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%	1.93%	2.22%	35.78	37.19	35.10	37.92
Weekly	4.95%	5.78%	4.96%	5.18%	4.26%	4.89%	34.96	38.07	33.50	39.72
Monthly	10.49%	12.37%	10.26%	11.57%	8.86%	10.17%	33.39	39.86	30.56	43.55
Quarterly	15.72%	22.96%	16.02%	19.80%	15.35%	17.62%	31.29	42.53	26.84	49.58
Annual	—	—	—	—	30.69%	35.23%	26.84	49.58	19.75	67.40
Option Time Horizon	—	—	—	—	14.55%	16.70%	31.54	42.19	27.27	48.80

Calculation Notes: Computed at 2026-02-22T14:22 UTC | Reference Contract: Call option expiring 2026-05-15 (82 days) | Spot Price (S): $36.48 | Strike (K): $37.50 (first OTM call ≥ spot) | Observed Mid-Price: $1.8250 (Bid $1.6500 / Ask $2.0000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 30.69% (CRR binomial tree, American, n=20 steps) | BS IV: 31.05% (European Black-Scholes) | Yahoo IV (Annual): 35.23% → 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 15.17 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%	1.63%
-5.20% to -3.44%	213	2.67%	4.29%
-3.44% to -1.67%	777	9.73%	14.02%
-1.67% to 0.10%	3034	37.98%	52.00%
0.10% to 1.86%	2772	34.70%	86.69%
1.86% to 3.63%	685	8.57%	95.27%
3.63% to 5.39%	223	2.79%	98.06%
5.39% to 7.16%	74	0.93%	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%	82.01%	68.27%
±2σ	-4.61%	4.81%	95.26%	95.45%
±3σ	-6.97%	7.16%	98.20%	99.73%

Descriptive Statistics

Mean	0.096%
Standard Error	0.026%
Median	0.027%
Mode	0.000%
Standard Deviation	2.355%
Sample Variance	5.548%
Kurtosis	15.17
Skewness	0.01
Range	50.804%
Minimum	-29.167%
Maximum	21.637%
Count	7989

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.583%	4012	50.22%	0.795%
Negative	-1.509%	3699	46.30%	-0.699%
Zero	0.000%	278	3.48%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.27%
20	1 Month	2.98%
60	1 Quarter	2.30%
250	1 Year	2.25%
750	3 Years	1.99%
1,250	5 Years	2.22%
2,500	10 Years	2.24%
5,000	20 Years	2.25%
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 22.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.33%	0	0.00%	0.00%
-4.33% to -2.51%	0	0.00%	0.00%
-2.51% to -0.69%	0	0.00%	0.00%
-0.69% to 1.14%	789	9.87%	9.87%
1.14% to 2.96%	4497	56.28%	66.16%
2.96% to 4.78%	1603	20.06%	86.22%
4.78% to 6.60%	589	7.37%	93.59%
6.60% to 8.43%	239	2.99%	96.58%
8.43% to 10.25%	111	1.39%	97.97%
Greater than 10.25%	162	2.03%	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%	7.82%	95.68%	95.45%
±3σ	-4.33%	10.25%	97.97%	99.73%

Descriptive Statistics

Mean	2.959%
Standard Error	0.027%
Median	2.229%
Mode	2.778%
Standard Deviation	2.430%
Sample Variance	5.904%
Kurtosis	22.10
Skewness	3.57
Range	35.318%
Minimum	0.267%
Maximum	35.585%
Count	7990

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.959%	7990	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 10.26 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%	76	0.95%	0.95%
-6.54% to -4.92%	85	1.06%	2.02%
-4.92% to -3.29%	198	2.48%	4.49%
-3.29% to -1.66%	777	9.72%	14.22%
-1.66% to -0.03%	2828	35.39%	49.61%
-0.03% to 1.60%	2877	36.01%	85.62%
1.60% to 3.23%	764	9.56%	95.18%
3.23% to 4.86%	231	2.89%	98.07%
4.86% to 6.48%	79	0.99%	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%	80.73%	68.27%
±2σ	-4.37%	4.31%	94.68%	95.45%
±3σ	-6.54%	6.48%	98.11%	99.73%

Descriptive Statistics

Mean	-0.030%
Standard Error	0.024%
Median	-0.018%
Mode	0.000%
Standard Deviation	2.171%
Sample Variance	4.714%
Kurtosis	10.26
Skewness	0.40
Range	38.533%
Minimum	-16.250%
Maximum	22.283%
Count	7990

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.483%	3724	46.61%	0.691%
Negative	-1.440%	3999	50.05%	-0.721%
Zero	0.000%	267	3.34%	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 5.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.41%	11	0.66%	0.66%
-14.41% to -10.70%	30	1.80%	2.46%
-10.70% to -6.98%	43	2.58%	5.04%
-6.98% to -3.27%	182	10.92%	15.97%
-3.27% to 0.45%	577	34.63%	50.60%
0.45% to 4.16%	569	34.15%	84.75%
4.16% to 7.88%	161	9.66%	94.42%
7.88% to 11.60%	63	3.78%	98.20%
11.60% to 15.31%	17	1.02%	99.22%
Greater than 15.31%	13	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.50%	5.40%	78.39%	68.27%
±2σ	-9.46%	10.36%	94.00%	95.45%
±3σ	-14.41%	15.31%	98.56%	99.73%

Descriptive Statistics

Mean	0.449%
Standard Error	0.121%
Median	0.428%
Mode	0.000%
Standard Deviation	4.954%
Sample Variance	24.540%
Kurtosis	5.38
Skewness	0.16
Range	64.000%
Minimum	-28.328%
Maximum	35.672%
Count	1666

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.501%	914	54.86%	1.921%
Negative	-3.353%	731	43.88%	-1.471%
Zero	0.000%	21	1.26%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.98%
12	1 Quarter	5.25%
52	1 Year	5.04%
156	3 Years	4.62%
260	5 Years	5.18%
520	10 Years	5.21%
1,040	20 Years	5.18%
2,600	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 3.20. Further, an Excess Kurtosis of 18.22 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.12%	0	0.00%	0.00%
-10.12% to -5.79%	0	0.00%	0.00%
-5.79% to -1.45%	0	0.00%	0.00%
-1.45% to 2.88%	204	12.24%	12.24%
2.88% to 7.22%	899	53.93%	66.17%
7.22% to 11.55%	315	18.90%	85.06%
11.55% to 15.89%	135	8.10%	93.16%
15.89% to 20.22%	59	3.54%	96.70%
20.22% to 24.56%	24	1.44%	98.14%
Greater than 24.56%	31	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.44%	13.00%	88.12%	68.27%
±2σ	-4.34%	18.78%	95.68%	95.45%
±3σ	-10.12%	24.56%	98.14%	99.73%

Descriptive Statistics

Mean	7.216%
Standard Error	0.142%
Median	5.358%
Mode	3.279%
Standard Deviation	5.780%
Sample Variance	33.406%
Kurtosis	18.22
Skewness	3.20
Range	69.422%
Minimum	0.749%
Maximum	70.171%
Count	1667

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.216%	1667	100.00%	7.216%
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 7.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.03%	5	0.30%	0.30%
-15.03% to -11.31%	20	1.20%	1.50%
-11.31% to -7.59%	54	3.24%	4.74%
-7.59% to -3.88%	188	11.28%	16.02%
-3.88% to -0.16%	614	36.83%	52.85%
-0.16% to 3.56%	542	32.51%	85.36%
3.56% to 7.28%	150	9.00%	94.36%
7.28% to 11.00%	49	2.94%	97.30%
11.00% to 14.72%	24	1.44%	98.74%
Greater than 14.72%	21	1.26%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.11%	4.80%	78.76%	68.27%
±2σ	-10.07%	9.76%	94.54%	95.45%
±3σ	-15.03%	14.72%	98.44%	99.73%

Descriptive Statistics

Mean	-0.156%
Standard Error	0.121%
Median	-0.411%
Mode	0.000%
Standard Deviation	4.959%
Sample Variance	24.589%
Kurtosis	7.26
Skewness	1.07
Range	63.902%
Minimum	-22.188%
Maximum	41.714%
Count	1667

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.584%	747	44.81%	1.606%
Negative	-3.261%	901	54.05%	-1.763%
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 4.73 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.48%	1	0.26%	0.26%
-29.48% to -21.61%	6	1.57%	1.83%
-21.61% to -13.75%	14	3.66%	5.48%
-13.75% to -5.88%	52	13.58%	19.06%
-5.88% to 1.98%	121	31.59%	50.65%
1.98% to 9.85%	122	31.85%	82.51%
9.85% to 17.71%	46	12.01%	94.52%
17.71% to 25.58%	13	3.39%	97.91%
25.58% to 33.45%	5	1.31%	99.22%
Greater than 33.45%	3	0.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.50%	12.47%	75.20%	68.27%
±2σ	-18.99%	22.96%	94.78%	95.45%
±3σ	-29.48%	33.45%	98.96%	99.73%

Descriptive Statistics

Mean	1.984%
Standard Error	0.536%
Median	1.908%
Mode	-1.775%
Standard Deviation	10.487%
Sample Variance	109.985%
Kurtosis	4.73
Skewness	0.69
Range	104.923%
Minimum	-37.615%
Maximum	67.308%
Count	383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.913%	233	60.84%	4.814%
Negative	-7.322%	148	38.64%	-2.829%
Zero	0.000%	2	0.52%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.98%
12	1 Year	11.72%
36	3 Years	10.73%
60	5 Years	11.57%
120	10 Years	11.90%
240	20 Years	11.53%
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 12.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.18%	0	0.00%	0.00%
-20.18% to -10.90%	0	0.00%	0.00%
-10.90% to -1.63%	0	0.00%	0.00%
-1.63% to 7.65%	60	15.62%	15.62%
7.65% to 16.93%	190	49.48%	65.10%
16.93% to 26.21%	75	19.53%	84.64%
26.21% to 35.48%	33	8.59%	93.23%
35.48% to 44.76%	14	3.65%	96.88%
44.76% to 54.04%	4	1.04%	97.92%
Greater than 54.04%	8	2.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.56%	29.30%	87.76%	68.27%
±2σ	-7.81%	41.67%	95.31%	95.45%
±3σ	-20.18%	54.04%	97.92%	99.73%

Descriptive Statistics

Mean	16.929%
Standard Error	0.631%
Median	13.358%
Mode	6.667%
Standard Deviation	12.370%
Sample Variance	153.015%
Kurtosis	12.04
Skewness	2.78
Range	103.239%
Minimum	3.761%
Maximum	107.000%
Count	384

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.929%	384	100.00%	16.929%
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 4.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.62%	1	0.26%	0.26%
-31.62% to -23.92%	3	0.78%	1.04%
-23.92% to -16.22%	11	2.86%	3.91%
-16.22% to -8.53%	53	13.80%	17.71%
-8.53% to -0.83%	147	38.28%	55.99%
-0.83% to 6.87%	101	26.30%	82.29%
6.87% to 14.56%	41	10.68%	92.97%
14.56% to 22.26%	16	4.17%	97.14%
22.26% to 29.96%	6	1.56%	98.70%
Greater than 29.96%	5	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.09%	9.43%	75.52%	68.27%
±2σ	-21.36%	19.70%	94.53%	95.45%
±3σ	-31.62%	29.96%	98.44%	99.73%

Descriptive Statistics

Mean	-0.830%
Standard Error	0.524%
Median	-1.666%
Mode	-7.692%
Standard Deviation	10.263%
Sample Variance	105.334%
Kurtosis	4.02
Skewness	0.84
Range	100.778%
Minimum	-41.954%
Maximum	58.824%
Count	384

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.414%	151	39.32%	3.309%
Negative	-6.821%	233	60.68%	-4.139%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.10. Further, an Excess Kurtosis of 0.39 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.57%	0	0.00%	0.00%
-41.57% to -29.78%	3	2.34%	2.34%
-29.78% to -17.99%	7	5.47%	7.81%
-17.99% to -6.20%	14	10.94%	18.75%
-6.20% to 5.59%	38	29.69%	48.44%
5.59% to 17.39%	41	32.03%	80.47%
17.39% to 29.18%	15	11.72%	92.19%
29.18% to 40.97%	9	7.03%	99.22%
40.97% to 52.76%	1	0.78%	100.00%
Greater than 52.76%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.13%	21.32%	72.66%	68.27%
±2σ	-25.85%	37.04%	95.31%	95.45%
±3σ	-41.57%	52.76%	100.00%	99.73%

Descriptive Statistics

Mean	5.594%
Standard Error	1.390%
Median	5.761%
Mode	-41.284%
Standard Deviation	15.722%
Sample Variance	247.173%
Kurtosis	0.39
Skewness	-0.10
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	-10.435%	45	35.16%	-3.669%
Zero	0.000%	1	0.78%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	20.08%
12	3 Years	18.80%
20	5 Years	19.80%
40	10 Years	21.46%
80	20 Years	20.43%
200	50 Years	27.44%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.67%	0	0.00%	0.00%
-36.67% to -19.45%	0	0.00%	0.00%
-19.45% to -2.23%	0	0.00%	0.00%
-2.23% to 14.99%	20	15.50%	15.50%
14.99% to 32.22%	66	51.16%	66.67%
32.22% to 49.44%	20	15.50%	82.17%
49.44% to 66.66%	16	12.40%	94.57%
66.66% to 83.88%	4	3.10%	97.67%
83.88% to 101.11%	1	0.78%	98.45%
Greater than 101.11%	2	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.25%	55.18%	86.05%	68.27%
±2σ	-13.71%	78.14%	95.35%	95.45%
±3σ	-36.67%	101.11%	98.45%	99.73%

Descriptive Statistics

Mean	32.216%
Standard Error	2.022%
Median	24.026%
Mode	8.512%
Standard Deviation	22.963%
Sample Variance	527.287%
Kurtosis	9.34
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	32.216%	129	100.00%	32.216%
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 1.34. Further, an Excess Kurtosis of 3.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -51.02%	0	0.00%	0.00%
-51.02% to -39.00%	0	0.00%	0.00%
-39.00% to -26.99%	3	2.33%	2.33%
-26.99% to -14.97%	22	17.05%	19.38%
-14.97% to -2.96%	49	37.98%	57.36%
-2.96% to 9.06%	35	27.13%	84.50%
9.06% to 21.07%	10	7.75%	92.25%
21.07% to 33.09%	5	3.88%	96.12%
33.09% to 45.10%	3	2.33%	98.45%
Greater than 45.10%	2	1.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.98%	13.06%	76.74%	68.27%
±2σ	-35.00%	29.08%	96.12%	95.45%
±3σ	-51.02%	45.10%	98.45%	99.73%

Descriptive Statistics

Mean	-2.958%
Standard Error	1.410%
Median	-5.955%
Mode	-31.066%
Standard Deviation	16.020%
Sample Variance	256.646%
Kurtosis	3.27
Skewness	1.34
Range	99.816%
Minimum	-31.066%
Maximum	68.750%
Count	129

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.619%	48	37.21%	4.695%
Negative	-12.189%	81	62.79%	-7.654%
Zero	0.000%	0	0.00%	0.000%

CPRT Deep Analytical Report