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%	3.12%	3.00%	3.44%	3.42%	3.45%	133.63	143.11	129.14	148.09
Weekly	7.24%	7.79%	7.22%	8.19%	7.54%	7.60%	128.25	149.12	118.94	160.79
Monthly	14.44%	17.70%	14.93%	18.64%	15.69%	15.83%	118.21	161.79	101.04	189.27
Quarterly	25.45%	38.77%	30.32%	34.41%	27.18%	27.41%	105.38	181.48	80.30	238.16
Annual	—	—	—	—	54.36%	54.82%	80.30	238.16	46.63	410.14
Option Time Horizon	—	—	—	—	20.52%	20.69%	112.64	169.78	91.74	208.45

Calculation Notes: Computed at 2026-03-23T16:41 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $138.29 | Strike (K): $140.00 (first OTM call ≥ spot) | Observed Mid-Price: $10.8500 (Bid $10.3000 / Ask $11.4000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 54.36% (CRR binomial tree, American, n=20 steps) | BS IV: 54.30% (European Black-Scholes) | Yahoo IV (Annual): 54.82% → 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 16.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.70%	18	0.63%	0.63%
-9.70% to -7.25%	20	0.70%	1.33%
-7.25% to -4.80%	81	2.84%	4.17%
-4.80% to -2.34%	310	10.87%	15.04%
-2.34% to 0.11%	1015	35.58%	50.61%
0.11% to 2.57%	987	34.60%	85.21%
2.57% to 5.02%	304	10.66%	95.86%
5.02% to 7.47%	70	2.45%	98.32%
7.47% to 9.93%	21	0.74%	99.05%
Greater than 9.93%	27	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.16%	3.38%	81.32%	68.27%
±2σ	-6.43%	6.66%	95.79%	95.45%
±3σ	-9.70%	9.93%	98.42%	99.73%

Descriptive Statistics

Mean	0.112%
Standard Error	0.061%
Median	0.070%
Mode	0.000%
Standard Deviation	3.272%
Sample Variance	10.705%
Kurtosis	16.47
Skewness	-0.41
Range	65.146%
Minimum	-37.934%
Maximum	27.212%
Count	2853

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.216%	1451	50.86%	1.127%
Negative	-2.148%	1348	47.25%	-1.015%
Zero	0.000%	54	1.89%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.21%
20	1 Month	4.04%
60	1 Quarter	3.88%
250	1 Year	3.60%
750	3 Years	3.20%
1,250	5 Years	3.44%
2,500	10 Years	4.01%
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 6.67. Further, an Excess Kurtosis of 87.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.35%	0	0.00%	0.00%
-5.35% to -3.00%	0	0.00%	0.00%
-3.00% to -0.66%	0	0.00%	0.00%
-0.66% to 1.68%	181	6.34%	6.34%
1.68% to 4.02%	1694	59.36%	65.70%
4.02% to 6.36%	652	22.85%	88.54%
6.36% to 8.70%	194	6.80%	95.34%
8.70% to 11.04%	63	2.21%	97.55%
11.04% to 13.38%	27	0.95%	98.49%
Greater than 13.38%	43	1.51%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.90%	7.14%	91.56%	68.27%
±2σ	-2.22%	10.26%	96.95%	95.45%
±3σ	-5.35%	13.38%	98.49%	99.73%

Descriptive Statistics

Mean	4.019%
Standard Error	0.058%
Median	3.279%
Mode	3.571%
Standard Deviation	3.122%
Sample Variance	9.747%
Kurtosis	87.31
Skewness	6.67
Range	64.839%
Minimum	0.722%
Maximum	65.561%
Count	2854

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.019%	2854	100.00%	4.019%
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 2.77. Further, an Excess Kurtosis of 39.82 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.98%	17	0.60%	0.60%
-8.98% to -6.73%	14	0.49%	1.09%
-6.73% to -4.47%	83	2.91%	3.99%
-4.47% to -2.22%	303	10.62%	14.61%
-2.22% to 0.03%	1074	37.63%	52.24%
0.03% to 2.28%	960	33.64%	85.88%
2.28% to 4.53%	282	9.88%	95.76%
4.53% to 6.79%	76	2.66%	98.42%
6.79% to 9.04%	25	0.88%	99.30%
Greater than 9.04%	20	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.97%	3.03%	81.11%	68.27%
±2σ	-5.98%	6.04%	96.25%	95.45%
±3σ	-8.98%	9.04%	98.70%	99.73%

Descriptive Statistics

Mean	0.030%
Standard Error	0.056%
Median	0.000%
Mode	0.000%
Standard Deviation	3.003%
Sample Variance	9.020%
Kurtosis	39.82
Skewness	2.77
Range	64.655%
Minimum	-17.391%
Maximum	47.264%
Count	2854

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.038%	1372	48.07%	0.980%
Negative	-1.908%	1421	49.79%	-0.950%
Zero	0.000%	61	2.14%	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 -21.18%	3	0.51%	0.51%
-21.18% to -15.75%	5	0.84%	1.35%
-15.75% to -10.31%	24	4.05%	5.41%
-10.31% to -4.88%	66	11.15%	16.55%
-4.88% to 0.55%	211	35.64%	52.20%
0.55% to 5.98%	194	32.77%	84.97%
5.98% to 11.42%	57	9.63%	94.59%
11.42% to 16.85%	20	3.38%	97.97%
16.85% to 22.28%	4	0.68%	98.65%
Greater than 22.28%	8	1.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.69%	7.79%	77.87%	68.27%
±2σ	-13.94%	15.04%	95.27%	95.45%
±3σ	-21.18%	22.28%	98.14%	99.73%

Descriptive Statistics

Mean	0.551%
Standard Error	0.298%
Median	0.311%
Mode	0.000%
Standard Deviation	7.244%
Sample Variance	52.478%
Kurtosis	5.43
Skewness	0.74
Range	79.205%
Minimum	-32.219%
Maximum	46.986%
Count	592

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.340%	310	52.37%	2.796%
Negative	-4.763%	279	47.13%	-2.245%
Zero	0.000%	3	0.51%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.81%
12	1 Quarter	8.85%
52	1 Year	8.68%
156	3 Years	7.76%
260	5 Years	8.19%
520	10 Years	9.56%
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 3.31. Further, an Excess Kurtosis of 16.87 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.90%	0	0.00%	0.00%
-12.90% to -7.06%	0	0.00%	0.00%
-7.06% to -1.22%	0	0.00%	0.00%
-1.22% to 4.62%	57	9.61%	9.61%
4.62% to 10.46%	341	57.50%	67.12%
10.46% to 16.30%	124	20.91%	88.03%
16.30% to 22.14%	31	5.23%	93.25%
22.14% to 27.98%	19	3.20%	96.46%
27.98% to 33.82%	9	1.52%	97.98%
Greater than 33.82%	12	2.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.68%	18.25%	89.54%	68.27%
±2σ	-5.11%	26.04%	95.45%	95.45%
±3σ	-12.90%	33.82%	97.98%	99.73%

Descriptive Statistics

Mean	10.463%
Standard Error	0.320%
Median	8.489%
Mode	3.717%
Standard Deviation	7.787%
Sample Variance	60.632%
Kurtosis	16.87
Skewness	3.31
Range	78.133%
Minimum	1.841%
Maximum	79.974%
Count	593

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.463%	593	100.00%	10.463%
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 5.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.63%	4	0.67%	0.67%
-21.63% to -16.22%	6	1.01%	1.69%
-16.22% to -10.81%	17	2.87%	4.55%
-10.81% to -5.39%	71	11.97%	16.53%
-5.39% to 0.02%	215	36.26%	52.78%
0.02% to 5.44%	186	31.37%	84.15%
5.44% to 10.85%	53	8.94%	93.09%
10.85% to 16.27%	29	4.89%	97.98%
16.27% to 21.68%	5	0.84%	98.82%
Greater than 21.68%	7	1.18%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.20%	7.24%	77.23%	68.27%
±2σ	-14.42%	14.46%	95.62%	95.45%
±3σ	-21.63%	21.68%	98.15%	99.73%

Descriptive Statistics

Mean	0.023%
Standard Error	0.296%
Median	-0.361%
Mode	-4.693%
Standard Deviation	7.219%
Sample Variance	52.117%
Kurtosis	5.24
Skewness	0.81
Range	75.460%
Minimum	-28.711%
Maximum	46.749%
Count	593

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.343%	281	47.39%	2.532%
Negative	-4.799%	310	52.28%	-2.509%
Zero	0.000%	2	0.34%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.21. Further, an Excess Kurtosis of 0.37 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.96%	1	0.74%	0.74%
-40.96% to -30.13%	0	0.00%	0.74%
-30.13% to -19.30%	6	4.41%	5.15%
-19.30% to -8.47%	22	16.18%	21.32%
-8.47% to 2.35%	44	32.35%	53.68%
2.35% to 13.18%	33	24.26%	77.94%
13.18% to 24.01%	22	16.18%	94.12%
24.01% to 34.84%	4	2.94%	97.06%
34.84% to 45.67%	4	2.94%	100.00%
Greater than 45.67%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.09%	16.79%	66.91%	68.27%
±2σ	-26.52%	31.23%	94.12%	95.45%
±3σ	-40.96%	45.67%	99.26%	99.73%

Descriptive Statistics

Mean	2.354%
Standard Error	1.238%
Median	1.036%
Mode	0.000%
Standard Deviation	14.439%
Sample Variance	208.487%
Kurtosis	0.37
Skewness	0.21
Range	81.774%
Minimum	-42.154%
Maximum	39.620%
Count	136

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.627%	73	53.68%	6.778%
Negative	-9.864%	61	44.85%	-4.424%
Zero	0.000%	2	1.47%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	15.03%
12	1 Year	18.45%
36	3 Years	18.26%
60	5 Years	18.64%
120	10 Years	21.65%
240	20 Years	21.99%
600	50 Years	21.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.19. Further, an Excess Kurtosis of 27.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.48%	0	0.00%	0.00%
-27.48% to -14.20%	0	0.00%	0.00%
-14.20% to -0.93%	0	0.00%	0.00%
-0.93% to 12.35%	12	8.76%	8.76%
12.35% to 25.62%	74	54.01%	62.77%
25.62% to 38.89%	36	26.28%	89.05%
38.89% to 52.17%	9	6.57%	95.62%
52.17% to 65.44%	1	0.73%	96.35%
65.44% to 78.72%	3	2.19%	98.54%
Greater than 78.72%	2	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	7.92%	43.32%	91.97%	68.27%
±2σ	-9.78%	61.02%	95.62%	95.45%
±3σ	-27.48%	78.72%	98.54%	99.73%

Descriptive Statistics

Mean	25.620%
Standard Error	1.512%
Median	21.595%
Mode	8.571%
Standard Deviation	17.699%
Sample Variance	313.245%
Kurtosis	27.32
Skewness	4.19
Range	154.694%
Minimum	8.571%
Maximum	163.265%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.620%	137	100.00%	25.620%
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 1.08. Further, an Excess Kurtosis of 3.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.77%	0	0.00%	0.00%
-44.77% to -33.57%	0	0.00%	0.00%
-33.57% to -22.37%	6	4.38%	4.38%
-22.37% to -11.17%	25	18.25%	22.63%
-11.17% to 0.03%	42	30.66%	53.28%
0.03% to 11.23%	39	28.47%	81.75%
11.23% to 22.43%	16	11.68%	93.43%
22.43% to 33.63%	6	4.38%	97.81%
33.63% to 44.83%	2	1.46%	99.27%
Greater than 44.83%	1	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.91%	14.96%	70.80%	68.27%
±2σ	-29.84%	29.89%	96.35%	95.45%
±3σ	-44.77%	44.83%	99.27%	99.73%

Descriptive Statistics

Mean	0.027%
Standard Error	1.276%
Median	-1.045%
Mode	0.000%
Standard Deviation	14.934%
Sample Variance	223.017%
Kurtosis	3.52
Skewness	1.08
Range	101.628%
Minimum	-28.490%
Maximum	73.138%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.884%	64	46.72%	5.552%
Negative	-10.660%	71	51.83%	-5.525%
Zero	0.000%	2	1.46%	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 0.25 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.73%	0	0.00%	0.00%
-68.73% to -49.65%	1	2.22%	2.22%
-49.65% to -30.56%	1	2.22%	4.44%
-30.56% to -11.47%	6	13.33%	17.78%
-11.47% to 7.62%	19	42.22%	60.00%
7.62% to 26.71%	9	20.00%	80.00%
26.71% to 45.80%	4	8.89%	88.89%
45.80% to 64.89%	5	11.11%	100.00%
64.89% to 83.97%	0	0.00%	100.00%
Greater than 83.97%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.83%	33.07%	68.89%	68.27%
±2σ	-43.28%	58.52%	95.56%	95.45%
±3σ	-68.73%	83.97%	100.00%	99.73%

Descriptive Statistics

Mean	7.620%
Standard Error	3.794%
Median	2.414%
Mode	-57.154%
Standard Deviation	25.451%
Sample Variance	647.764%
Kurtosis	0.25
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	-14.363%	18	40.00%	-5.745%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	32.95%
12	3 Years	36.57%
20	5 Years	34.41%
40	10 Years	38.90%
80	20 Years	40.02%
200	50 Years	40.02%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.97. Further, an Excess Kurtosis of 10.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.34%	0	0.00%	0.00%
-63.34% to -34.26%	0	0.00%	0.00%
-34.26% to -5.19%	0	0.00%	0.00%
-5.19% to 23.89%	5	10.87%	10.87%
23.89% to 52.96%	27	58.70%	69.57%
52.96% to 82.03%	8	17.39%	86.96%
82.03% to 111.11%	4	8.70%	95.65%
111.11% to 140.18%	0	0.00%	95.65%
140.18% to 169.26%	0	0.00%	95.65%
Greater than 169.26%	2	4.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.19%	91.73%	93.48%	68.27%
±2σ	-24.57%	130.49%	95.65%	95.45%
±3σ	-63.34%	169.26%	95.65%	99.73%

Descriptive Statistics

Mean	52.960%
Standard Error	5.716%
Median	41.059%
Mode	16.524%
Standard Deviation	38.766%
Sample Variance	1502.825%
Kurtosis	10.39
Skewness	2.97
Range	205.797%
Minimum	16.524%
Maximum	222.321%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	52.960%	46	100.00%	52.960%
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 2.19. Further, an Excess Kurtosis of 7.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -90.69%	0	0.00%	0.00%
-90.69% to -67.94%	0	0.00%	0.00%
-67.94% to -45.20%	0	0.00%	0.00%
-45.20% to -22.46%	8	17.39%	17.39%
-22.46% to 0.28%	19	41.30%	58.70%
0.28% to 23.02%	13	28.26%	86.96%
23.02% to 45.76%	3	6.52%	93.48%
45.76% to 68.51%	2	4.35%	97.83%
68.51% to 91.25%	0	0.00%	97.83%
Greater than 91.25%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-30.04%	30.60%	76.09%	68.27%
±2σ	-60.36%	60.92%	95.65%	95.45%
±3σ	-90.68%	91.25%	97.83%	99.73%

Descriptive Statistics

Mean	0.281%
Standard Error	4.471%
Median	-3.279%
Mode	-38.908%
Standard Deviation	30.322%
Sample Variance	919.435%
Kurtosis	7.59
Skewness	2.19
Range	172.660%
Minimum	-38.908%
Maximum	133.752%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.996%	19	41.30%	9.911%
Negative	-17.039%	26	56.52%	-9.631%
Zero	0.000%	1	2.17%	0.000%

ENVA Deep Analytical Report