ORLY - 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	2.07%	1.93%	1.92%	2.00%	2.04%	2.17%	87.30	90.93	85.54	92.81
Weekly	4.51%	4.53%	4.41%	4.60%	4.49%	4.78%	85.19	93.19	81.45	97.46
Monthly	8.41%	9.88%	8.31%	9.89%	9.34%	9.96%	81.16	97.82	73.92	107.40
Quarterly	13.45%	15.69%	13.05%	15.93%	16.18%	17.24%	75.79	104.74	64.47	123.13
Annual	—	—	—	—	32.35%	34.49%	64.47	123.13	46.65	170.16
Option Time Horizon	—	—	—	—	12.21%	13.02%	78.86	100.67	69.79	113.75

Calculation Notes: Computed at 2026-03-23T16:38 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $89.10 | Strike (K): $90.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.1500 (Bid $4.0000 / Ask $4.3000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 32.35% (CRR binomial tree, American, n=20 steps) | BS IV: 32.43% (European Black-Scholes) | Yahoo IV (Annual): 34.49% → 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 10.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.11%	57	0.69%	0.69%
-6.11% to -4.56%	76	0.92%	1.62%
-4.56% to -3.01%	227	2.76%	4.38%
-3.01% to -1.45%	914	11.12%	15.49%
-1.45% to 0.10%	3001	36.50%	51.99%
0.10% to 1.65%	2695	32.77%	84.76%
1.65% to 3.20%	870	10.58%	95.34%
3.20% to 4.76%	222	2.70%	98.04%
4.76% to 6.31%	78	0.95%	98.99%
Greater than 6.31%	83	1.01%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.97%	2.17%	80.47%	68.27%
±2σ	-4.04%	4.24%	95.37%	95.45%
±3σ	-6.11%	6.31%	98.30%	99.73%

Descriptive Statistics

Mean	0.098%
Standard Error	0.023%
Median	0.028%
Mode	0.000%
Standard Deviation	2.070%
Sample Variance	4.285%
Kurtosis	10.03
Skewness	0.41
Range	39.094%
Minimum	-18.892%
Maximum	20.202%
Count	8223

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.449%	4161	50.60%	0.733%
Negative	-1.395%	3743	45.52%	-0.635%
Zero	0.000%	319	3.88%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.34%
20	1 Month	2.40%
60	1 Quarter	2.28%
250	1 Year	2.13%
750	3 Years	1.90%
1,250	5 Years	2.00%
2,500	10 Years	2.18%
5,000	20 Years	2.31%
12,500	50 Years	2.72%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.72. Further, an Excess Kurtosis of 32.63 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.12%	0	0.00%	0.00%
-3.12% to -1.68%	0	0.00%	0.00%
-1.68% to -0.23%	0	0.00%	0.00%
-0.23% to 1.22%	1026	12.48%	12.48%
1.22% to 2.67%	4426	53.82%	66.29%
2.67% to 4.11%	1621	19.71%	86.00%
4.11% to 5.56%	611	7.43%	93.43%
5.56% to 7.01%	262	3.19%	96.62%
7.01% to 8.46%	98	1.19%	97.81%
Greater than 8.46%	180	2.19%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.74%	4.60%	88.29%	68.27%
±2σ	-1.19%	6.53%	95.88%	95.45%
±3σ	-3.12%	8.46%	97.81%	99.73%

Descriptive Statistics

Mean	2.667%
Standard Error	0.021%
Median	2.148%
Mode	2.632%
Standard Deviation	1.930%
Sample Variance	3.724%
Kurtosis	32.63
Skewness	3.72
Range	41.650%
Minimum	0.285%
Maximum	41.935%
Count	8224

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.667%	8224	100.00%	2.667%
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 0.15. Further, an Excess Kurtosis of 9.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.81%	71	0.86%	0.86%
-5.81% to -4.37%	64	0.78%	1.64%
-4.37% to -2.93%	257	3.12%	4.77%
-2.93% to -1.49%	900	10.94%	15.71%
-1.49% to -0.05%	2740	33.32%	49.03%
-0.05% to 1.39%	2866	34.85%	83.88%
1.39% to 2.83%	939	11.42%	95.29%
2.83% to 4.27%	246	2.99%	98.29%
4.27% to 5.71%	72	0.88%	99.16%
Greater than 5.71%	69	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.97%	1.87%	78.39%	68.27%
±2σ	-3.89%	3.79%	95.49%	95.45%
±3σ	-5.81%	5.71%	98.30%	99.73%

Descriptive Statistics

Mean	-0.048%
Standard Error	0.021%
Median	-0.008%
Mode	0.000%
Standard Deviation	1.921%
Sample Variance	3.690%
Kurtosis	9.38
Skewness	0.15
Range	38.807%
Minimum	-20.625%
Maximum	18.182%
Count	8224

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.366%	3752	45.62%	0.623%
Negative	-1.338%	4124	50.15%	-0.671%
Zero	0.000%	348	4.23%	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 7.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.05%	12	0.70%	0.70%
-13.05% to -9.67%	16	0.93%	1.63%
-9.67% to -6.29%	44	2.56%	4.19%
-6.29% to -2.91%	208	12.11%	16.31%
-2.91% to 0.47%	626	36.46%	52.77%
0.47% to 3.85%	534	31.10%	83.87%
3.85% to 7.23%	190	11.07%	94.93%
7.23% to 10.61%	49	2.85%	97.79%
10.61% to 13.99%	15	0.87%	98.66%
Greater than 13.99%	23	1.34%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.04%	4.98%	79.27%	68.27%
±2σ	-8.54%	9.48%	94.93%	95.45%
±3σ	-13.05%	13.99%	97.96%	99.73%

Descriptive Statistics

Mean	0.470%
Standard Error	0.109%
Median	0.232%
Mode	0.000%
Standard Deviation	4.507%
Sample Variance	20.317%
Kurtosis	7.14
Skewness	0.64
Range	60.092%
Minimum	-22.222%
Maximum	37.870%
Count	1717

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.305%	919	53.52%	1.769%
Negative	-2.878%	775	45.14%	-1.299%
Zero	0.000%	23	1.34%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	5.09%
12	1 Quarter	5.70%
52	1 Year	5.03%
156	3 Years	4.38%
260	5 Years	4.60%
520	10 Years	4.99%
1,040	20 Years	5.28%
2,600	50 Years	6.08%

High-to-Low 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 11.88 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.29%	0	0.00%	0.00%
-7.29% to -3.90%	0	0.00%	0.00%
-3.90% to -0.50%	0	0.00%	0.00%
-0.50% to 2.90%	243	14.14%	14.14%
2.90% to 6.29%	887	51.63%	65.77%
6.29% to 9.69%	337	19.62%	85.39%
9.69% to 13.09%	126	7.33%	92.72%
13.09% to 16.48%	58	3.38%	96.10%
16.48% to 19.88%	33	1.92%	98.02%
Greater than 19.88%	34	1.98%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.76%	10.82%	87.14%	68.27%
±2σ	-2.76%	15.35%	95.58%	95.45%
±3σ	-7.29%	19.88%	98.02%	99.73%

Descriptive Statistics

Mean	6.294%
Standard Error	0.109%
Median	4.966%
Mode	2.632%
Standard Deviation	4.529%
Sample Variance	20.509%
Kurtosis	11.88
Skewness	2.77
Range	42.217%
Minimum	1.331%
Maximum	43.548%
Count	1718

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.294%	1718	100.00%	6.294%
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 0.59. Further, an Excess Kurtosis of 5.99 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.47%	10	0.58%	0.58%
-13.47% to -10.17%	20	1.16%	1.75%
-10.17% to -6.86%	53	3.08%	4.83%
-6.86% to -3.55%	206	11.99%	16.82%
-3.55% to -0.24%	573	33.35%	50.17%
-0.24% to 3.07%	595	34.63%	84.81%
3.07% to 6.38%	178	10.36%	95.17%
6.38% to 9.69%	44	2.56%	97.73%
9.69% to 13.00%	22	1.28%	99.01%
Greater than 13.00%	17	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.65%	4.17%	78.81%	68.27%
±2σ	-9.06%	8.58%	94.82%	95.45%
±3σ	-13.48%	13.00%	98.43%	99.73%

Descriptive Statistics

Mean	-0.239%
Standard Error	0.106%
Median	-0.244%
Mode	0.000%
Standard Deviation	4.412%
Sample Variance	19.467%
Kurtosis	5.99
Skewness	0.59
Range	55.838%
Minimum	-25.751%
Maximum	30.087%
Count	1718

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.042%	788	45.87%	1.395%
Negative	-3.117%	901	52.45%	-1.635%
Zero	0.000%	29	1.69%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.85. 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 -23.27%	1	0.25%	0.25%
-23.27% to -16.96%	2	0.51%	0.76%
-16.96% to -10.66%	12	3.04%	3.80%
-10.66% to -4.35%	60	15.19%	18.99%
-4.35% to 1.96%	132	33.42%	52.41%
1.96% to 8.27%	120	30.38%	82.78%
8.27% to 14.57%	47	11.90%	94.68%
14.57% to 20.88%	14	3.54%	98.23%
20.88% to 27.19%	4	1.01%	99.24%
Greater than 27.19%	3	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.45%	10.37%	74.43%	68.27%
±2σ	-14.86%	18.78%	96.46%	95.45%
±3σ	-23.27%	27.19%	98.99%	99.73%

Descriptive Statistics

Mean	1.959%
Standard Error	0.423%
Median	1.764%
Mode	0.000%
Standard Deviation	8.410%
Sample Variance	70.730%
Kurtosis	7.26
Skewness	0.85
Range	99.856%
Minimum	-38.954%
Maximum	60.902%
Count	395

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.807%	237	60.00%	4.084%
Negative	-5.379%	156	39.49%	-2.124%
Zero	0.000%	2	0.51%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.95%
12	1 Year	10.36%
36	3 Years	9.46%
60	5 Years	9.89%
120	10 Years	10.65%
240	20 Years	11.08%
600	50 Years	12.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.85. Further, an Excess Kurtosis of 24.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.74%	0	0.00%	0.00%
-15.74% to -8.33%	0	0.00%	0.00%
-8.33% to -0.92%	0	0.00%	0.00%
-0.92% to 6.50%	42	10.61%	10.61%
6.50% to 13.91%	210	53.03%	63.64%
13.91% to 21.32%	91	22.98%	86.62%
21.32% to 28.73%	30	7.58%	94.19%
28.73% to 36.15%	10	2.53%	96.72%
36.15% to 43.56%	7	1.77%	98.48%
Greater than 43.56%	6	1.52%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.03%	23.79%	90.66%	68.27%
±2σ	-5.86%	33.67%	95.96%	95.45%
±3σ	-15.74%	43.56%	98.48%	99.73%

Descriptive Statistics

Mean	13.909%
Standard Error	0.497%
Median	11.545%
Mode	5.072%
Standard Deviation	9.883%
Sample Variance	97.669%
Kurtosis	24.77
Skewness	3.85
Range	101.294%
Minimum	3.251%
Maximum	104.545%
Count	396

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.909%	396	100.00%	13.909%
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 1.40. Further, an Excess Kurtosis of 12.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.10%	1	0.25%	0.25%
-26.10% to -19.87%	3	0.76%	1.01%
-19.87% to -13.64%	12	3.03%	4.04%
-13.64% to -7.40%	61	15.40%	19.44%
-7.40% to -1.17%	132	33.33%	52.78%
-1.17% to 5.06%	117	29.55%	82.32%
5.06% to 11.29%	50	12.63%	94.95%
11.29% to 17.53%	13	3.28%	98.23%
17.53% to 23.76%	6	1.52%	99.75%
Greater than 23.76%	1	0.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.48%	7.14%	76.52%	68.27%
±2σ	-17.79%	15.45%	95.96%	95.45%
±3σ	-26.10%	23.76%	99.49%	99.73%

Descriptive Statistics

Mean	-1.172%
Standard Error	0.418%
Median	-1.668%
Mode	0.000%
Standard Deviation	8.310%
Sample Variance	69.048%
Kurtosis	12.76
Skewness	1.40
Range	104.786%
Minimum	-36.215%
Maximum	68.571%
Count	396

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.974%	161	40.66%	2.429%
Negative	-6.172%	231	58.33%	-3.600%
Zero	0.000%	4	1.01%	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 0.58 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -34.56%	1	0.76%	0.76%
-34.56% to -24.47%	0	0.00%	0.76%
-24.47% to -14.38%	5	3.79%	4.55%
-14.38% to -4.30%	24	18.18%	22.73%
-4.30% to 5.79%	38	28.79%	51.52%
5.79% to 15.88%	35	26.52%	78.03%
15.88% to 25.96%	16	12.12%	90.15%
25.96% to 36.05%	12	9.09%	99.24%
36.05% to 46.14%	0	0.00%	99.24%
Greater than 46.14%	1	0.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.66%	19.24%	70.45%	68.27%
±2σ	-21.11%	32.69%	96.97%	95.45%
±3σ	-34.56%	46.14%	98.48%	99.73%

Descriptive Statistics

Mean	5.790%
Standard Error	1.171%
Median	4.774%
Mode	-39.828%
Standard Deviation	13.450%
Sample Variance	180.913%
Kurtosis	0.58
Skewness	0.11
Range	87.397%
Minimum	-39.828%
Maximum	47.569%
Count	132

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.509%	90	68.18%	8.529%
Negative	-8.610%	42	31.82%	-2.740%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	14.06%
12	3 Years	13.97%
20	5 Years	15.93%
40	10 Years	18.35%
80	20 Years	19.70%
200	50 Years	22.85%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.24. Further, an Excess Kurtosis of 7.08 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.16%	0	0.00%	0.00%
-21.16% to -9.39%	0	0.00%	0.00%
-9.39% to 2.37%	0	0.00%	0.00%
2.37% to 14.14%	24	18.05%	18.05%
14.14% to 25.90%	63	47.37%	65.41%
25.90% to 37.67%	25	18.80%	84.21%
37.67% to 49.43%	11	8.27%	92.48%
49.43% to 61.20%	5	3.76%	96.24%
61.20% to 72.97%	3	2.26%	98.50%
Greater than 72.97%	2	1.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	10.22%	41.59%	85.71%	68.27%
±2σ	-5.47%	57.28%	95.49%	95.45%
±3σ	-21.16%	72.97%	98.50%	99.73%

Descriptive Statistics

Mean	25.904%
Standard Error	1.360%
Median	21.389%
Mode	6.850%
Standard Deviation	15.687%
Sample Variance	246.071%
Kurtosis	7.08
Skewness	2.24
Range	97.695%
Minimum	6.850%
Maximum	104.545%
Count	133

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.904%	133	100.00%	25.904%
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 1.23. Further, an Excess Kurtosis of 5.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -42.91%	0	0.00%	0.00%
-42.91% to -33.13%	0	0.00%	0.00%
-33.13% to -23.34%	3	2.26%	2.26%
-23.34% to -13.56%	27	20.30%	22.56%
-13.56% to -3.77%	41	30.83%	53.38%
-3.77% to 6.02%	36	27.07%	80.45%
6.02% to 15.80%	20	15.04%	95.49%
15.80% to 25.59%	4	3.01%	98.50%
25.59% to 35.37%	1	0.75%	99.25%
Greater than 35.37%	1	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.82%	9.28%	72.18%	68.27%
±2σ	-29.87%	22.33%	96.24%	95.45%
±3σ	-42.91%	35.37%	99.25%	99.73%

Descriptive Statistics

Mean	-3.770%
Standard Error	1.131%
Median	-4.733%
Mode	-31.948%
Standard Deviation	13.048%
Sample Variance	170.246%
Kurtosis	5.23
Skewness	1.23
Range	98.138%
Minimum	-31.948%
Maximum	66.190%
Count	133

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.048%	44	33.08%	3.324%
Negative	-10.601%	89	66.92%	-7.094%
Zero	0.000%	0	0.00%	0.000%

ORLY Deep Analytical Report