CPRT - 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	2.35%	2.43%	2.17%	2.22%	2.26%	2.48%	32.74	34.26	32.01	35.05
Weekly	4.96%	5.78%	4.96%	5.21%	4.99%	5.46%	31.87	35.21	30.32	37.01
Monthly	10.49%	12.36%	10.26%	11.70%	10.38%	11.36%	30.19	37.16	27.22	41.22
Quarterly	15.79%	22.95%	16.11%	20.00%	17.98%	19.68%	27.98	40.09	23.38	47.99
Annual	—	—	—	—	35.95%	39.36%	23.38	47.99	16.32	68.75
Option Time Horizon	—	—	—	—	13.57%	14.85%	29.24	38.36	25.53	43.94

Calculation Notes: Computed at 2026-03-23T16:38 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $33.49 | Strike (K): $35.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.2750 (Bid $1.1500 / Ask $1.4000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 35.95% (CRR binomial tree, American, n=20 steps) | BS IV: 36.21% (European Black-Scholes) | Yahoo IV (Annual): 39.36% → 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 0.01. Further, an Excess Kurtosis of 15.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.97%	63	0.79%	0.79%
-6.97% to -5.20%	67	0.84%	1.62%
-5.20% to -3.44%	214	2.67%	4.29%
-3.44% to -1.67%	780	9.74%	14.03%
-1.67% to 0.10%	3040	37.95%	51.99%
0.10% to 1.86%	2781	34.72%	86.70%
1.86% to 3.63%	686	8.56%	95.27%
3.63% to 5.39%	224	2.80%	98.06%
5.39% to 7.16%	74	0.92%	98.99%
Greater than 7.16%	81	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.26%	2.45%	81.99%	68.27%
±2σ	-4.62%	4.80%	95.27%	95.45%
±3σ	-6.97%	7.16%	98.20%	99.73%

Descriptive Statistics

Mean	0.095%
Standard Error	0.026%
Median	0.026%
Mode	0.000%
Standard Deviation	2.355%
Sample Variance	5.544%
Kurtosis	15.14
Skewness	0.01
Range	50.804%
Minimum	-29.167%
Maximum	21.637%
Count	8010

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.582%	4022	50.21%	0.794%
Negative	-1.510%	3710	46.32%	-0.699%
Zero	0.000%	278	3.47%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.74%
20	1 Month	3.01%
60	1 Quarter	2.76%
250	1 Year	2.32%
750	3 Years	2.02%
1,250	5 Years	2.22%
2,500	10 Years	2.24%
5,000	20 Years	2.26%
12,500	50 Years	3.02%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.57. Further, an Excess Kurtosis of 22.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.32%	0	0.00%	0.00%
-4.32% to -2.50%	0	0.00%	0.00%
-2.50% to -0.68%	0	0.00%	0.00%
-0.68% to 1.14%	795	9.92%	9.92%
1.14% to 2.96%	4504	56.22%	66.15%
2.96% to 4.78%	1609	20.08%	86.23%
4.78% to 6.60%	591	7.38%	93.61%
6.60% to 8.42%	239	2.98%	96.59%
8.42% to 10.24%	111	1.39%	97.98%
Greater than 10.24%	162	2.02%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.53%	5.39%	89.34%	68.27%
±2σ	-1.90%	7.81%	95.69%	95.45%
±3σ	-4.32%	10.24%	97.98%	99.73%

Descriptive Statistics

Mean	2.959%
Standard Error	0.027%
Median	2.231%
Mode	2.778%
Standard Deviation	2.427%
Sample Variance	5.891%
Kurtosis	22.14
Skewness	3.57
Range	35.318%
Minimum	0.267%
Maximum	35.585%
Count	8011

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.959%	8011	100.00%	2.959%
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 0.40. Further, an Excess Kurtosis of 10.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.54%	77	0.96%	0.96%
-6.54% to -4.91%	84	1.05%	2.01%
-4.91% to -3.28%	198	2.47%	4.48%
-3.28% to -1.66%	781	9.75%	14.23%
-1.66% to -0.03%	2838	35.43%	49.66%
-0.03% to 1.60%	2879	35.94%	85.59%
1.60% to 3.23%	768	9.59%	95.18%
3.23% to 4.85%	230	2.87%	98.05%
4.85% to 6.48%	81	1.01%	99.06%
Greater than 6.48%	75	0.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.20%	2.14%	80.71%	68.27%
±2σ	-4.37%	4.31%	94.68%	95.45%
±3σ	-6.54%	6.48%	98.10%	99.73%

Descriptive Statistics

Mean	-0.029%
Standard Error	0.024%
Median	-0.018%
Mode	0.000%
Standard Deviation	2.170%
Sample Variance	4.711%
Kurtosis	10.24
Skewness	0.40
Range	38.533%
Minimum	-16.250%
Maximum	22.283%
Count	8011

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.484%	3735	46.62%	0.692%
Negative	-1.439%	4009	50.04%	-0.720%
Zero	0.000%	267	3.33%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.16. Further, an Excess Kurtosis of 5.33 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.44%	11	0.66%	0.66%
-14.44% to -10.72%	30	1.80%	2.46%
-10.72% to -7.00%	44	2.63%	5.09%
-7.00% to -3.28%	183	10.96%	16.05%
-3.28% to 0.44%	575	34.43%	50.48%
0.44% to 4.16%	572	34.25%	84.73%
4.16% to 7.88%	161	9.64%	94.37%
7.88% to 11.60%	65	3.89%	98.26%
11.60% to 15.32%	16	0.96%	99.22%
Greater than 15.32%	13	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.52%	5.40%	78.26%	68.27%
±2σ	-9.48%	10.36%	94.01%	95.45%
±3σ	-14.44%	15.32%	98.56%	99.73%

Descriptive Statistics

Mean	0.444%
Standard Error	0.121%
Median	0.428%
Mode	0.000%
Standard Deviation	4.960%
Sample Variance	24.603%
Kurtosis	5.33
Skewness	0.16
Range	64.000%
Minimum	-28.328%
Maximum	35.672%
Count	1670

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.506%	915	54.79%	1.921%
Negative	-3.361%	734	43.95%	-1.477%
Zero	0.000%	21	1.26%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.48%
12	1 Quarter	7.17%
52	1 Year	5.32%
156	3 Years	4.73%
260	5 Years	5.21%
520	10 Years	5.24%
1,040	20 Years	5.20%
2,600	50 Years	6.89%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.20. Further, an Excess Kurtosis of 18.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.11%	0	0.00%	0.00%
-10.11% to -5.77%	0	0.00%	0.00%
-5.77% to -1.44%	0	0.00%	0.00%
-1.44% to 2.89%	206	12.33%	12.33%
2.89% to 7.22%	898	53.74%	66.07%
7.22% to 11.55%	317	18.97%	85.04%
11.55% to 15.88%	136	8.14%	93.18%
15.88% to 20.21%	59	3.53%	96.71%
20.21% to 24.55%	24	1.44%	98.14%
Greater than 24.55%	31	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.44%	13.00%	88.09%	68.27%
±2σ	-4.33%	18.77%	95.69%	95.45%
±3σ	-10.11%	24.55%	98.14%	99.73%

Descriptive Statistics

Mean	7.220%
Standard Error	0.141%
Median	5.376%
Mode	3.279%
Standard Deviation	5.775%
Sample Variance	33.350%
Kurtosis	18.23
Skewness	3.20
Range	69.422%
Minimum	0.749%
Maximum	70.171%
Count	1671

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.220%	1671	100.00%	7.220%
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 1.07. Further, an Excess Kurtosis of 7.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.04%	5	0.30%	0.30%
-15.04% to -11.32%	20	1.20%	1.50%
-11.32% to -7.60%	54	3.23%	4.73%
-7.60% to -3.87%	189	11.31%	16.04%
-3.87% to -0.15%	616	36.86%	52.90%
-0.15% to 3.58%	543	32.50%	85.40%
3.58% to 7.30%	149	8.92%	94.31%
7.30% to 11.02%	50	2.99%	97.31%
11.02% to 14.75%	24	1.44%	98.74%
Greater than 14.75%	21	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.11%	4.82%	78.70%	68.27%
±2σ	-10.08%	9.78%	94.49%	95.45%
±3σ	-15.04%	14.75%	98.44%	99.73%

Descriptive Statistics

Mean	-0.149%
Standard Error	0.121%
Median	-0.407%
Mode	0.000%
Standard Deviation	4.965%
Sample Variance	24.654%
Kurtosis	7.19
Skewness	1.07
Range	63.902%
Minimum	-22.188%
Maximum	41.714%
Count	1671

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.594%	750	44.88%	1.613%
Negative	-3.265%	902	53.98%	-1.762%
Zero	0.000%	19	1.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.69. Further, an Excess Kurtosis of 4.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.51%	1	0.26%	0.26%
-29.51% to -21.64%	6	1.56%	1.82%
-21.64% to -13.77%	13	3.39%	5.21%
-13.77% to -5.91%	53	13.80%	19.01%
-5.91% to 1.96%	122	31.77%	50.78%
1.96% to 9.82%	122	31.77%	82.55%
9.82% to 17.69%	46	11.98%	94.53%
17.69% to 25.56%	13	3.39%	97.92%
25.56% to 33.42%	5	1.30%	99.22%
Greater than 33.42%	3	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.53%	12.45%	75.52%	68.27%
±2σ	-19.02%	22.93%	94.79%	95.45%
±3σ	-29.51%	33.42%	98.96%	99.73%

Descriptive Statistics

Mean	1.958%
Standard Error	0.535%
Median	1.877%
Mode	-1.775%
Standard Deviation	10.488%
Sample Variance	110.007%
Kurtosis	4.72
Skewness	0.69
Range	104.923%
Minimum	-37.615%
Maximum	67.308%
Count	384

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.913%	233	60.68%	4.801%
Negative	-7.328%	149	38.80%	-2.843%
Zero	0.000%	2	0.52%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	15.52%
12	1 Year	12.43%
36	3 Years	10.89%
60	5 Years	11.70%
120	10 Years	11.96%
240	20 Years	11.56%
600	50 Years	15.23%

High-to-Low 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 12.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.13%	0	0.00%	0.00%
-20.13% to -10.86%	0	0.00%	0.00%
-10.86% to -1.59%	0	0.00%	0.00%
-1.59% to 7.67%	62	16.10%	16.10%
7.67% to 16.94%	188	48.83%	64.94%
16.94% to 26.20%	76	19.74%	84.68%
26.20% to 35.47%	33	8.57%	93.25%
35.47% to 44.74%	14	3.64%	96.88%
44.74% to 54.00%	4	1.04%	97.92%
Greater than 54.00%	8	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.58%	29.29%	87.53%	68.27%
±2σ	-7.77%	41.65%	95.32%	95.45%
±3σ	-20.13%	54.00%	97.92%	99.73%

Descriptive Statistics

Mean	16.938%
Standard Error	0.630%
Median	13.422%
Mode	6.667%
Standard Deviation	12.355%
Sample Variance	152.652%
Kurtosis	12.06
Skewness	2.78
Range	103.239%
Minimum	3.761%
Maximum	107.000%
Count	385

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.938%	385	100.00%	16.938%
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 0.84. Further, an Excess Kurtosis of 4.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.59%	1	0.26%	0.26%
-31.59% to -23.90%	3	0.78%	1.04%
-23.90% to -16.20%	11	2.86%	3.90%
-16.20% to -8.50%	53	13.77%	17.66%
-8.50% to -0.81%	147	38.18%	55.84%
-0.81% to 6.89%	102	26.49%	82.34%
6.89% to 14.59%	41	10.65%	92.99%
14.59% to 22.28%	16	4.16%	97.14%
22.28% to 29.98%	6	1.56%	98.70%
Greater than 29.98%	5	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.07%	9.45%	75.58%	68.27%
±2σ	-21.33%	19.72%	94.55%	95.45%
±3σ	-31.59%	29.98%	98.44%	99.73%

Descriptive Statistics

Mean	-0.808%
Standard Error	0.523%
Median	-1.603%
Mode	-7.692%
Standard Deviation	10.262%
Sample Variance	105.302%
Kurtosis	4.01
Skewness	0.84
Range	100.778%
Minimum	-41.954%
Maximum	58.824%
Count	385

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.410%	152	39.48%	3.320%
Negative	-6.821%	233	60.52%	-4.128%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.11. 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 -41.85%	0	0.00%	0.00%
-41.85% to -30.00%	3	2.34%	2.34%
-30.00% to -18.16%	7	5.47%	7.81%
-18.16% to -6.31%	14	10.94%	18.75%
-6.31% to 5.54%	38	29.69%	48.44%
5.54% to 17.38%	41	32.03%	80.47%
17.38% to 29.23%	15	11.72%	92.19%
29.23% to 41.07%	9	7.03%	99.22%
41.07% to 52.92%	1	0.78%	100.00%
Greater than 52.92%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.26%	21.33%	72.66%	68.27%
±2σ	-26.05%	37.12%	95.31%	95.45%
±3σ	-41.85%	52.92%	100.00%	99.73%

Descriptive Statistics

Mean	5.536%
Standard Error	1.396%
Median	5.761%
Mode	-41.284%
Standard Deviation	15.794%
Sample Variance	249.437%
Kurtosis	0.35
Skewness	-0.11
Range	89.110%
Minimum	-41.284%
Maximum	47.826%
Count	128

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.458%	82	64.06%	9.262%
Negative	-10.600%	45	35.16%	-3.727%
Zero	0.000%	1	0.78%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	21.08%
12	3 Years	19.13%
20	5 Years	20.00%
40	10 Years	21.56%
80	20 Years	20.48%
200	50 Years	27.47%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.50. Further, an Excess Kurtosis of 9.36 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.58%	0	0.00%	0.00%
-36.58% to -19.37%	0	0.00%	0.00%
-19.37% to -2.16%	0	0.00%	0.00%
-2.16% to 15.05%	20	15.50%	15.50%
15.05% to 32.26%	66	51.16%	66.67%
32.26% to 49.47%	20	15.50%	82.17%
49.47% to 66.68%	16	12.40%	94.57%
66.68% to 83.89%	4	3.10%	97.67%
83.89% to 101.10%	1	0.78%	98.45%
Greater than 101.10%	2	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.32%	55.21%	86.05%	68.27%
±2σ	-13.63%	78.16%	95.35%	95.45%
±3σ	-36.58%	101.10%	98.45%	99.73%

Descriptive Statistics

Mean	32.263%
Standard Error	2.020%
Median	24.052%
Mode	8.512%
Standard Deviation	22.946%
Sample Variance	526.521%
Kurtosis	9.36
Skewness	2.50
Range	152.481%
Minimum	8.512%
Maximum	160.993%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.263%	129	100.00%	32.263%
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 1.33. Further, an Excess Kurtosis of 3.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.20%	0	0.00%	0.00%
-51.20% to -39.12%	0	0.00%	0.00%
-39.12% to -27.04%	3	2.33%	2.33%
-27.04% to -14.96%	22	17.05%	19.38%
-14.96% to -2.88%	49	37.98%	57.36%
-2.88% to 9.20%	35	27.13%	84.50%
9.20% to 21.28%	10	7.75%	92.25%
21.28% to 33.36%	5	3.88%	96.12%
33.36% to 45.44%	3	2.33%	98.45%
Greater than 45.44%	2	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.99%	13.23%	75.97%	68.27%
±2σ	-35.10%	29.34%	96.12%	95.45%
±3σ	-51.20%	45.44%	98.45%	99.73%

Descriptive Statistics

Mean	-2.881%
Standard Error	1.418%
Median	-5.955%
Mode	-31.066%
Standard Deviation	16.108%
Sample Variance	259.475%
Kurtosis	3.14
Skewness	1.33
Range	99.816%
Minimum	-31.066%
Maximum	68.750%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.826%	48	37.21%	4.772%
Negative	-12.189%	81	62.79%	-7.654%
Zero	0.000%	0	0.00%	0.000%

CPRT Deep Analytical Report