%	0.00%
-63.94% to -34.77%	0	0.00%	0.00%
-34.77% to -5.60%	0	0.00%	0.00%
-5.60% to 23.58%	5	10.87%	10.87%
23.58% to 52.75%	27	58.70%	69.57%
52.75% to 81.93%	8	17.39%	86.96%
81.93% to 111.10%	4	8.70%	95.65%
111.10% to 140.28%	0	0.00%	95.65%
140.28% to 169.45%	0	0.00%	95.65%
Greater than 169.45%	2	4.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.85%	91.65%	93.48%	68.27%
±2σ	-25.05%	130.55%	95.65%	95.45%
±3σ	-63.94%	169.45%	95.65%	99.73%

Descriptive Statistics

Mean	52.753%
Standard Error	5.735%
Median	41.060%
Mode	16.524%
Standard Deviation	38.899%
Sample Variance	1513.164%
Kurtosis	10.27
Skewness	2.95
Range	205.797%
Minimum	16.524%
Maximum	222.321%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.753%	46	100.00%	52.753%
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 2.21. Further, an Excess Kurtosis of 7.71 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -90.63%	0	0.00%	0.00%
-90.63% to -67.93%	0	0.00%	0.00%
-67.93% to -45.23%	0	0.00%	0.00%
-45.23% to -22.53%	8	17.39%	17.39%
-22.53% to 0.17%	19	41.30%	58.70%
0.17% to 22.87%	13	28.26%	86.96%
22.87% to 45.57%	3	6.52%	93.48%
45.57% to 68.27%	2	4.35%	97.83%
68.27% to 90.97%	0	0.00%	97.83%
Greater than 90.97%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.10%	30.44%	76.09%	68.27%
±2σ	-60.37%	60.71%	95.65%	95.45%
±3σ	-90.63%	90.98%	97.83%	99.73%

Descriptive Statistics

Mean	0.171%
Standard Error	4.463%
Median	-3.278%
Mode	-38.908%
Standard Deviation	30.268%
Sample Variance	916.164%
Kurtosis	7.71
Skewness	2.21
Range	172.660%
Minimum	-38.908%
Maximum	133.752%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.729%	19	41.30%	9.801%
Negative	-17.039%	26	56.52%	-9.631%
Zero	0.000%	1	2.17%	0.000%

ENVA Deep Analytical Report