META - 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	2.50%	1.55%	1.81%	3.20%	2.65%	2.69%	585.54	617.45	570.21	634.06
Weekly	5.37%	5.22%	5.52%	7.77%	5.84%	5.93%	567.17	637.46	534.99	675.80
Monthly	10.89%	11.27%	11.52%	17.12%	12.16%	12.34%	532.44	679.03	471.48	766.83
Quarterly	20.10%	21.67%	22.99%	34.83%	21.06%	21.37%	487.09	742.25	394.58	916.26
Annual	—	—	—	—	42.12%	42.75%	394.58	916.26	258.94	1396.25
Option Time Horizon	—	—	—	—	15.90%	16.14%	512.90	704.91	437.50	826.38

Calculation Notes: Computed at 2026-03-23T16:30 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $601.28 | Strike (K): $605.00 (first OTM call ≥ spot) | Observed Mid-Price: $37.5250 (Bid $37.3500 / Ask $37.7000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.35% | Binomial IV (Annual): 42.12% (CRR binomial tree, American, n=20 steps) | BS IV: 41.93% (European Black-Scholes) | Yahoo IV (Annual): 42.75% → 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
2026-03-16	$0.5250
2025-12-15	$0.5250
2025-09-22	$0.5250
2025-06-16	$0.5250
2025-03-14	$0.5250
2024-12-16	$0.5000
2024-09-16	$0.5000
2024-06-14	$0.5000
2024-02-21	$0.5000

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.44. Further, an Excess Kurtosis of 20.23 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.39%	21	0.60%	0.60%
-7.39% to -5.51%	29	0.83%	1.44%
-5.51% to -3.64%	120	3.45%	4.89%
-3.64% to -1.76%	345	9.92%	14.80%
-1.76% to 0.11%	1244	35.76%	50.56%
0.11% to 1.99%	1203	34.58%	85.14%
1.99% to 3.86%	375	10.78%	95.92%
3.86% to 5.73%	90	2.59%	98.51%
5.73% to 7.61%	27	0.78%	99.28%
Greater than 7.61%	25	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.39%	2.61%	80.91%	68.27%
±2σ	-4.89%	5.11%	95.77%	95.45%
±3σ	-7.39%	7.61%	98.68%	99.73%

Descriptive Statistics

Mean	0.111%
Standard Error	0.042%
Median	0.095%
Mode	0.000%
Standard Deviation	2.499%
Sample Variance	6.245%
Kurtosis	20.23
Skewness	0.44
Range	56.001%
Minimum	-26.390%
Maximum	29.611%
Count	3479

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.664%	1816	52.20%	0.869%
Negative	-1.597%	1651	47.46%	-0.758%
Zero	0.000%	12	0.34%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.31%
20	1 Month	2.75%
60	1 Quarter	2.85%
250	1 Year	2.91%
750	3 Years	2.87%
1,250	5 Years	3.20%
2,500	10 Years	2.84%
5,000	20 Years	2.94%
12,500	50 Years	2.94%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -1.95%	0	0.00%	0.00%
-1.95% to -0.79%	0	0.00%	0.00%
-0.79% to 0.37%	0	0.00%	0.00%
0.37% to 1.53%	686	19.71%	19.71%
1.53% to 2.69%	1454	41.78%	61.49%
2.69% to 3.85%	766	22.01%	83.51%
3.85% to 5.01%	320	9.20%	92.70%
5.01% to 6.17%	137	3.94%	96.64%
6.17% to 7.34%	60	1.72%	98.36%
Greater than 7.34%	57	1.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.14%	4.24%	79.02%	68.27%
±2σ	-0.40%	5.79%	95.92%	95.45%
±3σ	-1.95%	7.34%	98.36%	99.73%

Descriptive Statistics

Mean	2.692%
Standard Error	0.026%
Median	2.337%
Mode	2.173%
Standard Deviation	1.548%
Sample Variance	2.396%
Kurtosis	10.12
Skewness	2.24
Range	18.049%
Minimum	0.372%
Maximum	18.421%
Count	3480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.692%	3480	100.00%	2.692%
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 0.16. Further, an Excess Kurtosis of 2.91 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.41%	16	0.46%	0.46%
-5.41% to -4.06%	42	1.21%	1.67%
-4.06% to -2.70%	120	3.45%	5.11%
-2.70% to -1.35%	502	14.43%	19.54%
-1.35% to 0.01%	1096	31.49%	51.03%
0.01% to 1.36%	1055	30.32%	81.35%
1.36% to 2.72%	429	12.33%	93.68%
2.72% to 4.07%	146	4.20%	97.87%
4.07% to 5.43%	44	1.26%	99.14%
Greater than 5.43%	30	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.80%	1.81%	75.00%	68.27%
±2σ	-3.60%	3.62%	94.80%	95.45%
±3σ	-5.41%	5.43%	98.68%	99.73%

Descriptive Statistics

Mean	0.008%
Standard Error	0.031%
Median	-0.028%
Mode	0.000%
Standard Deviation	1.806%
Sample Variance	3.261%
Kurtosis	2.91
Skewness	0.16
Range	23.052%
Minimum	-13.060%
Maximum	9.992%
Count	3480

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.355%	1708	49.08%	0.665%
Negative	-1.295%	1766	50.75%	-0.657%
Zero	0.000%	6	0.17%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.08. Further, an Excess Kurtosis of 5.98 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.57%	5	0.69%	0.69%
-15.57% to -11.54%	9	1.25%	1.94%
-11.54% to -7.51%	16	2.22%	4.16%
-7.51% to -3.48%	96	13.30%	17.45%
-3.48% to 0.55%	240	33.24%	50.69%
0.55% to 4.57%	238	32.96%	83.66%
4.57% to 8.60%	81	11.22%	94.88%
8.60% to 12.63%	21	2.91%	97.78%
12.63% to 16.66%	12	1.66%	99.45%
Greater than 16.66%	4	0.55%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.83%	5.92%	78.53%	68.27%
±2σ	-10.20%	11.29%	95.01%	95.45%
±3σ	-15.57%	16.66%	98.75%	99.73%

Descriptive Statistics

Mean	0.545%
Standard Error	0.200%
Median	0.518%
Mode	-0.900%
Standard Deviation	5.371%
Sample Variance	28.848%
Kurtosis	5.98
Skewness	0.08
Range	64.211%
Minimum	-28.203%
Maximum	36.008%
Count	722

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.888%	403	55.82%	2.170%
Negative	-3.678%	319	44.18%	-1.625%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.94%
12	1 Quarter	7.29%
52	1 Year	7.08%
156	3 Years	6.93%
260	5 Years	7.77%
520	10 Years	6.85%
1,040	20 Years	7.14%
2,600	50 Years	7.14%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.12. Further, an Excess Kurtosis of 15.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.19%	0	0.00%	0.00%
-8.19% to -4.28%	0	0.00%	0.00%
-4.28% to -0.36%	0	0.00%	0.00%
-0.36% to 3.55%	110	15.21%	15.21%
3.55% to 7.46%	345	47.72%	62.93%
7.46% to 11.38%	170	23.51%	86.45%
11.38% to 15.29%	61	8.44%	94.88%
15.29% to 19.20%	11	1.52%	96.40%
19.20% to 23.11%	12	1.66%	98.06%
Greater than 23.11%	14	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.25%	12.68%	88.24%	68.27%
±2σ	-2.97%	17.90%	95.85%	95.45%
±3σ	-8.19%	23.11%	98.06%	99.73%

Descriptive Statistics

Mean	7.462%
Standard Error	0.194%
Median	6.205%
Mode	4.188%
Standard Deviation	5.217%
Sample Variance	27.222%
Kurtosis	15.47
Skewness	3.12
Range	48.139%
Minimum	1.267%
Maximum	49.406%
Count	723

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.462%	723	100.00%	7.462%
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 1.43. Further, an Excess Kurtosis of 10.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.69%	2	0.28%	0.28%
-16.69% to -12.55%	4	0.55%	0.83%
-12.55% to -8.41%	18	2.49%	3.32%
-8.41% to -4.26%	97	13.42%	16.74%
-4.26% to -0.12%	266	36.79%	53.53%
-0.12% to 4.02%	215	29.74%	83.26%
4.02% to 8.16%	90	12.45%	95.71%
8.16% to 12.31%	14	1.94%	97.65%
12.31% to 16.45%	8	1.11%	98.76%
Greater than 16.45%	9	1.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.64%	5.40%	79.11%	68.27%
±2σ	-11.17%	10.93%	95.44%	95.45%
±3σ	-16.69%	16.45%	98.48%	99.73%

Descriptive Statistics

Mean	-0.121%
Standard Error	0.205%
Median	-0.434%
Mode	-3.698%
Standard Deviation	5.524%
Sample Variance	30.515%
Kurtosis	10.01
Skewness	1.43
Range	66.823%
Minimum	-26.334%
Maximum	40.489%
Count	723

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.086%	322	44.54%	1.820%
Negative	-3.508%	400	55.33%	-1.941%
Zero	0.000%	1	0.14%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.25. Further, an Excess Kurtosis of 2.45 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -30.26%	2	1.20%	1.20%
-30.26% to -22.09%	1	0.60%	1.81%
-22.09% to -13.92%	3	1.81%	3.61%
-13.92% to -5.75%	25	15.06%	18.67%
-5.75% to 2.42%	61	36.75%	55.42%
2.42% to 10.59%	46	27.71%	83.13%
10.59% to 18.76%	18	10.84%	93.98%
18.76% to 26.94%	7	4.22%	98.19%
26.94% to 35.11%	2	1.20%	99.40%
Greater than 35.11%	1	0.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.47%	13.32%	74.70%	68.27%
±2σ	-19.37%	24.21%	95.18%	95.45%
±3σ	-30.26%	35.11%	98.19%	99.73%

Descriptive Statistics

Mean	2.422%
Standard Error	0.846%
Median	1.774%
Mode	-32.634%
Standard Deviation	10.895%
Sample Variance	118.707%
Kurtosis	2.45
Skewness	0.25
Range	80.544%
Minimum	-32.634%
Maximum	47.910%
Count	166

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.645%	101	60.84%	5.260%
Negative	-7.246%	65	39.16%	-2.837%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	16.06%
12	1 Year	14.43%
36	3 Years	15.04%
60	5 Years	17.12%
120	10 Years	15.10%
240	20 Years	15.86%
600	50 Years	15.86%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.14. Further, an Excess Kurtosis of 6.25 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.10%	0	0.00%	0.00%
-16.10% to -7.64%	0	0.00%	0.00%
-7.64% to 0.81%	0	0.00%	0.00%
0.81% to 9.27%	32	19.16%	19.16%
9.27% to 17.72%	70	41.92%	61.08%
17.72% to 26.18%	42	25.15%	86.23%
26.18% to 34.63%	12	7.19%	93.41%
34.63% to 43.09%	4	2.40%	95.81%
43.09% to 51.54%	2	1.20%	97.01%
Greater than 51.54%	5	2.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.45%	29.00%	83.23%	68.27%
±2σ	-4.82%	40.27%	95.81%	95.45%
±3σ	-16.10%	51.54%	97.01%	99.73%

Descriptive Statistics

Mean	17.722%
Standard Error	0.872%
Median	15.380%
Mode	3.817%
Standard Deviation	11.273%
Sample Variance	127.075%
Kurtosis	6.25
Skewness	2.14
Range	68.615%
Minimum	3.817%
Maximum	72.432%
Count	167

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.722%	167	100.00%	17.722%
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 1.37. Further, an Excess Kurtosis of 5.00 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.30%	0	0.00%	0.00%
-35.30% to -26.66%	1	0.60%	0.60%
-26.66% to -18.03%	5	2.99%	3.59%
-18.03% to -9.39%	24	14.37%	17.96%
-9.39% to -0.75%	62	37.13%	55.09%
-0.75% to 7.88%	50	29.94%	85.03%
7.88% to 16.52%	17	10.18%	95.21%
16.52% to 25.16%	4	2.40%	97.60%
25.16% to 33.79%	0	0.00%	97.60%
Greater than 33.79%	4	2.40%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.27%	10.76%	77.25%	68.27%
±2σ	-23.78%	22.28%	96.41%	95.45%
±3σ	-35.30%	33.79%	97.60%	99.73%

Descriptive Statistics

Mean	-0.753%
Standard Error	0.891%
Median	-1.250%
Mode	-32.147%
Standard Deviation	11.515%
Sample Variance	132.600%
Kurtosis	5.00
Skewness	1.37
Range	81.206%
Minimum	-32.147%
Maximum	49.059%
Count	167

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.662%	70	41.92%	3.631%
Negative	-7.547%	97	58.08%	-4.384%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.36. Further, an Excess Kurtosis of 1.00 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -52.17%	0	0.00%	0.00%
-52.17% to -37.10%	1	1.82%	1.82%
-37.10% to -22.03%	1	1.82%	3.64%
-22.03% to -6.96%	8	14.55%	18.18%
-6.96% to 8.12%	20	36.36%	54.55%
8.12% to 23.19%	14	25.45%	80.00%
23.19% to 38.26%	7	12.73%	92.73%
38.26% to 53.34%	2	3.64%	96.36%
53.34% to 68.41%	2	3.64%	100.00%
Greater than 68.41%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.98%	28.22%	72.73%	68.27%
±2σ	-32.08%	48.31%	92.73%	95.45%
±3σ	-52.17%	68.41%	100.00%	99.73%

Descriptive Statistics

Mean	8.118%
Standard Error	2.710%
Median	5.409%
Mode	-41.446%
Standard Deviation	20.097%
Sample Variance	403.879%
Kurtosis	1.00
Skewness	0.36
Range	102.767%
Minimum	-41.446%
Maximum	61.321%
Count	55

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.244%	38	69.09%	11.914%
Negative	-12.283%	17	30.91%	-3.797%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	25.80%
12	3 Years	29.61%
20	5 Years	34.83%
40	10 Years	28.38%
80	20 Years	29.31%
200	50 Years	29.31%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.66. Further, an Excess Kurtosis of 2.69 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.50%	0	0.00%	0.00%
-29.50% to -13.25%	0	0.00%	0.00%
-13.25% to 3.00%	0	0.00%	0.00%
3.00% to 19.26%	11	19.64%	19.64%
19.26% to 35.51%	27	48.21%	67.86%
35.51% to 51.77%	8	14.29%	82.14%
51.77% to 68.02%	4	7.14%	89.29%
68.02% to 84.28%	3	5.36%	94.64%
84.28% to 100.53%	2	3.57%	98.21%
Greater than 100.53%	1	1.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.84%	57.19%	78.57%	68.27%
±2σ	-7.83%	78.86%	94.64%	95.45%
±3σ	-29.50%	100.53%	98.21%	99.73%

Descriptive Statistics

Mean	35.513%
Standard Error	2.896%
Median	29.347%
Mode	9.363%
Standard Deviation	21.672%
Sample Variance	469.662%
Kurtosis	2.69
Skewness	1.66
Range	98.874%
Minimum	9.363%
Maximum	108.237%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	35.513%	56	100.00%	35.513%
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 2.01. Further, an Excess Kurtosis of 6.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -70.97%	0	0.00%	0.00%
-70.97% to -53.73%	0	0.00%	0.00%
-53.73% to -36.49%	2	3.57%	3.57%
-36.49% to -19.25%	8	14.29%	17.86%
-19.25% to -2.01%	24	42.86%	60.71%
-2.01% to 15.23%	15	26.79%	87.50%
15.23% to 32.47%	4	7.14%	94.64%
32.47% to 49.71%	0	0.00%	94.64%
49.71% to 66.95%	1	1.79%	96.43%
Greater than 66.95%	2	3.57%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-25.00%	20.98%	82.14%	68.27%
±2σ	-47.98%	43.96%	94.64%	95.45%
±3σ	-70.97%	66.95%	96.43%	99.73%

Descriptive Statistics

Mean	-2.009%
Standard Error	3.072%
Median	-4.723%
Mode	-38.403%
Standard Deviation	22.986%
Sample Variance	528.347%
Kurtosis	6.15
Skewness	2.01
Range	132.093%
Minimum	-38.403%
Maximum	93.690%
Count	56

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	19.578%	19	33.93%	6.643%
Negative	-13.094%	37	66.07%	-8.651%
Zero	0.000%	0	0.00%	0.000%

META Deep Analytical Report