ENPH - 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	5.04%	4.04%	4.33%	5.77%	5.08%	5.12%	39.60	43.83	37.64	46.11
Weekly	11.56%	10.94%	11.72%	13.91%	11.17%	11.27%	37.26	46.58	33.32	52.09
Monthly	23.89%	25.25%	22.42%	29.37%	23.26%	23.47%	33.01	52.57	26.16	66.34
Quarterly	44.61%	37.60%	38.50%	51.89%	40.29%	40.65%	27.85	62.33	18.61	93.25
Annual	—	—	—	—	80.57%	81.30%	18.61	93.25	8.32	208.72
Option Time Horizon	—	—	—	—	30.41%	30.69%	30.74	56.47	22.68	76.54

Calculation Notes: Computed at 2026-03-23T16:40 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $41.66 | Strike (K): $45.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.8750 (Bid $3.7500 / Ask $4.0000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 80.57% (CRR binomial tree, American, n=20 steps) | BS IV: 81.53% (European Black-Scholes) | Yahoo IV (Annual): 81.30% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.58. Further, an Excess Kurtosis of 8.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.95%	21	0.60%	0.60%
-14.95% to -11.16%	22	0.63%	1.22%
-11.16% to -7.38%	119	3.39%	4.61%
-7.38% to -3.60%	431	12.27%	16.88%
-3.60% to 0.17%	1224	34.84%	51.72%
0.17% to 3.96%	1113	31.68%	83.40%
3.96% to 7.74%	415	11.81%	95.22%
7.74% to 11.52%	97	2.76%	97.98%
11.52% to 15.29%	34	0.97%	98.95%
Greater than 15.29%	37	1.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.87%	5.21%	78.62%	68.27%
±2σ	-9.90%	10.26%	95.96%	95.45%
±3σ	-14.95%	15.30%	98.35%	99.73%

Descriptive Statistics

Mean	0.175%
Standard Error	0.085%
Median	0.000%
Mode	0.000%
Standard Deviation	5.040%
Sample Variance	25.398%
Kurtosis	8.47
Skewness	0.58
Range	79.811%
Minimum	-37.366%
Maximum	42.445%
Count	3513

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.683%	1735	49.39%	1.819%
Negative	-3.380%	1708	48.62%	-1.643%
Zero	0.000%	70	1.99%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	6.67%
20	1 Month	6.35%
60	1 Quarter	6.47%
250	1 Year	6.20%
750	3 Years	5.58%
1,250	5 Years	5.77%
2,500	10 Years	6.60%
5,000	20 Years	6.88%
12,500	50 Years	6.88%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.21. Further, an Excess Kurtosis of 21.33 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 -2.32%	0	0.00%	0.00%
-2.32% to 0.71%	0	0.00%	0.00%
0.71% to 3.74%	609	17.33%	17.33%
3.74% to 6.77%	1588	45.19%	62.52%
6.77% to 9.80%	795	22.62%	85.15%
9.80% to 12.83%	305	8.68%	93.82%
12.83% to 15.86%	108	3.07%	96.90%
15.86% to 18.89%	50	1.42%	98.32%
Greater than 18.89%	59	1.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.73%	10.81%	84.86%	68.27%
±2σ	-1.31%	14.85%	96.16%	95.45%
±3σ	-5.35%	18.89%	98.32%	99.73%

Descriptive Statistics

Mean	6.772%
Standard Error	0.068%
Median	5.854%
Mode	4.000%
Standard Deviation	4.040%
Sample Variance	16.319%
Kurtosis	21.33
Skewness	3.21
Range	56.122%
Minimum	0.840%
Maximum	56.962%
Count	3514

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.772%	3514	100.00%	6.772%
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 0.65. Further, an Excess Kurtosis of 5.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.78%	17	0.48%	0.48%
-12.78% to -9.54%	27	0.77%	1.25%
-9.54% to -6.29%	135	3.84%	5.09%
-6.29% to -3.05%	483	13.75%	18.84%
-3.05% to 0.20%	1147	32.64%	51.48%
0.20% to 3.44%	1064	30.28%	81.76%
3.44% to 6.69%	429	12.21%	93.97%
6.69% to 9.94%	143	4.07%	98.04%
9.94% to 13.18%	49	1.39%	99.43%
Greater than 13.18%	20	0.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.13%	4.53%	75.01%	68.27%
±2σ	-8.46%	8.85%	95.25%	95.45%
±3σ	-12.78%	13.18%	98.95%	99.73%

Descriptive Statistics

Mean	0.199%
Standard Error	0.073%
Median	0.064%
Mode	0.000%
Standard Deviation	4.327%
Sample Variance	18.725%
Kurtosis	5.64
Skewness	0.65
Range	55.965%
Minimum	-20.420%
Maximum	35.545%
Count	3514

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.307%	1768	50.31%	1.664%
Negative	-3.086%	1668	47.47%	-1.465%
Zero	0.000%	78	2.22%	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 2.63 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.80%	4	0.55%	0.55%
-33.80% to -25.13%	7	0.96%	1.51%
-25.13% to -16.46%	27	3.70%	5.21%
-16.46% to -7.79%	99	13.58%	18.79%
-7.79% to 0.89%	235	32.24%	51.03%
0.89% to 9.56%	228	31.28%	82.30%
9.56% to 18.23%	91	12.48%	94.79%
18.23% to 26.91%	17	2.33%	97.12%
26.91% to 35.58%	15	2.06%	99.18%
Greater than 35.58%	6	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.68%	12.45%	76.41%	68.27%
±2σ	-22.24%	24.02%	94.51%	95.45%
±3σ	-33.80%	35.58%	98.63%	99.73%

Descriptive Statistics

Mean	0.887%
Standard Error	0.428%
Median	0.650%
Mode	0.000%
Standard Deviation	11.564%
Sample Variance	133.731%
Kurtosis	2.63
Skewness	0.49
Range	100.815%
Minimum	-39.828%
Maximum	60.987%
Count	729

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.939%	381	52.26%	4.672%
Negative	-8.044%	343	47.05%	-3.785%
Zero	0.000%	5	0.69%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.00%
12	1 Quarter	17.10%
52	1 Year	14.72%
156	3 Years	13.38%
260	5 Years	13.91%
520	10 Years	15.71%
1,040	20 Years	16.13%
2,600	50 Years	16.13%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.74. Further, an Excess Kurtosis of 12.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.18%	0	0.00%	0.00%
-15.18% to -6.97%	0	0.00%	0.00%
-6.97% to 1.23%	0	0.00%	0.00%
1.23% to 9.44%	117	16.03%	16.03%
9.44% to 17.64%	343	46.99%	63.01%
17.64% to 25.85%	160	21.92%	84.93%
25.85% to 34.05%	56	7.67%	92.60%
34.05% to 42.26%	26	3.56%	96.16%
42.26% to 50.46%	18	2.47%	98.63%
Greater than 50.46%	10	1.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.70%	28.58%	85.48%	68.27%
±2σ	-4.24%	39.52%	95.21%	95.45%
±3σ	-15.18%	50.46%	98.63%	99.73%

Descriptive Statistics

Mean	17.642%
Standard Error	0.405%
Median	14.438%
Mode	7.955%
Standard Deviation	10.940%
Sample Variance	119.678%
Kurtosis	12.91
Skewness	2.74
Range	99.709%
Minimum	3.911%
Maximum	103.620%
Count	730

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.642%	730	100.00%	17.642%
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 4.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.56%	2	0.27%	0.27%
-34.56% to -25.77%	5	0.68%	0.96%
-25.77% to -16.98%	26	3.56%	4.52%
-16.98% to -8.19%	101	13.84%	18.36%
-8.19% to 0.60%	260	35.62%	53.97%
0.60% to 9.39%	206	28.22%	82.19%
9.39% to 18.18%	90	12.33%	94.52%
18.18% to 26.97%	21	2.88%	97.40%
26.97% to 35.76%	10	1.37%	98.77%
Greater than 35.76%	9	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.12%	12.32%	77.26%	68.27%
±2σ	-22.84%	24.04%	94.38%	95.45%
±3σ	-34.56%	35.76%	98.49%	99.73%

Descriptive Statistics

Mean	0.596%
Standard Error	0.434%
Median	-0.056%
Mode	0.000%
Standard Deviation	11.720%
Sample Variance	137.353%
Kurtosis	4.76
Skewness	1.09
Range	109.129%
Minimum	-37.326%
Maximum	71.803%
Count	730

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.121%	357	48.90%	4.461%
Negative	-7.709%	366	50.14%	-3.865%
Zero	0.000%	7	0.96%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.11. Further, an Excess Kurtosis of 2.49 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.11%	0	0.00%	0.00%
-68.11% to -50.19%	1	0.60%	0.60%
-50.19% to -32.27%	4	2.38%	2.98%
-32.27% to -14.35%	30	17.86%	20.83%
-14.35% to 3.56%	63	37.50%	58.33%
3.56% to 21.48%	40	23.81%	82.14%
21.48% to 39.40%	18	10.71%	92.86%
39.40% to 57.32%	9	5.36%	98.21%
57.32% to 75.24%	1	0.60%	98.81%
Greater than 75.24%	2	1.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.33%	27.46%	73.81%	68.27%
±2σ	-44.22%	51.35%	95.24%	95.45%
±3σ	-68.11%	75.24%	98.81%	99.73%

Descriptive Statistics

Mean	3.565%
Standard Error	1.843%
Median	-0.817%
Mode	-53.611%
Standard Deviation	23.892%
Sample Variance	570.812%
Kurtosis	2.49
Skewness	1.11
Range	163.791%
Minimum	-53.611%
Maximum	110.180%
Count	168

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.124%	81	48.21%	10.667%
Negative	-13.874%	86	51.19%	-7.102%
Zero	0.000%	1	0.59%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	33.61%
12	1 Year	29.40%
36	3 Years	28.65%
60	5 Years	29.37%
120	10 Years	35.72%
240	20 Years	36.19%
600	50 Years	36.19%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.49. Further, an Excess Kurtosis of 9.05 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.23%	0	0.00%	0.00%
-32.23% to -13.29%	0	0.00%	0.00%
-13.29% to 5.65%	0	0.00%	0.00%
5.65% to 24.58%	28	16.57%	16.57%
24.58% to 43.52%	71	42.01%	58.58%
43.52% to 62.46%	47	27.81%	86.39%
62.46% to 81.39%	12	7.10%	93.49%
81.39% to 100.33%	7	4.14%	97.63%
100.33% to 119.27%	0	0.00%	97.63%
Greater than 119.27%	4	2.37%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	18.27%	68.77%	83.43%	68.27%
±2σ	-6.98%	94.02%	96.45%	95.45%
±3σ	-32.23%	119.27%	97.63%	99.73%

Descriptive Statistics

Mean	43.521%
Standard Error	1.942%
Median	37.179%
Mode	29.188%
Standard Deviation	25.249%
Sample Variance	637.520%
Kurtosis	9.05
Skewness	2.49
Range	164.239%
Minimum	10.307%
Maximum	174.546%
Count	169

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.521%	169	100.00%	43.521%
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 3.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -65.50%	0	0.00%	0.00%
-65.50% to -48.69%	1	0.59%	0.59%
-48.69% to -31.87%	9	5.33%	5.92%
-31.87% to -15.06%	28	16.57%	22.49%
-15.06% to 1.76%	47	27.81%	50.30%
1.76% to 18.58%	49	28.99%	79.29%
18.58% to 35.39%	25	14.79%	94.08%
35.39% to 52.21%	6	3.55%	97.63%
52.21% to 69.03%	3	1.78%	99.41%
Greater than 69.03%	1	0.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.66%	24.18%	72.78%	68.27%
±2σ	-43.08%	46.61%	95.86%	95.45%
±3σ	-65.51%	69.03%	99.41%	99.73%

Descriptive Statistics

Mean	1.761%
Standard Error	1.725%
Median	1.087%
Mode	-52.422%
Standard Deviation	22.422%
Sample Variance	502.730%
Kurtosis	3.35
Skewness	0.87
Range	168.590%
Minimum	-52.422%
Maximum	116.168%
Count	169

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.979%	88	52.07%	9.362%
Negative	-16.057%	80	47.34%	-7.601%
Zero	0.000%	1	0.59%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.17. Further, an Excess Kurtosis of 2.26 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -122.81%	0	0.00%	0.00%
-122.81% to -89.35%	0	0.00%	0.00%
-89.35% to -55.89%	0	0.00%	0.00%
-55.89% to -22.43%	17	30.36%	30.36%
-22.43% to 11.03%	15	26.79%	57.14%
11.03% to 44.49%	12	21.43%	78.57%
44.49% to 77.95%	8	14.29%	92.86%
77.95% to 111.42%	3	5.36%	98.21%
111.42% to 144.88%	0	0.00%	98.21%
Greater than 144.88%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.58%	55.65%	73.21%	68.27%
±2σ	-78.19%	100.26%	98.21%	95.45%
±3σ	-122.81%	144.88%	98.21%	99.73%

Descriptive Statistics

Mean	11.034%
Standard Error	5.962%
Median	3.008%
Mode	-52.983%
Standard Deviation	44.614%
Sample Variance	1990.390%
Kurtosis	2.26
Skewness	1.17
Range	233.361%
Minimum	-52.983%
Maximum	180.378%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.406%	31	55.36%	22.921%
Negative	-26.627%	25	44.64%	-11.887%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	47.05%
12	3 Years	47.06%
20	5 Years	51.89%
40	10 Years	69.20%
80	20 Years	66.92%
200	50 Years	66.92%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.67. Further, an Excess Kurtosis of 0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.51%	0	0.00%	0.00%
-25.51% to 2.69%	0	0.00%	0.00%
2.69% to 30.89%	2	3.51%	3.51%
30.89% to 59.09%	11	19.30%	22.81%
59.09% to 87.29%	18	31.58%	54.39%
87.29% to 115.50%	14	24.56%	78.95%
115.50% to 143.70%	7	12.28%	91.23%
143.70% to 171.90%	2	3.51%	94.74%
171.90% to 200.10%	3	5.26%	100.00%
Greater than 200.10%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	49.69%	124.90%	70.18%	68.27%
±2σ	12.09%	162.50%	94.74%	95.45%
±3σ	-25.51%	200.10%	100.00%	99.73%

Descriptive Statistics

Mean	87.294%
Standard Error	4.980%
Median	84.802%
Mode	24.471%
Standard Deviation	37.602%
Sample Variance	1413.904%
Kurtosis	0.03
Skewness	0.67
Range	154.529%
Minimum	24.471%
Maximum	179.000%
Count	57

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	87.294%	57	100.00%	87.294%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.61. Further, an Excess Kurtosis of -0.23 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -111.35%	0	0.00%	0.00%
-111.35% to -82.47%	0	0.00%	0.00%
-82.47% to -53.60%	1	1.75%	1.75%
-53.60% to -24.73%	17	29.82%	31.58%
-24.73% to 4.15%	14	24.56%	56.14%
4.15% to 33.02%	9	15.79%	71.93%
33.02% to 61.90%	11	19.30%	91.23%
61.90% to 90.78%	4	7.02%	98.25%
90.78% to 119.65%	1	1.75%	100.00%
Greater than 119.65%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-34.35%	42.65%	70.18%	68.27%
±2σ	-72.85%	81.15%	96.49%	95.45%
±3σ	-111.35%	119.65%	100.00%	99.73%

Descriptive Statistics

Mean	4.150%
Standard Error	5.099%
Median	-1.987%
Mode	-56.306%
Standard Deviation	38.500%
Sample Variance	1482.238%
Kurtosis	-0.23
Skewness	0.61
Range	165.951%
Minimum	-56.306%
Maximum	109.645%
Count	57

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	38.964%	26	45.61%	17.773%
Negative	-25.048%	31	54.39%	-13.623%
Zero	0.000%	0	0.00%	0.000%

ENPH Deep Analytical Report