CHWY - 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%	2.92%	3.42%	5.22%	4.10%	4.15%	22.62	24.56	21.72	25.58
Weekly	8.41%	7.15%	8.01%	12.24%	9.02%	9.14%	21.54	25.79	19.68	28.23
Monthly	16.44%	15.84%	15.82%	27.77%	18.77%	19.03%	19.54	28.44	16.19	34.31
Quarterly	30.47%	35.43%	30.25%	49.19%	32.51%	32.96%	17.03	32.62	12.30	45.16
Annual	—	—	—	—	65.01%	65.92%	12.30	45.16	6.42	86.51
Option Time Horizon	—	—	—	—	24.54%	24.88%	18.44	30.13	14.43	38.50

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $23.57 | Strike (K): $25.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.8000 (Bid $1.7000 / Ask $1.9000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 65.01% (CRR binomial tree, American, n=20 steps) | BS IV: 65.80% (European Black-Scholes) | Yahoo IV (Annual): 65.92% → 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 0.64. Further, an Excess Kurtosis of 4.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.55%	7	0.41%	0.41%
-11.55% to -8.65%	15	0.88%	1.29%
-8.65% to -5.75%	66	3.88%	5.17%
-5.75% to -2.85%	228	13.40%	18.58%
-2.85% to 0.05%	562	33.04%	51.62%
0.05% to 2.95%	500	29.39%	81.01%
2.95% to 5.85%	224	13.17%	94.18%
5.85% to 8.75%	62	3.64%	97.82%
8.75% to 11.65%	23	1.35%	99.18%
Greater than 11.65%	14	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.82%	3.92%	75.25%	68.27%
±2σ	-7.68%	7.79%	95.30%	95.45%
±3σ	-11.55%	11.65%	98.77%	99.73%

Descriptive Statistics

Mean	0.051%
Standard Error	0.094%
Median	-0.050%
Mode	0.000%
Standard Deviation	3.867%
Sample Variance	14.955%
Kurtosis	4.11
Skewness	0.64
Range	43.747%
Minimum	-16.603%
Maximum	27.144%
Count	1701

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.928%	834	49.03%	1.436%
Negative	-2.739%	860	50.56%	-1.385%
Zero	0.000%	7	0.41%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.23%
20	1 Month	4.42%
60	1 Quarter	4.31%
250	1 Year	3.92%
750	3 Years	4.58%
1,250	5 Years	5.22%
2,500	10 Years	5.41%
5,000	20 Years	5.41%
12,500	50 Years	5.41%

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 22.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.45%	0	0.00%	0.00%
-3.45% to -1.26%	0	0.00%	0.00%
-1.26% to 0.93%	0	0.00%	0.00%
0.93% to 3.13%	321	18.86%	18.86%
3.13% to 5.32%	729	42.83%	61.69%
5.32% to 7.51%	376	22.09%	83.78%
7.51% to 9.70%	162	9.52%	93.30%
9.70% to 11.89%	57	3.35%	96.65%
11.89% to 14.08%	29	1.70%	98.35%
Greater than 14.08%	28	1.65%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.40%	8.24%	81.61%	68.27%
±2σ	-0.53%	11.16%	95.65%	95.45%
±3σ	-3.45%	14.08%	98.35%	99.73%

Descriptive Statistics

Mean	5.317%
Standard Error	0.071%
Median	4.627%
Mode	2.577%
Standard Deviation	2.922%
Sample Variance	8.536%
Kurtosis	22.76
Skewness	3.01
Range	42.833%
Minimum	1.182%
Maximum	44.015%
Count	1702

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.317%	1702	100.00%	5.317%
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 -0.11. Further, an Excess Kurtosis of 1.45 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.17%	11	0.65%	0.65%
-10.17% to -7.60%	25	1.47%	2.12%
-7.60% to -5.03%	66	3.88%	5.99%
-5.03% to -2.46%	231	13.57%	19.57%
-2.46% to 0.11%	513	30.14%	49.71%
0.11% to 2.67%	518	30.43%	80.14%
2.67% to 5.24%	240	14.10%	94.24%
5.24% to 7.81%	73	4.29%	98.53%
7.81% to 10.38%	18	1.06%	99.59%
Greater than 10.38%	7	0.41%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.32%	3.53%	72.97%	68.27%
±2σ	-6.74%	6.95%	94.42%	95.45%
±3σ	-10.17%	10.38%	98.94%	99.73%

Descriptive Statistics

Mean	0.106%
Standard Error	0.083%
Median	0.115%
Mode	0.000%
Standard Deviation	3.424%
Sample Variance	11.723%
Kurtosis	1.45
Skewness	-0.11
Range	31.464%
Minimum	-14.444%
Maximum	17.020%
Count	1702

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.604%	881	51.76%	1.348%
Negative	-2.590%	816	47.94%	-1.242%
Zero	0.000%	5	0.29%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.73. Further, an Excess Kurtosis of 1.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.98%	1	0.28%	0.28%
-24.98% to -18.68%	0	0.00%	0.28%
-18.68% to -12.37%	19	5.38%	5.67%
-12.37% to -6.06%	51	14.45%	20.11%
-6.06% to 0.24%	117	33.14%	53.26%
0.24% to 6.55%	94	26.63%	79.89%
6.55% to 12.85%	49	13.88%	93.77%
12.85% to 19.16%	13	3.68%	97.45%
19.16% to 25.46%	5	1.42%	98.87%
Greater than 25.46%	4	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.17%	8.65%	72.52%	68.27%
±2σ	-16.57%	17.05%	96.03%	95.45%
±3σ	-24.98%	25.46%	98.58%	99.73%

Descriptive Statistics

Mean	0.241%
Standard Error	0.447%
Median	-0.564%
Mode	6.724%
Standard Deviation	8.407%
Sample Variance	70.674%
Kurtosis	1.82
Skewness	0.73
Range	61.505%
Minimum	-27.166%
Maximum	34.339%
Count	353

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.983%	169	47.88%	3.343%
Negative	-5.951%	184	52.12%	-3.102%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	10.42%
12	1 Quarter	10.39%
52	1 Year	8.94%
156	3 Years	10.71%
260	5 Years	12.24%
520	10 Years	12.69%
1,040	20 Years	12.69%
2,600	50 Years	12.69%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.72. Further, an Excess Kurtosis of 4.48 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.81%	0	0.00%	0.00%
-7.81% to -2.45%	0	0.00%	0.00%
-2.45% to 2.91%	0	0.00%	0.00%
2.91% to 8.27%	77	21.75%	21.75%
8.27% to 13.63%	136	38.42%	60.17%
13.63% to 18.99%	79	22.32%	82.49%
18.99% to 24.35%	33	9.32%	91.81%
24.35% to 29.71%	16	4.52%	96.33%
29.71% to 35.07%	7	1.98%	98.31%
Greater than 35.07%	6	1.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.49%	20.78%	75.42%	68.27%
±2σ	-0.66%	27.92%	95.48%	95.45%
±3σ	-7.81%	35.07%	98.31%	99.73%

Descriptive Statistics

Mean	13.632%
Standard Error	0.380%
Median	12.078%
Mode	5.562%
Standard Deviation	7.146%
Sample Variance	51.060%
Kurtosis	4.48
Skewness	1.72
Range	51.188%
Minimum	3.419%
Maximum	54.607%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.632%	354	100.00%	13.632%
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 0.16. Further, an Excess Kurtosis of 1.20 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.46%	1	0.28%	0.28%
-23.46% to -17.46%	5	1.41%	1.69%
-17.46% to -11.45%	15	4.24%	5.93%
-11.45% to -5.45%	50	14.12%	20.06%
-5.45% to 0.56%	107	30.23%	50.28%
0.56% to 6.56%	103	29.10%	79.38%
6.56% to 12.57%	48	13.56%	92.94%
12.57% to 18.57%	22	6.21%	99.15%
18.57% to 24.57%	2	0.56%	99.72%
Greater than 24.57%	1	0.28%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.45%	8.56%	72.32%	68.27%
±2σ	-15.46%	16.57%	95.48%	95.45%
±3σ	-23.46%	24.57%	99.44%	99.73%

Descriptive Statistics

Mean	0.557%
Standard Error	0.425%
Median	0.540%
Mode	1.882%
Standard Deviation	8.006%
Sample Variance	64.091%
Kurtosis	1.20
Skewness	0.16
Range	62.520%
Minimum	-24.304%
Maximum	38.216%
Count	354

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.452%	187	52.83%	3.408%
Negative	-6.081%	166	46.89%	-2.852%
Zero	0.000%	1	0.28%	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 -0.35 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -48.53%	0	0.00%	0.00%
-48.53% to -36.19%	0	0.00%	0.00%
-36.19% to -23.86%	4	4.94%	4.94%
-23.86% to -11.53%	16	19.75%	24.69%
-11.53% to 0.81%	28	34.57%	59.26%
0.81% to 13.14%	13	16.05%	75.31%
13.14% to 25.47%	12	14.81%	90.12%
25.47% to 37.80%	6	7.41%	97.53%
37.80% to 50.14%	2	2.47%	100.00%
Greater than 50.14%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.64%	17.25%	71.60%	68.27%
±2σ	-32.08%	33.69%	95.06%	95.45%
±3σ	-48.53%	50.14%	100.00%	99.73%

Descriptive Statistics

Mean	0.806%
Standard Error	1.827%
Median	-1.245%
Mode	-29.263%
Standard Deviation	16.444%
Sample Variance	270.393%
Kurtosis	-0.35
Skewness	0.47
Range	70.757%
Minimum	-29.263%
Maximum	41.494%
Count	81

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.509%	37	45.68%	7.084%
Negative	-11.558%	44	54.32%	-6.278%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.24%
12	1 Year	19.51%
36	3 Years	25.34%
60	5 Years	27.77%
120	10 Years	27.96%
240	20 Years	27.96%
600	50 Years	27.96%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.51. Further, an Excess Kurtosis of 2.55 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.06%	0	0.00%	0.00%
-15.06% to -3.18%	0	0.00%	0.00%
-3.18% to 8.70%	0	0.00%	0.00%
8.70% to 20.58%	17	20.73%	20.73%
20.58% to 32.46%	35	42.68%	63.41%
32.46% to 44.34%	13	15.85%	79.27%
44.34% to 56.21%	12	14.63%	93.90%
56.21% to 68.09%	2	2.44%	96.34%
68.09% to 79.97%	1	1.22%	97.56%
Greater than 79.97%	2	2.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	16.62%	48.30%	79.27%	68.27%
±2σ	0.78%	64.13%	95.12%	95.45%
±3σ	-15.06%	79.97%	97.56%	99.73%

Descriptive Statistics

Mean	32.456%
Standard Error	1.749%
Median	26.677%
Mode	12.452%
Standard Deviation	15.839%
Sample Variance	250.875%
Kurtosis	2.55
Skewness	1.51
Range	79.740%
Minimum	12.452%
Maximum	92.192%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.456%	82	100.00%	32.456%
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 0.25. Further, an Excess Kurtosis of -0.29 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.25%	0	0.00%	0.00%
-45.25% to -33.39%	0	0.00%	0.00%
-33.39% to -21.52%	3	3.66%	3.66%
-21.52% to -9.66%	20	24.39%	28.05%
-9.66% to 2.21%	19	23.17%	51.22%
2.21% to 14.07%	22	26.83%	78.05%
14.07% to 25.93%	12	14.63%	92.68%
25.93% to 37.80%	4	4.88%	97.56%
37.80% to 49.66%	2	2.44%	100.00%
Greater than 49.66%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.61%	18.02%	69.51%	68.27%
±2σ	-29.43%	33.84%	96.34%	95.45%
±3σ	-45.25%	49.66%	100.00%	99.73%

Descriptive Statistics

Mean	2.205%
Standard Error	1.747%
Median	1.879%
Mode	-29.750%
Standard Deviation	15.818%
Sample Variance	250.203%
Kurtosis	-0.29
Skewness	0.25
Range	71.560%
Minimum	-29.750%
Maximum	41.810%
Count	82

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.211%	47	57.32%	7.572%
Negative	-12.574%	35	42.68%	-5.367%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.64. Further, an Excess Kurtosis of -0.17 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -88.54%	0	0.00%	0.00%
-88.54% to -65.68%	0	0.00%	0.00%
-65.68% to -42.83%	1	3.70%	3.70%
-42.83% to -19.98%	5	18.52%	22.22%
-19.98% to 2.88%	9	33.33%	55.56%
2.88% to 25.73%	7	25.93%	81.48%
25.73% to 48.59%	2	7.41%	88.89%
48.59% to 71.44%	3	11.11%	100.00%
71.44% to 94.29%	0	0.00%	100.00%
Greater than 94.29%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-27.59%	33.35%	66.67%	68.27%
±2σ	-58.07%	63.82%	96.30%	95.45%
±3σ	-88.54%	94.29%	100.00%	99.73%

Descriptive Statistics

Mean	2.878%
Standard Error	5.864%
Median	-2.133%
Mode	-42.979%
Standard Deviation	30.472%
Sample Variance	928.529%
Kurtosis	-0.17
Skewness	0.64
Range	108.271%
Minimum	-42.979%
Maximum	65.292%
Count	27

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	29.683%	12	44.44%	13.192%
Negative	-18.566%	15	55.56%	-10.315%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	27.75%
12	3 Years	46.58%
20	5 Years	49.19%
40	10 Years	51.41%
80	20 Years	51.41%
200	50 Years	51.41%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 0.81 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.30%	0	0.00%	0.00%
-41.30% to -14.72%	0	0.00%	0.00%
-14.72% to 11.86%	0	0.00%	0.00%
11.86% to 38.43%	6	21.43%	21.43%
38.43% to 65.01%	12	42.86%	64.29%
65.01% to 91.58%	4	14.29%	78.57%
91.58% to 118.16%	3	10.71%	89.29%
118.16% to 144.73%	2	7.14%	96.43%
144.73% to 171.31%	1	3.57%	100.00%
Greater than 171.31%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	29.57%	100.44%	71.43%	68.27%
±2σ	-5.86%	135.87%	96.43%	95.45%
±3σ	-41.30%	171.31%	100.00%	99.73%

Descriptive Statistics

Mean	65.006%
Standard Error	6.696%
Median	50.926%
Mode	26.236%
Standard Deviation	35.434%
Sample Variance	1255.599%
Kurtosis	0.81
Skewness	1.20
Range	137.064%
Minimum	26.236%
Maximum	163.300%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	65.006%	28	100.00%	65.006%
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 0.59. Further, an Excess Kurtosis of -0.08 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.28%	0	0.00%	0.00%
-85.28% to -62.59%	0	0.00%	0.00%
-62.59% to -39.90%	0	0.00%	0.00%
-39.90% to -17.21%	6	21.43%	21.43%
-17.21% to 5.47%	9	32.14%	53.57%
5.47% to 28.16%	7	25.00%	78.57%
28.16% to 50.85%	3	10.71%	89.29%
50.85% to 73.54%	3	10.71%	100.00%
73.54% to 96.23%	0	0.00%	100.00%
Greater than 96.23%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-24.78%	35.73%	64.29%	68.27%
±2σ	-55.03%	65.98%	96.43%	95.45%
±3σ	-85.28%	96.23%	100.00%	99.73%

Descriptive Statistics

Mean	5.474%
Standard Error	5.717%
Median	0.370%
Mode	-38.981%
Standard Deviation	30.252%
Sample Variance	915.186%
Kurtosis	-0.08
Skewness	0.59
Range	112.287%
Minimum	-38.981%
Maximum	73.306%
Count	28

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	28.538%	14	50.00%	14.269%
Negative	-17.589%	14	50.00%	-8.794%
Zero	0.000%	0	0.00%	0.000%

CHWY Deep Analytical Report