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%	2.92%	2.36%	2.45%	189.23	198.37	184.82	203.11
Weekly	5.68%	5.39%	5.62%	7.11%	5.19%	5.40%	183.95	204.07	174.64	214.95
Monthly	11.00%	10.68%	10.54%	15.08%	10.81%	11.24%	173.90	215.86	156.09	240.49
Quarterly	20.83%	25.48%	20.64%	25.21%	18.72%	19.46%	160.68	233.63	133.25	281.72
Annual	—	—	—	—	37.43%	38.92%	133.25	281.72	91.64	409.62
Option Time Horizon	—	—	—	—	14.13%	14.69%	168.22	223.15	146.06	257.02

Calculation Notes: Computed at 2026-03-23T16:31 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $193.75 | Strike (K): $195.00 (first OTM call ≥ spot) | Observed Mid-Price: $10.6500 (Bid $10.3500 / Ask $10.9500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.85% | Binomial IV (Annual): 37.43% (CRR binomial tree, American, n=20 steps) | BS IV: 37.31% (European Black-Scholes) | Yahoo IV (Annual): 38.92% → 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 10.00 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	0.58%	0.58%
-7.75% to -5.78%	45	0.82%	1.41%
-5.78% to -3.82%	194	3.55%	4.95%
-3.82% to -1.86%	636	11.62%	16.58%
-1.86% to 0.10%	1891	34.56%	51.14%
0.10% to 2.07%	1818	33.23%	84.37%
2.07% to 4.03%	596	10.89%	95.27%
4.03% to 5.99%	156	2.85%	98.12%
5.99% to 7.96%	51	0.93%	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%	79.07%	68.27%
±2σ	-5.13%	5.34%	95.23%	95.45%
±3σ	-7.75%	7.96%	98.46%	99.73%

Descriptive Statistics

Mean	0.104%
Standard Error	0.035%
Median	0.056%
Mode	0.000%
Standard Deviation	2.617%
Sample Variance	6.848%
Kurtosis	10.00
Skewness	0.35
Range	53.193%
Minimum	-27.148%
Maximum	26.045%
Count	5471

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.834%	2801	51.20%	0.939%
Negative	-1.723%	2652	48.47%	-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	3.09%
20	1 Month	4.13%
60	1 Quarter	3.80%
250	1 Year	3.07%
750	3 Years	2.69%
1,250	5 Years	2.92%
2,500	10 Years	2.73%
5,000	20 Years	3.21%
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 3.93. Further, an Excess Kurtosis of 42.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.14%	0	0.00%	0.00%
-3.14% to -1.57%	0	0.00%	0.00%
-1.57% to -0.01%	0	0.00%	0.00%
-0.01% to 1.56%	883	16.14%	16.14%
1.56% to 3.12%	2575	47.06%	63.19%
3.12% to 4.68%	1218	22.26%	85.45%
4.68% to 6.25%	445	8.13%	93.59%
6.25% to 7.81%	186	3.40%	96.98%
7.81% 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%	86.11%	68.27%
±2σ	-1.05%	7.29%	96.29%	95.45%
±3σ	-3.14%	9.38%	98.28%	99.73%

Descriptive Statistics

Mean	3.120%
Standard Error	0.028%
Median	2.599%
Mode	1.694%
Standard Deviation	2.086%
Sample Variance	4.352%
Kurtosis	42.10
Skewness	3.93
Range	45.173%
Minimum	0.528%
Maximum	45.701%
Count	5472

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.120%	5472	100.00%	3.120%
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 18.59 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	1.22%	1.85%
-5.06% to -3.39%	166	3.03%	4.88%
-3.39% to -1.71%	655	11.97%	16.85%
-1.71% to -0.04%	1830	33.44%	50.29%
-0.04% to 1.64%	1816	33.19%	83.48%
1.64% to 3.31%	616	11.26%	94.74%
3.31% to 4.99%	191	3.49%	98.23%
4.99% to 6.67%	63	1.15%	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%	77.87%	68.27%
±2σ	-4.50%	4.43%	94.99%	95.45%
±3σ	-6.74%	6.67%	98.76%	99.73%

Descriptive Statistics

Mean	-0.037%
Standard Error	0.030%
Median	-0.049%
Mode	0.000%
Standard Deviation	2.234%
Sample Variance	4.991%
Kurtosis	18.59
Skewness	0.86
Range	50.929%
Minimum	-13.322%
Maximum	37.607%
Count	5472

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.554%	2645	48.34%	0.751%
Negative	-1.539%	2804	51.24%	-0.789%
Zero	0.000%	23	0.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.43. Further, an Excess Kurtosis of 3.17 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%	1.94%
-12.28% to -8.02%	37	3.26%	5.20%
-8.02% to -3.76%	153	13.49%	18.69%
-3.76% to 0.50%	353	31.13%	49.82%
0.50% to 4.76%	372	32.80%	82.63%
4.76% to 9.02%	129	11.38%	94.00%
9.02% to 13.28%	49	4.32%	98.32%
13.28% to 17.54%	10	0.88%	99.21%
Greater than 17.54%	9	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.18%	6.18%	75.66%	68.27%
±2σ	-10.86%	11.86%	94.44%	95.45%
±3σ	-16.54%	17.54%	98.77%	99.73%

Descriptive Statistics

Mean	0.503%
Standard Error	0.169%
Median	0.521%
Mode	0.605%
Standard Deviation	5.680%
Sample Variance	32.262%
Kurtosis	3.17
Skewness	0.43
Range	51.818%
Minimum	-21.026%
Maximum	30.792%
Count	1134

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.247%	618	54.50%	2.314%
Negative	-3.982%	516	45.50%	-1.812%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.80%
12	1 Quarter	9.02%
52	1 Year	7.39%
156	3 Years	6.53%
260	5 Years	7.11%
520	10 Years	6.51%
1,040	20 Years	7.59%
2,600	50 Years	7.88%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.96%	0	0.00%	0.00%
-7.96% to -3.91%	0	0.00%	0.00%
-3.91% to 0.13%	0	0.00%	0.00%
0.13% to 4.18%	214	18.85%	18.85%
4.18% to 8.22%	504	44.41%	63.26%
8.22% to 12.27%	232	20.44%	83.70%
12.27% to 16.32%	103	9.07%	92.78%
16.32% to 20.36%	47	4.14%	96.92%
20.36% to 24.41%	11	0.97%	97.89%
Greater than 24.41%	24	2.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.83%	13.62%	84.05%	68.27%
±2σ	-2.56%	19.02%	95.95%	95.45%
±3σ	-7.96%	24.41%	97.89%	99.73%

Descriptive Statistics

Mean	8.225%
Standard Error	0.160%
Median	6.766%
Mode	6.573%
Standard Deviation	5.395%
Sample Variance	29.105%
Kurtosis	7.79
Skewness	2.25
Range	45.159%
Minimum	1.266%
Maximum	46.425%
Count	1135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.225%	1135	100.00%	8.225%
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 2.93 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 -12.81%	8	0.70%	1.23%
-12.81% to -8.60%	48	4.23%	5.46%
-8.60% to -4.39%	145	12.78%	18.24%
-4.39% to -0.17%	394	34.71%	52.95%
-0.17% to 4.04%	333	29.34%	82.29%
4.04% to 8.25%	136	11.98%	94.27%
8.25% to 12.46%	37	3.26%	97.53%
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%	75.77%	68.27%
±2σ	-11.41%	11.05%	94.45%	95.45%
±3σ	-17.02%	16.67%	98.59%	99.73%

Descriptive Statistics

Mean	-0.175%
Standard Error	0.167%
Median	-0.456%
Mode	-7.935%
Standard Deviation	5.615%
Sample Variance	31.531%
Kurtosis	2.93
Skewness	0.41
Range	51.291%
Minimum	-24.799%
Maximum	26.492%
Count	1135

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.334%	508	44.76%	1.940%
Negative	-3.841%	625	55.07%	-2.115%
Zero	0.000%	2	0.18%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.43. Further, an Excess Kurtosis of 1.05 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.92%	1	0.38%	0.38%
-30.92% to -22.67%	0	0.00%	0.38%
-22.67% to -14.42%	12	4.60%	4.98%
-14.42% to -6.17%	45	17.24%	22.22%
-6.17% to 2.08%	80	30.65%	52.87%
2.08% to 10.34%	70	26.82%	79.69%
10.34% to 18.59%	35	13.41%	93.10%
18.59% to 26.84%	10	3.83%	96.93%
26.84% to 35.09%	6	2.30%	99.23%
Greater than 35.09%	2	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.92%	13.09%	71.26%	68.27%
±2σ	-19.92%	24.09%	95.79%	95.45%
±3σ	-30.92%	35.09%	98.85%	99.73%

Descriptive Statistics

Mean	2.084%
Standard Error	0.681%
Median	1.362%
Mode	7.928%
Standard Deviation	11.002%
Sample Variance	121.039%
Kurtosis	1.05
Skewness	0.43
Range	76.296%
Minimum	-36.033%
Maximum	40.263%
Count	261

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.425%	146	55.94%	5.272%
Negative	-7.235%	115	44.06%	-3.188%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.65%
12	1 Year	13.80%
36	3 Years	14.00%
60	5 Years	15.08%
120	10 Years	13.82%
240	20 Years	16.23%
600	50 Years	17.03%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.48. Further, an Excess Kurtosis of 12.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.19%	0	0.00%	0.00%
-13.19% to -5.18%	0	0.00%	0.00%
-5.18% to 2.83%	0	0.00%	0.00%
2.83% to 10.84%	55	20.99%	20.99%
10.84% to 18.85%	103	39.31%	60.31%
18.85% to 26.86%	60	22.90%	83.21%
26.86% to 34.87%	23	8.78%	91.98%
34.87% to 42.87%	12	4.58%	96.56%
42.87% to 50.88%	5	1.91%	98.47%
Greater than 50.88%	4	1.53%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.17%	29.53%	79.77%	68.27%
±2σ	-2.51%	40.20%	96.18%	95.45%
±3σ	-13.19%	50.88%	98.47%	99.73%

Descriptive Statistics

Mean	18.849%
Standard Error	0.660%
Median	16.189%
Mode	11.123%
Standard Deviation	10.678%
Sample Variance	114.011%
Kurtosis	12.29
Skewness	2.48
Range	93.925%
Minimum	4.845%
Maximum	98.770%
Count	262

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.849%	262	100.00%	18.849%
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 2.43 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -32.57%	0	0.00%	0.00%
-32.57% to -24.66%	4	1.53%	1.53%
-24.66% to -16.76%	9	3.44%	4.96%
-16.76% to -8.86%	43	16.41%	21.37%
-8.86% to -0.96%	76	29.01%	50.38%
-0.96% to 6.94%	77	29.39%	79.77%
6.94% to 14.84%	36	13.74%	93.51%
14.84% to 22.74%	14	5.34%	98.85%
22.74% to 30.64%	2	0.76%	99.62%
Greater than 30.64%	1	0.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.50%	9.57%	70.99%	68.27%
±2σ	-22.03%	20.11%	95.42%	95.45%
±3σ	-32.57%	30.64%	99.62%	99.73%

Descriptive Statistics

Mean	-0.961%
Standard Error	0.651%
Median	-1.341%
Mode	-2.567%
Standard Deviation	10.535%
Sample Variance	110.993%
Kurtosis	2.43
Skewness	0.52
Range	82.722%
Minimum	-28.458%
Maximum	54.264%
Count	262

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.347%	111	42.37%	3.536%
Negative	-7.803%	151	57.63%	-4.497%
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 1.21 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.67%	0	0.00%	0.00%
-55.67% to -40.05%	1	1.15%	1.15%
-40.05% to -24.43%	2	2.30%	3.45%
-24.43% to -8.80%	15	17.24%	20.69%
-8.80% to 6.82%	30	34.48%	55.17%
6.82% to 22.45%	26	29.89%	85.06%
22.45% to 38.07%	6	6.90%	91.95%
38.07% to 53.70%	3	3.45%	95.40%
53.70% to 69.32%	4	4.60%	100.00%
Greater than 69.32%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.01%	27.66%	73.56%	68.27%
±2σ	-34.84%	48.49%	93.10%	95.45%
±3σ	-55.67%	69.32%	100.00%	99.73%

Descriptive Statistics

Mean	6.823%
Standard Error	2.233%
Median	5.434%
Mode	-51.466%
Standard Deviation	20.832%
Sample Variance	433.965%
Kurtosis	1.21
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	-13.498%	30	34.48%	-4.655%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.52%
12	3 Years	24.46%
20	5 Years	25.21%
40	10 Years	23.39%
80	20 Years	28.45%
200	50 Years	30.29%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.46. Further, an Excess Kurtosis of 17.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.76%	0	0.00%	0.00%
-39.76% to -20.65%	0	0.00%	0.00%
-20.65% to -1.54%	0	0.00%	0.00%
-1.54% to 17.57%	10	11.36%	11.36%
17.57% to 36.68%	47	53.41%	64.77%
36.68% to 55.79%	20	22.73%	87.50%
55.79% to 74.91%	7	7.95%	95.45%
74.91% to 94.02%	2	2.27%	97.73%
94.02% to 113.13%	0	0.00%	97.73%
Greater than 113.13%	2	2.27%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.20%	62.16%	87.50%	68.27%
±2σ	-14.28%	87.65%	97.73%	95.45%
±3σ	-39.76%	113.13%	97.73%	99.73%

Descriptive Statistics

Mean	36.683%
Standard Error	2.716%
Median	29.425%
Mode	10.269%
Standard Deviation	25.482%
Sample Variance	649.315%
Kurtosis	17.37
Skewness	3.46
Range	183.665%
Minimum	10.269%
Maximum	193.934%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.683%	88	100.00%	36.683%
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 1.82. Further, an Excess Kurtosis of 8.31 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -64.26%	0	0.00%	0.00%
-64.26% to -48.78%	0	0.00%	0.00%
-48.78% to -33.31%	5	5.68%	5.68%
-33.31% to -17.83%	9	10.23%	15.91%
-17.83% to -2.35%	37	42.05%	57.95%
-2.35% to 13.13%	23	26.14%	84.09%
13.13% to 28.61%	9	10.23%	94.32%
28.61% to 44.09%	3	3.41%	97.73%
44.09% to 59.57%	1	1.14%	98.86%
Greater than 59.57%	1	1.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.99%	18.29%	79.55%	68.27%
±2σ	-43.62%	38.93%	97.73%	95.45%
±3σ	-64.26%	59.57%	98.86%	99.73%

Descriptive Statistics

Mean	-2.347%
Standard Error	2.200%
Median	-5.169%
Mode	-39.099%
Standard Deviation	20.639%
Sample Variance	425.957%
Kurtosis	8.31
Skewness	1.82
Range	146.237%
Minimum	-39.099%
Maximum	107.138%
Count	88

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.672%	33	37.50%	6.252%
Negative	-13.758%	55	62.50%	-8.599%
Zero	0.000%	0	0.00%	0.000%

CRM Deep Analytical Report