BRK-B - 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	1.40%	1.28%	1.23%	—	1.08%	1.22%	492.85	503.61	487.55	509.08
Weekly	3.08%	3.24%	3.02%	—	2.38%	2.69%	486.49	510.19	475.06	522.47
Monthly	5.48%	6.89%	5.41%	—	4.95%	5.60%	474.13	523.49	451.23	550.06
Quarterly	8.68%	10.13%	8.45%	—	8.58%	9.69%	457.26	542.81	419.68	591.41
Annual	—	—	—	—	17.15%	19.39%	419.68	591.41	353.53	702.07
Option Time Horizon	—	—	—	—	6.60%	7.46%	466.39	532.17	436.62	568.47

Calculation Notes: Computed at 2026-02-22T14:16 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $498.20 | Strike (K): $500.00 (first OTM call ≥ spot) | Observed Mid-Price: $13.5500 (Bid $13.0000 / Ask $14.1000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 17.15% (CRR binomial tree, American, n=20 steps) | BS IV: 17.12% (European Black-Scholes) | Yahoo IV (Annual): 19.39% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.78. Further, an Excess Kurtosis of 12.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -4.15%	55	0.73%	0.73%
-4.15% to -3.10%	65	0.87%	1.60%
-3.10% to -2.05%	209	2.79%	4.39%
-2.05% to -1.00%	797	10.64%	15.03%
-1.00% to 0.05%	2768	36.94%	51.97%
0.05% to 1.10%	2476	33.04%	85.01%
1.10% to 2.15%	767	10.24%	95.25%
2.15% to 3.20%	203	2.71%	97.96%
3.20% to 4.25%	75	1.00%	98.96%
Greater than 4.25%	78	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.35%	1.45%	80.53%	68.27%
±2σ	-2.75%	2.85%	95.14%	95.45%
±3σ	-4.15%	4.25%	98.23%	99.73%

Descriptive Statistics

Mean	0.051%
Standard Error	0.016%
Median	0.000%
Mode	0.000%
Standard Deviation	1.399%
Sample Variance	1.957%
Kurtosis	12.42
Skewness	0.78
Range	30.208%
Minimum	-10.944%
Maximum	19.264%
Count	7493

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.979%	3741	49.93%	0.489%
Negative	-0.894%	3672	49.01%	-0.438%
Zero	0.000%	80	1.07%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.60. Further, an Excess Kurtosis of 47.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.22%	0	0.00%	0.00%
-2.22% to -1.26%	0	0.00%	0.00%
-1.26% to -0.30%	0	0.00%	0.00%
-0.30% to 0.66%	660	8.81%	8.81%
0.66% to 1.61%	4312	57.54%	66.35%
1.61% to 2.57%	1557	20.78%	87.12%
2.57% to 3.53%	525	7.01%	94.13%
3.53% to 4.48%	205	2.74%	96.86%
4.48% to 5.44%	89	1.19%	98.05%
Greater than 5.44%	146	1.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.34%	2.89%	89.85%	68.27%
±2σ	-0.94%	4.16%	96.13%	95.45%
±3σ	-2.22%	5.44%	98.05%	99.73%

Descriptive Statistics

Mean	1.612%
Standard Error	0.015%
Median	1.255%
Mode	0.718%
Standard Deviation	1.276%
Sample Variance	1.629%
Kurtosis	47.35
Skewness	4.60
Range	28.162%
Minimum	0.105%
Maximum	28.267%
Count	7494

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.612%	7494	100.00%	1.612%
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 Left Skewed (Extreme Negative Tail Risk) with a Skewness factor of -1.21. 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 -3.66%	71	0.95%	0.95%
-3.66% to -2.74%	63	0.84%	1.79%
-2.74% to -1.82%	196	2.62%	4.40%
-1.82% to -0.90%	800	10.68%	15.08%
-0.90% to 0.02%	2602	34.72%	49.80%
0.02% to 0.94%	2626	35.04%	84.84%
0.94% to 1.85%	780	10.41%	95.25%
1.85% to 2.77%	231	3.08%	98.33%
2.77% to 3.69%	74	0.99%	99.32%
Greater than 3.69%	51	0.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.21%	1.24%	80.41%	68.27%
±2σ	-2.43%	2.47%	95.38%	95.45%
±3σ	-3.66%	3.69%	98.37%	99.73%

Descriptive Statistics

Mean	0.016%
Standard Error	0.014%
Median	0.018%
Mode	0.000%
Standard Deviation	1.225%
Sample Variance	1.501%
Kurtosis	20.23
Skewness	-1.21
Range	30.049%
Minimum	-20.635%
Maximum	9.414%
Count	7494

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.815%	3794	50.63%	0.413%
Negative	-0.827%	3598	48.01%	-0.397%
Zero	0.000%	102	1.36%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.05. Further, an Excess Kurtosis of 4.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.00%	14	0.90%	0.90%
-9.00% to -6.69%	16	1.03%	1.93%
-6.69% to -4.38%	51	3.28%	5.21%
-4.38% to -2.07%	168	10.81%	16.02%
-2.07% to 0.24%	549	35.33%	51.35%
0.24% to 2.55%	493	31.72%	83.08%
2.55% to 4.87%	187	12.03%	95.11%
4.87% to 7.17%	44	2.83%	97.94%
7.17% to 9.49%	15	0.97%	98.91%
Greater than 9.49%	17	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.84%	3.32%	78.44%	68.27%
±2σ	-5.92%	6.41%	94.59%	95.45%
±3σ	-9.00%	9.49%	98.01%	99.73%

Descriptive Statistics

Mean	0.243%
Standard Error	0.078%
Median	0.168%
Mode	0.000%
Standard Deviation	3.081%
Sample Variance	9.494%
Kurtosis	4.65
Skewness	0.05
Range	35.882%
Minimum	-17.483%
Maximum	18.399%
Count	1554

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.223%	831	53.48%	1.189%
Negative	-2.047%	718	46.20%	-0.946%
Zero	0.000%	5	0.32%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.81. Further, an Excess Kurtosis of 28.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.57%	0	0.00%	0.00%
-5.57% to -3.14%	0	0.00%	0.00%
-3.14% to -0.71%	0	0.00%	0.00%
-0.71% to 1.72%	172	11.06%	11.06%
1.72% to 4.15%	837	53.83%	64.89%
4.15% to 6.58%	331	21.29%	86.17%
6.58% to 9.01%	113	7.27%	93.44%
9.01% to 11.44%	46	2.96%	96.40%
11.44% to 13.87%	28	1.80%	98.20%
Greater than 13.87%	28	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.91%	7.39%	89.39%	68.27%
±2σ	-2.33%	10.63%	95.76%	95.45%
±3σ	-5.57%	13.87%	98.20%	99.73%

Descriptive Statistics

Mean	4.146%
Standard Error	0.082%
Median	3.240%
Mode	1.585%
Standard Deviation	3.240%
Sample Variance	10.501%
Kurtosis	28.24
Skewness	3.81
Range	45.917%
Minimum	0.383%
Maximum	46.300%
Count	1555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.146%	1555	100.00%	4.146%
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 0.60. Further, an Excess Kurtosis of 4.60 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.13%	9	0.58%	0.58%
-9.13% to -6.87%	20	1.29%	1.86%
-6.87% to -4.60%	48	3.09%	4.95%
-4.60% to -2.33%	195	12.54%	17.49%
-2.33% to -0.07%	520	33.44%	50.93%
-0.07% to 2.20%	526	33.83%	84.76%
2.20% to 4.46%	153	9.84%	94.60%
4.46% to 6.73%	50	3.22%	97.81%
6.73% to 8.99%	16	1.03%	98.84%
Greater than 8.99%	18	1.16%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.09%	2.95%	78.01%	68.27%
±2σ	-6.11%	5.97%	94.08%	95.45%
±3σ	-9.13%	8.99%	98.26%	99.73%

Descriptive Statistics

Mean	-0.068%
Standard Error	0.077%
Median	-0.106%
Mode	0.000%
Standard Deviation	3.021%
Sample Variance	9.127%
Kurtosis	4.60
Skewness	0.60
Range	31.956%
Minimum	-13.227%
Maximum	18.729%
Count	1555

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.128%	740	47.59%	1.013%
Negative	-2.086%	806	51.83%	-1.081%
Zero	0.000%	9	0.58%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.26. Further, an Excess Kurtosis of 1.49 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.39%	0	0.00%	0.00%
-15.39% to -11.28%	7	1.96%	1.96%
-11.28% to -7.17%	14	3.92%	5.88%
-7.17% to -3.06%	47	13.17%	19.05%
-3.06% to 1.05%	116	32.49%	51.54%
1.05% to 5.16%	103	28.85%	80.39%
5.16% to 9.27%	46	12.89%	93.28%
9.27% to 13.38%	19	5.32%	98.60%
13.38% to 17.49%	3	0.84%	99.44%
Greater than 17.49%	2	0.56%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.43%	6.53%	72.55%	68.27%
±2σ	-9.91%	12.01%	94.68%	95.45%
±3σ	-15.39%	17.49%	99.44%	99.73%

Descriptive Statistics

Mean	1.047%
Standard Error	0.290%
Median	0.848%
Mode	-1.992%
Standard Deviation	5.480%
Sample Variance	30.030%
Kurtosis	1.49
Skewness	0.26
Range	40.650%
Minimum	-14.261%
Maximum	26.389%
Count	357

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.668%	201	56.30%	2.628%
Negative	-3.642%	155	43.42%	-1.581%
Zero	0.000%	1	0.28%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.67. Further, an Excess Kurtosis of 20.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.37%	0	0.00%	0.00%
-11.37% to -6.20%	0	0.00%	0.00%
-6.20% to -1.03%	0	0.00%	0.00%
-1.03% to 4.14%	38	10.61%	10.61%
4.14% to 9.31%	197	55.03%	65.64%
9.31% to 14.48%	68	18.99%	84.64%
14.48% to 19.66%	36	10.06%	94.69%
19.66% to 24.82%	12	3.35%	98.04%
24.82% to 30.00%	0	0.00%	98.04%
Greater than 30.00%	7	1.96%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.42%	16.21%	89.94%	68.27%
±2σ	-4.47%	23.10%	97.49%	95.45%
±3σ	-11.37%	30.00%	98.04%	99.73%

Descriptive Statistics

Mean	9.314%
Standard Error	0.364%
Median	7.302%
Mode	5.438%
Standard Deviation	6.894%
Sample Variance	47.523%
Kurtosis	20.45
Skewness	3.67
Range	59.871%
Minimum	2.063%
Maximum	61.934%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.314%	358	100.00%	9.314%
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 0.20. Further, an Excess Kurtosis of 1.16 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.85%	1	0.28%	0.28%
-16.85% to -12.79%	3	0.84%	1.12%
-12.79% to -8.74%	18	5.03%	6.15%
-8.74% to -4.68%	51	14.25%	20.39%
-4.68% to -0.62%	108	30.17%	50.56%
-0.62% to 3.43%	112	31.28%	81.84%
3.43% to 7.49%	41	11.45%	93.30%
7.49% to 11.54%	14	3.91%	97.21%
11.54% to 15.60%	7	1.96%	99.16%
Greater than 15.60%	3	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.03%	4.78%	72.63%	68.27%
±2σ	-11.44%	10.19%	94.69%	95.45%
±3σ	-16.85%	15.60%	98.88%	99.73%

Descriptive Statistics

Mean	-0.625%
Standard Error	0.286%
Median	-0.696%
Mode	-21.044%
Standard Deviation	5.407%
Sample Variance	29.231%
Kurtosis	1.16
Skewness	0.20
Range	38.076%
Minimum	-21.044%
Maximum	17.032%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.878%	161	44.97%	1.744%
Negative	-4.326%	196	54.75%	-2.368%
Zero	0.000%	1	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.23. Further, an Excess Kurtosis of 2.14 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.96%	0	0.00%	0.00%
-22.96% to -16.45%	3	2.52%	2.52%
-16.45% to -9.94%	4	3.36%	5.88%
-9.94% to -3.43%	12	10.08%	15.97%
-3.43% to 3.08%	42	35.29%	51.26%
3.08% to 9.59%	35	29.41%	80.67%
9.59% to 16.10%	17	14.29%	94.96%
16.10% to 22.61%	4	3.36%	98.32%
22.61% to 29.12%	1	0.84%	99.16%
Greater than 29.12%	1	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.60%	11.76%	71.43%	68.27%
±2σ	-14.28%	20.44%	94.12%	95.45%
±3σ	-22.96%	29.12%	99.16%	99.73%

Descriptive Statistics

Mean	3.080%
Standard Error	0.796%
Median	2.832%
Mode	16.403%
Standard Deviation	8.681%
Sample Variance	75.365%
Kurtosis	2.14
Skewness	0.23
Range	59.013%
Minimum	-22.161%
Maximum	36.852%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.760%	86	72.27%	4.885%
Negative	-6.509%	33	27.73%	-1.805%
Zero	0.000%	0	0.00%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.21. Further, an Excess Kurtosis of 6.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.17%	0	0.00%	0.00%
-14.17% to -6.57%	0	0.00%	0.00%
-6.57% to 1.03%	0	0.00%	0.00%
1.03% to 8.63%	19	15.83%	15.83%
8.63% to 16.23%	56	46.67%	62.50%
16.23% to 23.83%	32	26.67%	89.17%
23.83% to 31.43%	5	4.17%	93.33%
31.43% to 39.03%	2	1.67%	95.00%
39.03% to 46.63%	3	2.50%	97.50%
Greater than 46.63%	3	2.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.10%	26.36%	87.50%	68.27%
±2σ	-4.04%	36.50%	95.00%	95.45%
±3σ	-14.17%	46.63%	97.50%	99.73%

Descriptive Statistics

Mean	16.230%
Standard Error	0.925%
Median	13.444%
Mode	4.570%
Standard Deviation	10.134%
Sample Variance	102.694%
Kurtosis	6.14
Skewness	2.21
Range	57.364%
Minimum	4.570%
Maximum	61.934%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.230%	120	100.00%	16.230%
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 0.77. Further, an Excess Kurtosis of 2.54 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.36%	0	0.00%	0.00%
-27.36% to -21.02%	1	0.83%	0.83%
-21.02% to -14.68%	3	2.50%	3.33%
-14.68% to -8.34%	19	15.83%	19.17%
-8.34% to -2.00%	44	36.67%	55.83%
-2.00% to 4.34%	33	27.50%	83.33%
4.34% to 10.68%	12	10.00%	93.33%
10.68% to 17.02%	4	3.33%	96.67%
17.02% to 23.36%	2	1.67%	98.33%
Greater than 23.36%	2	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.45%	6.45%	71.67%	68.27%
±2σ	-18.90%	14.90%	94.17%	95.45%
±3σ	-27.36%	23.36%	98.33%	99.73%

Descriptive Statistics

Mean	-1.999%
Standard Error	0.772%
Median	-2.496%
Mode	-26.231%
Standard Deviation	8.452%
Sample Variance	71.441%
Kurtosis	2.54
Skewness	0.77
Range	56.243%
Minimum	-26.231%
Maximum	30.012%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.544%	40	33.33%	2.181%
Negative	-6.271%	80	66.67%	-4.181%
Zero	0.000%	0	0.00%	0.000%

BRK-B Deep Analytical Report