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%	1.27%	1.22%	—	1.47%	1.61%	472.52	486.57	465.64	493.75
Weekly	3.08%	3.24%	3.02%	—	3.23%	3.53%	464.27	495.21	449.53	511.44
Monthly	5.48%	6.89%	5.41%	—	6.71%	7.36%	448.35	512.79	419.23	548.41
Quarterly	8.69%	10.12%	8.45%	—	11.63%	12.74%	426.85	538.63	379.98	605.06
Annual	—	—	—	—	23.26%	25.49%	379.98	605.06	301.12	763.51
Option Time Horizon	—	—	—	—	8.78%	9.62%	439.19	523.49	402.27	571.53

Calculation Notes: Computed at 2026-03-23T16:30 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $479.49 | Strike (K): $480.00 (first OTM call ≥ spot) | Observed Mid-Price: $17.6250 (Bid $16.8000 / Ask $18.4500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 23.26% (CRR binomial tree, American, n=20 steps) | BS IV: 23.03% (European Black-Scholes) | Yahoo IV (Annual): 25.49% → 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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.78. Further, an Excess Kurtosis of 12.40 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%	56	0.75%	0.75%
-4.15% to -3.10%	65	0.87%	1.61%
-3.10% to -2.05%	209	2.78%	4.39%
-2.05% to -1.00%	797	10.61%	15.00%
-1.00% to 0.05%	2778	36.97%	51.97%
0.05% to 1.10%	2483	33.04%	85.01%
1.10% to 2.15%	768	10.22%	95.24%
2.15% to 3.20%	205	2.73%	97.96%
3.20% to 4.25%	74	0.98%	98.95%
Greater than 4.25%	79	1.05%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.35%	1.45%	80.54%	68.27%
±2σ	-2.75%	2.85%	95.14%	95.45%
±3σ	-4.15%	4.25%	98.22%	99.73%

Descriptive Statistics

Mean	0.050%
Standard Error	0.016%
Median	0.000%
Mode	0.000%
Standard Deviation	1.399%
Sample Variance	1.957%
Kurtosis	12.40
Skewness	0.78
Range	30.208%
Minimum	-10.944%
Maximum	19.264%
Count	7514

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.978%	3749	49.89%	0.488%
Negative	-0.893%	3685	49.04%	-0.438%
Zero	0.000%	80	1.06%	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 47.43 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.21%	0	0.00%	0.00%
-2.21% to -1.26%	0	0.00%	0.00%
-1.26% to -0.30%	0	0.00%	0.00%
-0.30% to 0.66%	660	8.78%	8.78%
0.66% to 1.61%	4324	57.54%	66.32%
1.61% to 2.57%	1564	20.81%	87.13%
2.57% to 3.52%	526	7.00%	94.13%
3.52% to 4.48%	205	2.73%	96.86%
4.48% to 5.44%	90	1.20%	98.06%
Greater than 5.44%	146	1.94%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.34%	2.89%	89.81%	68.27%
±2σ	-0.94%	4.16%	96.13%	95.45%
±3σ	-2.21%	5.44%	98.06%	99.73%

Descriptive Statistics

Mean	1.611%
Standard Error	0.015%
Median	1.256%
Mode	0.718%
Standard Deviation	1.275%
Sample Variance	1.625%
Kurtosis	47.43
Skewness	4.60
Range	28.162%
Minimum	0.105%
Maximum	28.267%
Count	7515

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.611%	7515	100.00%	1.611%
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 20.21 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%	72	0.96%	0.96%
-3.66% to -2.74%	62	0.83%	1.78%
-2.74% to -1.82%	196	2.61%	4.39%
-1.82% to -0.90%	803	10.69%	15.08%
-0.90% to 0.02%	2607	34.69%	49.77%
0.02% to 0.93%	2635	35.06%	84.83%
0.93% to 1.85%	783	10.42%	95.25%
1.85% to 2.77%	231	3.07%	98.32%
2.77% to 3.69%	75	1.00%	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%	80.36%	68.27%
±2σ	-2.43%	2.46%	95.36%	95.45%
±3σ	-3.66%	3.69%	98.36%	99.73%

Descriptive Statistics

Mean	0.016%
Standard Error	0.014%
Median	0.020%
Mode	0.000%
Standard Deviation	1.224%
Sample Variance	1.499%
Kurtosis	20.21
Skewness	-1.21
Range	30.049%
Minimum	-20.635%
Maximum	9.414%
Count	7515

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	0.814%	3807	50.66%	0.412%
Negative	-0.826%	3606	47.98%	-0.396%
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 4.64 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	3.27%	5.20%
-4.38% to -2.07%	170	10.91%	16.11%
-2.07% to 0.24%	550	35.30%	51.41%
0.24% to 2.55%	493	31.64%	83.06%
2.55% to 4.86%	188	12.07%	95.12%
4.86% to 7.17%	44	2.82%	97.95%
7.17% to 9.48%	15	0.96%	98.91%
Greater than 9.48%	17	1.09%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.84%	3.32%	78.43%	68.27%
±2σ	-5.92%	6.40%	94.61%	95.45%
±3σ	-9.00%	9.48%	98.01%	99.73%

Descriptive Statistics

Mean	0.240%
Standard Error	0.078%
Median	0.166%
Mode	0.000%
Standard Deviation	3.081%
Sample Variance	9.489%
Kurtosis	4.64
Skewness	0.05
Range	35.882%
Minimum	-17.483%
Maximum	18.399%
Count	1558

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.227%	831	53.34%	1.188%
Negative	-2.045%	722	46.34%	-0.948%
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 28.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.56%	0	0.00%	0.00%
-5.56% to -3.14%	0	0.00%	0.00%
-3.14% to -0.71%	0	0.00%	0.00%
-0.71% to 1.72%	172	11.03%	11.03%
1.72% to 4.15%	840	53.88%	64.91%
4.15% to 6.58%	332	21.30%	86.21%
6.58% to 9.00%	113	7.25%	93.46%
9.00% to 11.43%	46	2.95%	96.41%
11.43% to 13.86%	28	1.80%	98.20%
Greater than 13.86%	28	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.91%	7.38%	89.35%	68.27%
±2σ	-2.33%	10.62%	95.77%	95.45%
±3σ	-5.56%	13.86%	98.20%	99.73%

Descriptive Statistics

Mean	4.147%
Standard Error	0.082%
Median	3.243%
Mode	1.585%
Standard Deviation	3.237%
Sample Variance	10.481%
Kurtosis	28.27
Skewness	3.81
Range	45.917%
Minimum	0.383%
Maximum	46.300%
Count	1559

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.147%	1559	100.00%	4.147%
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 4.58 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 -6.86%	20	1.28%	1.86%
-6.86% to -4.60%	48	3.08%	4.94%
-4.60% to -2.33%	196	12.57%	17.51%
-2.33% to -0.07%	520	33.35%	50.87%
-0.07% to 2.20%	529	33.93%	84.80%
2.20% to 4.47%	153	9.81%	94.61%
4.47% to 6.73%	50	3.21%	97.82%
6.73% to 9.00%	16	1.03%	98.85%
Greater than 9.00%	18	1.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.09%	2.96%	77.93%	68.27%
±2σ	-6.11%	5.98%	94.10%	95.45%
±3σ	-9.13%	9.00%	98.27%	99.73%

Descriptive Statistics

Mean	-0.066%
Standard Error	0.077%
Median	-0.105%
Mode	0.000%
Standard Deviation	3.021%
Sample Variance	9.127%
Kurtosis	4.58
Skewness	0.60
Range	31.956%
Minimum	-13.227%
Maximum	18.729%
Count	1559

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.130%	743	47.66%	1.015%
Negative	-2.088%	807	51.76%	-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 0.27. Further, an Excess Kurtosis of 1.47 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -15.42%	0	0.00%	0.00%
-15.42% to -11.30%	7	1.96%	1.96%
-11.30% to -7.19%	14	3.91%	5.87%
-7.19% to -3.08%	48	13.41%	19.27%
-3.08% to 1.03%	116	32.40%	51.68%
1.03% to 5.15%	102	28.49%	80.17%
5.15% to 9.26%	47	13.13%	93.30%
9.26% to 13.37%	19	5.31%	98.60%
13.37% 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	-4.45%	6.52%	72.35%	68.27%
±2σ	-9.93%	12.00%	94.69%	95.45%
±3σ	-15.42%	17.49%	99.44%	99.73%

Descriptive Statistics

Mean	1.034%
Standard Error	0.290%
Median	0.847%
Mode	-1.992%
Standard Deviation	5.484%
Sample Variance	30.073%
Kurtosis	1.47
Skewness	0.27
Range	40.650%
Minimum	-14.261%
Maximum	26.389%
Count	358

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.675%	201	56.15%	2.625%
Negative	-3.651%	156	43.58%	-1.591%
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 20.51 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.35%	0	0.00%	0.00%
-11.35% to -6.19%	0	0.00%	0.00%
-6.19% to -1.02%	0	0.00%	0.00%
-1.02% to 4.14%	38	10.58%	10.58%
4.14% to 9.30%	198	55.15%	65.74%
9.30% to 14.47%	68	18.94%	84.68%
14.47% to 19.63%	36	10.03%	94.71%
19.63% to 24.80%	12	3.34%	98.05%
24.80% to 29.96%	0	0.00%	98.05%
Greater than 29.96%	7	1.95%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.42%	16.19%	89.97%	68.27%
±2σ	-4.47%	23.08%	97.49%	95.45%
±3σ	-11.35%	29.96%	98.05%	99.73%

Descriptive Statistics

Mean	9.305%
Standard Error	0.363%
Median	7.294%
Mode	5.438%
Standard Deviation	6.886%
Sample Variance	47.421%
Kurtosis	20.51
Skewness	3.67
Range	59.871%
Minimum	2.063%
Maximum	61.934%
Count	359

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.305%	359	100.00%	9.305%
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 1.15 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.83%	1	0.28%	0.28%
-16.83% to -12.78%	3	0.84%	1.11%
-12.78% to -8.73%	19	5.29%	6.41%
-8.73% to -4.67%	51	14.21%	20.61%
-4.67% to -0.62%	107	29.81%	50.42%
-0.62% to 3.44%	113	31.48%	81.89%
3.44% to 7.49%	41	11.42%	93.31%
7.49% to 11.54%	14	3.90%	97.21%
11.54% to 15.60%	7	1.95%	99.16%
Greater than 15.60%	3	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.02%	4.79%	72.42%	68.27%
±2σ	-11.43%	10.19%	94.71%	95.45%
±3σ	-16.83%	15.60%	98.89%	99.73%

Descriptive Statistics

Mean	-0.618%
Standard Error	0.285%
Median	-0.692%
Mode	-21.044%
Standard Deviation	5.405%
Sample Variance	29.215%
Kurtosis	1.15
Skewness	0.20
Range	38.076%
Minimum	-21.044%
Maximum	17.032%
Count	359

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.874%	162	45.12%	1.748%
Negative	-4.333%	196	54.60%	-2.366%
Zero	0.000%	1	0.28%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.25. Further, an Excess Kurtosis of 2.13 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -23.01%	0	0.00%	0.00%
-23.01% to -16.50%	3	2.52%	2.52%
-16.50% to -9.98%	4	3.36%	5.88%
-9.98% to -3.47%	12	10.08%	15.97%
-3.47% to 3.05%	43	36.13%	52.10%
3.05% to 9.56%	34	28.57%	80.67%
9.56% to 16.08%	17	14.29%	94.96%
16.08% to 22.59%	4	3.36%	98.32%
22.59% to 29.11%	1	0.84%	99.16%
Greater than 29.11%	1	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.64%	11.73%	70.59%	68.27%
±2σ	-14.32%	20.42%	94.12%	95.45%
±3σ	-23.01%	29.11%	99.16%	99.73%

Descriptive Statistics

Mean	3.048%
Standard Error	0.796%
Median	2.753%
Mode	16.403%
Standard Deviation	8.686%
Sample Variance	75.448%
Kurtosis	2.13
Skewness	0.25
Range	59.013%
Minimum	-22.161%
Maximum	36.852%
Count	119

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.796%	85	71.43%	4.854%
Negative	-6.322%	34	28.57%	-1.806%
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 2.22. Further, an Excess Kurtosis of 6.16 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.13%	0	0.00%	0.00%
-14.13% to -6.54%	0	0.00%	0.00%
-6.54% to 1.06%	0	0.00%	0.00%
1.06% to 8.65%	19	15.83%	15.83%
8.65% to 16.24%	56	46.67%	62.50%
16.24% to 23.84%	32	26.67%	89.17%
23.84% to 31.43%	5	4.17%	93.33%
31.43% to 39.02%	2	1.67%	95.00%
39.02% to 46.61%	3	2.50%	97.50%
Greater than 46.61%	3	2.50%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	6.12%	26.37%	87.50%	68.27%
±2σ	-4.01%	36.49%	95.00%	95.45%
±3σ	-14.13%	46.61%	97.50%	99.73%

Descriptive Statistics

Mean	16.242%
Standard Error	0.924%
Median	13.444%
Mode	4.570%
Standard Deviation	10.124%
Sample Variance	102.498%
Kurtosis	6.16
Skewness	2.22
Range	57.364%
Minimum	4.570%
Maximum	61.934%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	16.242%	120	100.00%	16.242%
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 0.76. Further, an Excess Kurtosis of 2.52 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.33%	0	0.00%	0.00%
-27.33% to -20.99%	1	0.83%	0.83%
-20.99% to -14.65%	3	2.50%	3.33%
-14.65% to -8.31%	19	15.83%	19.17%
-8.31% to -1.97%	43	35.83%	55.00%
-1.97% to 4.37%	34	28.33%	83.33%
4.37% to 10.71%	12	10.00%	93.33%
10.71% to 17.05%	4	3.33%	96.67%
17.05% to 23.39%	2	1.67%	98.33%
Greater than 23.39%	2	1.67%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-10.42%	6.49%	71.67%	68.27%
±2σ	-18.88%	14.94%	94.17%	95.45%
±3σ	-27.33%	23.39%	98.33%	99.73%

Descriptive Statistics

Mean	-1.968%
Standard Error	0.772%
Median	-2.479%
Mode	-26.231%
Standard Deviation	8.454%
Sample Variance	71.468%
Kurtosis	2.52
Skewness	0.76
Range	56.243%
Minimum	-26.231%
Maximum	30.012%
Count	120

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.391%	41	34.17%	2.184%
Negative	-6.307%	79	65.83%	-4.152%
Zero	0.000%	0	0.00%	0.000%

BRK-B Deep Analytical Report