CRM - 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	2.62%	2.09%	2.23%	2.90%	3.08%	3.19%	179.55	190.94	174.11	196.91
Weekly	5.68%	5.40%	5.62%	7.05%	6.77%	7.03%	173.04	198.13	161.71	212.01
Monthly	11.04%	10.67%	10.58%	15.05%	14.09%	14.62%	160.82	213.19	139.68	245.45
Quarterly	20.87%	25.51%	20.68%	25.08%	24.41%	25.33%	145.05	236.36	113.63	301.71
Annual	—	—	—	—	48.82%	50.66%	113.63	301.71	69.74	491.62
Option Time Horizon	—	—	—	—	18.78%	19.49%	153.46	223.41	127.18	269.57

Calculation Notes: Computed at 2026-02-22T14:17 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $185.16 | Strike (K): $190.00 (first OTM call ≥ spot) | Observed Mid-Price: $12.1750 (Bid $11.9500 / Ask $12.4000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.89% | Binomial IV (Annual): 48.82% (CRR binomial tree, American, n=20 steps) | BS IV: 49.24% (European Black-Scholes) | Yahoo IV (Annual): 50.66% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2025-12-18	$0.4160
2025-09-17	$0.4160
2025-06-18	$0.4160
2025-04-10	$0.4160
2024-12-18	$0.4000
2024-09-18	$0.4000
2024-07-09	$0.4000
2024-03-13	$0.4000

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.35. 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 -7.75%	32	0.59%	0.59%
-7.75% to -5.79%	45	0.83%	1.41%
-5.79% to -3.82%	194	3.56%	4.97%
-3.82% to -1.86%	632	11.60%	16.57%
-1.86% to 0.10%	1883	34.55%	51.12%
0.10% to 2.07%	1815	33.30%	84.42%
2.07% to 4.03%	592	10.86%	95.28%
4.03% to 5.99%	154	2.83%	98.11%
5.99% to 7.96%	51	0.94%	99.05%
Greater than 7.96%	52	0.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.51%	2.72%	79.12%	68.27%
±2σ	-5.13%	5.34%	95.21%	95.45%
±3σ	-7.75%	7.96%	98.46%	99.73%

Descriptive Statistics

Mean	0.103%
Standard Error	0.035%
Median	0.056%
Mode	0.000%
Standard Deviation	2.618%
Sample Variance	6.852%
Kurtosis	10.03
Skewness	0.35
Range	53.193%
Minimum	-27.148%
Maximum	26.045%
Count	5450

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.832%	2791	51.21%	0.938%
Negative	-1.723%	2641	48.46%	-0.835%
Zero	0.000%	18	0.33%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.05%
20	1 Month	4.43%
60	1 Quarter	3.25%
250	1 Year	2.99%
750	3 Years	2.66%
1,250	5 Years	2.90%
2,500	10 Years	2.71%
5,000	20 Years	3.20%
12,500	50 Years	3.30%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.94. Further, an Excess Kurtosis of 42.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.15%	0	0.00%	0.00%
-3.15% to -1.58%	0	0.00%	0.00%
-1.58% to -0.01%	0	0.00%	0.00%
-0.01% to 1.55%	872	16.00%	16.00%
1.55% to 3.12%	2576	47.26%	63.25%
3.12% to 4.68%	1214	22.27%	85.53%
4.68% to 6.25%	439	8.05%	93.58%
6.25% to 7.82%	185	3.39%	96.97%
7.82% to 9.38%	71	1.30%	98.28%
Greater than 9.38%	94	1.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.03%	5.21%	86.19%	68.27%
±2σ	-1.06%	7.29%	96.28%	95.45%
±3σ	-3.15%	9.38%	98.28%	99.73%

Descriptive Statistics

Mean	3.117%
Standard Error	0.028%
Median	2.594%
Mode	1.694%
Standard Deviation	2.088%
Sample Variance	4.358%
Kurtosis	42.16
Skewness	3.94
Range	45.173%
Minimum	0.528%
Maximum	45.701%
Count	5451

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.117%	5451	100.00%	3.117%
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 0.86. Further, an Excess Kurtosis of 18.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.74%	34	0.62%	0.62%
-6.74% to -5.06%	67	1.23%	1.85%
-5.06% to -3.39%	163	2.99%	4.84%
-3.39% to -1.71%	656	12.03%	16.88%
-1.71% to -0.04%	1822	33.43%	50.30%
-0.04% to 1.64%	1808	33.17%	83.47%
1.64% to 3.32%	615	11.28%	94.75%
3.32% to 4.99%	189	3.47%	98.22%
4.99% to 6.67%	63	1.16%	99.38%
Greater than 6.67%	34	0.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.27%	2.20%	77.91%	68.27%
±2σ	-4.50%	4.43%	94.99%	95.45%
±3σ	-6.74%	6.67%	98.75%	99.73%

Descriptive Statistics

Mean	-0.035%
Standard Error	0.030%
Median	-0.047%
Mode	0.000%
Standard Deviation	2.234%
Sample Variance	4.993%
Kurtosis	18.65
Skewness	0.86
Range	50.929%
Minimum	-13.322%
Maximum	37.607%
Count	5451

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.554%	2637	48.38%	0.752%
Negative	-1.537%	2791	51.20%	-0.787%
Zero	0.000%	23	0.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.44. Further, an Excess Kurtosis of 3.18 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.54%	5	0.44%	0.44%
-16.54% to -12.28%	17	1.50%	1.95%
-12.28% to -8.02%	37	3.27%	5.22%
-8.02% to -3.76%	152	13.45%	18.67%
-3.76% to 0.50%	352	31.15%	49.82%
0.50% to 4.76%	371	32.83%	82.65%
4.76% to 9.02%	128	11.33%	93.98%
9.02% to 13.28%	49	4.34%	98.32%
13.28% to 17.54%	10	0.88%	99.20%
Greater than 17.54%	9	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.18%	6.18%	75.75%	68.27%
±2σ	-10.86%	11.86%	94.51%	95.45%
±3σ	-16.54%	17.54%	98.76%	99.73%

Descriptive Statistics

Mean	0.500%
Standard Error	0.169%
Median	0.521%
Mode	0.605%
Standard Deviation	5.681%
Sample Variance	32.278%
Kurtosis	3.18
Skewness	0.44
Range	51.818%
Minimum	-21.026%
Maximum	30.792%
Count	1130

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.242%	616	54.51%	2.312%
Negative	-3.985%	514	45.49%	-1.813%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	9.88%
12	1 Quarter	8.10%
52	1 Year	7.17%
156	3 Years	6.53%
260	5 Years	7.05%
520	10 Years	6.47%
1,040	20 Years	7.58%
2,600	50 Years	7.87%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.25. Further, an Excess Kurtosis of 7.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.99%	0	0.00%	0.00%
-7.99% to -3.93%	0	0.00%	0.00%
-3.93% to 0.12%	0	0.00%	0.00%
0.12% to 4.17%	211	18.66%	18.66%
4.17% to 8.22%	505	44.65%	63.31%
8.22% to 12.27%	231	20.42%	83.73%
12.27% to 16.32%	102	9.02%	92.75%
16.32% to 20.37%	47	4.16%	96.91%
20.37% to 24.42%	11	0.97%	97.88%
Greater than 24.42%	24	2.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.82%	13.62%	84.08%	68.27%
±2σ	-2.58%	19.02%	95.93%	95.45%
±3σ	-7.98%	24.42%	97.88%	99.73%

Descriptive Statistics

Mean	8.218%
Standard Error	0.161%
Median	6.759%
Mode	6.573%
Standard Deviation	5.401%
Sample Variance	29.174%
Kurtosis	7.78
Skewness	2.25
Range	45.159%
Minimum	1.266%
Maximum	46.425%
Count	1131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.218%	1131	100.00%	8.218%
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 0.41. Further, an Excess Kurtosis of 2.94 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.02%	6	0.53%	0.53%
-17.02% to -12.80%	8	0.71%	1.24%
-12.80% to -8.59%	48	4.24%	5.48%
-8.59% to -4.38%	144	12.73%	18.21%
-4.38% to -0.17%	393	34.75%	52.96%
-0.17% to 4.04%	332	29.35%	82.32%
4.04% to 8.25%	135	11.94%	94.25%
8.25% to 12.46%	37	3.27%	97.52%
12.46% to 16.67%	18	1.59%	99.12%
Greater than 16.67%	10	0.88%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.79%	5.44%	75.95%	68.27%
±2σ	-11.40%	11.06%	94.43%	95.45%
±3σ	-17.02%	16.67%	98.59%	99.73%

Descriptive Statistics

Mean	-0.171%
Standard Error	0.167%
Median	-0.446%
Mode	-6.578%
Standard Deviation	5.615%
Sample Variance	31.531%
Kurtosis	2.94
Skewness	0.41
Range	51.291%
Minimum	-24.799%
Maximum	26.492%
Count	1131

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.329%	507	44.83%	1.941%
Negative	-3.839%	622	55.00%	-2.111%
Zero	0.000%	2	0.18%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.42. Further, an Excess Kurtosis of 1.02 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -31.05%	1	0.38%	0.38%
-31.05% to -22.77%	0	0.00%	0.38%
-22.77% to -14.49%	12	4.62%	5.00%
-14.49% to -6.20%	45	17.31%	22.31%
-6.20% to 2.08%	79	30.38%	52.69%
2.08% to 10.36%	71	27.31%	80.00%
10.36% to 18.64%	34	13.08%	93.08%
18.64% to 26.92%	10	3.85%	96.92%
26.92% to 35.20%	6	2.31%	99.23%
Greater than 35.20%	2	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.96%	13.12%	71.15%	68.27%
±2σ	-20.01%	24.16%	95.77%	95.45%
±3σ	-31.05%	35.20%	98.85%	99.73%

Descriptive Statistics

Mean	2.077%
Standard Error	0.685%
Median	1.382%
Mode	7.928%
Standard Deviation	11.042%
Sample Variance	121.918%
Kurtosis	1.02
Skewness	0.42
Range	76.296%
Minimum	-36.033%
Maximum	40.263%
Count	260

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.425%	146	56.15%	5.293%
Negative	-7.332%	114	43.85%	-3.215%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	19.03%
12	1 Year	14.13%
36	3 Years	14.34%
60	5 Years	15.05%
120	10 Years	13.82%
240	20 Years	16.25%
600	50 Years	17.06%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.14%	0	0.00%	0.00%
-13.14% to -5.14%	0	0.00%	0.00%
-5.14% to 2.87%	0	0.00%	0.00%
2.87% to 10.87%	54	20.69%	20.69%
10.87% to 18.88%	103	39.46%	60.15%
18.88% to 26.88%	60	22.99%	83.14%
26.88% to 34.88%	24	9.20%	92.34%
34.88% to 42.89%	11	4.21%	96.55%
42.89% to 50.89%	5	1.92%	98.47%
Greater than 50.89%	4	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.20%	29.55%	79.69%	68.27%
±2σ	-2.47%	40.22%	96.17%	95.45%
±3σ	-13.14%	50.89%	98.47%	99.73%

Descriptive Statistics

Mean	18.875%
Standard Error	0.661%
Median	16.210%
Mode	11.123%
Standard Deviation	10.672%
Sample Variance	113.898%
Kurtosis	12.35
Skewness	2.49
Range	93.925%
Minimum	4.845%
Maximum	98.770%
Count	261

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.875%	261	100.00%	18.875%
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 0.52. Further, an Excess Kurtosis of 2.36 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.69%	0	0.00%	0.00%
-32.69% to -24.75%	4	1.53%	1.53%
-24.75% to -16.82%	9	3.45%	4.98%
-16.82% to -8.88%	43	16.48%	21.46%
-8.88% to -0.94%	76	29.12%	50.57%
-0.94% to 7.00%	76	29.12%	79.69%
7.00% to 14.94%	35	13.41%	93.10%
14.94% to 22.87%	15	5.75%	98.85%
22.87% to 30.81%	2	0.77%	99.62%
Greater than 30.81%	1	0.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.53%	9.64%	71.26%	68.27%
±2σ	-22.11%	20.23%	95.40%	95.45%
±3σ	-32.69%	30.81%	99.62%	99.73%

Descriptive Statistics

Mean	-0.941%
Standard Error	0.655%
Median	-1.387%
Mode	-2.567%
Standard Deviation	10.584%
Sample Variance	112.029%
Kurtosis	2.36
Skewness	0.52
Range	82.722%
Minimum	-28.458%
Maximum	54.264%
Count	261

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.399%	111	42.53%	3.572%
Negative	-7.852%	150	57.47%	-4.513%
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 0.56. Further, an Excess Kurtosis of 1.19 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.83%	0	0.00%	0.00%
-55.83% to -40.18%	1	1.15%	1.15%
-40.18% to -24.53%	2	2.30%	3.45%
-24.53% to -8.88%	15	17.24%	20.69%
-8.88% to 6.78%	30	34.48%	55.17%
6.78% to 22.43%	26	29.89%	85.06%
22.43% to 38.08%	6	6.90%	91.95%
38.08% to 53.73%	3	3.45%	95.40%
53.73% to 69.39%	4	4.60%	100.00%
Greater than 69.39%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.09%	27.65%	74.71%	68.27%
±2σ	-34.96%	48.52%	93.10%	95.45%
±3σ	-55.83%	69.39%	100.00%	99.73%

Descriptive Statistics

Mean	6.777%
Standard Error	2.238%
Median	5.434%
Mode	-51.466%
Standard Deviation	20.870%
Sample Variance	435.573%
Kurtosis	1.19
Skewness	0.56
Range	115.732%
Minimum	-51.466%
Maximum	64.266%
Count	87

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.518%	57	65.52%	11.477%
Negative	-13.629%	30	34.48%	-4.700%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	17.86%
12	3 Years	24.24%
20	5 Years	25.08%
40	10 Years	23.33%
80	20 Years	28.42%
200	50 Years	30.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.45. Further, an Excess Kurtosis of 17.32 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.88%	0	0.00%	0.00%
-39.88% to -20.75%	0	0.00%	0.00%
-20.75% to -1.62%	0	0.00%	0.00%
-1.62% to 17.51%	10	11.36%	11.36%
17.51% to 36.64%	47	53.41%	64.77%
36.64% to 55.77%	20	22.73%	87.50%
55.77% to 74.90%	7	7.95%	95.45%
74.90% to 94.03%	2	2.27%	97.73%
94.03% to 113.16%	0	0.00%	97.73%
Greater than 113.16%	2	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.13%	62.14%	87.50%	68.27%
±2σ	-14.38%	87.65%	97.73%	95.45%
±3σ	-39.88%	113.16%	97.73%	99.73%

Descriptive Statistics

Mean	36.638%
Standard Error	2.719%
Median	29.425%
Mode	10.269%
Standard Deviation	25.507%
Sample Variance	650.606%
Kurtosis	17.32
Skewness	3.45
Range	183.665%
Minimum	10.269%
Maximum	193.934%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.638%	88	100.00%	36.638%
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 1.80. Further, an Excess Kurtosis of 8.20 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.34%	0	0.00%	0.00%
-64.34% to -48.82%	0	0.00%	0.00%
-48.82% to -33.31%	5	5.68%	5.68%
-33.31% to -17.80%	9	10.23%	15.91%
-17.80% to -2.29%	37	42.05%	57.95%
-2.29% to 13.22%	23	26.14%	84.09%
13.22% to 28.73%	9	10.23%	94.32%
28.73% to 44.24%	3	3.41%	97.73%
44.24% to 59.76%	1	1.14%	98.86%
Greater than 59.76%	1	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.97%	18.39%	80.68%	68.27%
±2σ	-43.65%	39.07%	97.73%	95.45%
±3σ	-64.34%	59.76%	98.86%	99.73%

Descriptive Statistics

Mean	-2.290%
Standard Error	2.205%
Median	-5.169%
Mode	-39.099%
Standard Deviation	20.682%
Sample Variance	427.743%
Kurtosis	8.20
Skewness	1.80
Range	146.237%
Minimum	-39.099%
Maximum	107.138%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.823%	33	37.50%	6.309%
Negative	-13.758%	55	62.50%	-8.599%
Zero	0.000%	0	0.00%	0.000%

CRM Deep Analytical Report