AFRM - 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	6.12%	4.39%	5.00%	7.84%	4.09%	4.17%	49.04	53.23	47.07	55.45
Weekly	13.27%	12.88%	13.30%	19.14%	9.01%	9.19%	46.69	55.91	42.66	61.18
Monthly	28.94%	29.76%	26.23%	41.54%	18.76%	19.13%	42.35	61.63	35.11	74.35
Quarterly	62.40%	65.65%	52.45%	79.71%	32.50%	33.13%	36.92	70.71	26.67	97.86
Annual	—	—	—	—	64.99%	66.26%	26.67	97.86	13.93	187.44
Option Time Horizon	—	—	—	—	25.00%	25.49%	39.79	65.60	30.99	84.23

Calculation Notes: Computed at 2026-02-22T14:19 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $51.09 | Strike (K): $52.50 (first OTM call ≥ spot) | Observed Mid-Price: $4.6250 (Bid $4.5000 / Ask $4.7500) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 64.99% (CRR binomial tree, American, n=20 steps) | BS IV: 65.36% (European Black-Scholes) | Yahoo IV (Annual): 66.26% → 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 0.99. Further, an Excess Kurtosis of 5.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.24%	6	0.47%	0.47%
-18.24% to -13.64%	12	0.94%	1.41%
-13.64% to -9.05%	39	3.04%	4.45%
-9.05% to -4.46%	164	12.80%	17.25%
-4.46% to 0.13%	445	34.74%	51.99%
0.13% to 4.72%	399	31.15%	83.14%
4.72% to 9.32%	140	10.93%	94.07%
9.32% to 13.91%	46	3.59%	97.66%
13.91% to 18.50%	14	1.09%	98.75%
Greater than 18.50%	16	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.99%	6.25%	78.38%	68.27%
±2σ	-12.11%	12.38%	95.00%	95.45%
±3σ	-18.24%	18.50%	98.28%	99.73%

Descriptive Statistics

Mean	0.132%
Standard Error	0.171%
Median	-0.136%
Mode	-2.491%
Standard Deviation	6.123%
Sample Variance	37.488%
Kurtosis	5.76
Skewness	0.99
Range	69.306%
Minimum	-22.634%
Maximum	46.672%
Count	1281

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.530%	629	49.10%	2.224%
Negative	-4.129%	649	50.66%	-2.092%
Zero	0.000%	3	0.23%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.11%
20	1 Month	6.31%
60	1 Quarter	5.37%
250	1 Year	6.13%
750	3 Years	6.76%
1,250	5 Years	7.84%
2,500	10 Years	7.90%
5,000	20 Years	7.90%
12,500	50 Years	7.90%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.54. Further, an Excess Kurtosis of 31.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.50%	0	0.00%	0.00%
-5.50% to -2.21%	0	0.00%	0.00%
-2.21% to 1.09%	0	0.00%	0.00%
1.09% to 4.39%	224	17.47%	17.47%
4.39% to 7.68%	564	43.99%	61.47%
7.68% to 10.98%	296	23.09%	84.56%
10.98% to 14.28%	115	8.97%	93.53%
14.28% to 17.57%	42	3.28%	96.80%
17.57% to 20.87%	23	1.79%	98.60%
Greater than 20.87%	18	1.40%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.29%	12.08%	81.83%	68.27%
±2σ	-1.11%	16.47%	96.10%	95.45%
±3σ	-5.50%	20.87%	98.60%	99.73%

Descriptive Statistics

Mean	7.683%
Standard Error	0.123%
Median	6.560%
Mode	6.443%
Standard Deviation	4.395%
Sample Variance	19.315%
Kurtosis	31.27
Skewness	3.54
Range	65.425%
Minimum	1.715%
Maximum	67.140%
Count	1282

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.683%	1282	100.00%	7.683%
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 Fairly Symmetrical with a Skewness factor of 0.15. Further, an Excess Kurtosis of 1.85 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.80%	7	0.55%	0.55%
-14.80% to -11.06%	12	0.94%	1.48%
-11.06% to -7.31%	51	3.98%	5.46%
-7.31% to -3.56%	180	14.04%	19.50%
-3.56% to 0.19%	404	31.51%	51.01%
0.19% to 3.94%	382	29.80%	80.81%
3.94% to 7.69%	161	12.56%	93.37%
7.69% to 11.44%	62	4.84%	98.21%
11.44% to 15.19%	18	1.40%	99.61%
Greater than 15.19%	5	0.39%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.81%	5.19%	73.40%	68.27%
±2σ	-9.81%	10.19%	94.54%	95.45%
±3σ	-14.80%	15.19%	99.06%	99.73%

Descriptive Statistics

Mean	0.192%
Standard Error	0.140%
Median	0.072%
Mode	0.000%
Standard Deviation	4.999%
Sample Variance	24.993%
Kurtosis	1.85
Skewness	0.15
Range	49.840%
Minimum	-21.619%
Maximum	28.221%
Count	1282

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.923%	645	50.31%	1.974%
Negative	-3.614%	632	49.30%	-1.782%
Zero	0.000%	5	0.39%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.62. Further, an Excess Kurtosis of 1.60 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.26%	0	0.00%	0.00%
-39.26% to -29.31%	2	0.75%	0.75%
-29.31% to -19.36%	13	4.89%	5.64%
-19.36% to -9.41%	41	15.41%	21.05%
-9.41% to 0.54%	83	31.20%	52.26%
0.54% to 10.49%	79	29.70%	81.95%
10.49% to 20.44%	30	11.28%	93.23%
20.44% to 30.39%	12	4.51%	97.74%
30.39% to 40.34%	4	1.50%	99.25%
Greater than 40.34%	2	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.73%	13.81%	71.05%	68.27%
±2σ	-26.00%	27.08%	95.86%	95.45%
±3σ	-39.26%	40.34%	99.25%	99.73%

Descriptive Statistics

Mean	0.540%
Standard Error	0.814%
Median	-0.828%
Mode	2.570%
Standard Deviation	13.268%
Sample Variance	176.040%
Kurtosis	1.60
Skewness	0.62
Range	92.212%
Minimum	-32.181%
Maximum	60.031%
Count	266

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.924%	129	48.50%	5.298%
Negative	-9.238%	137	51.50%	-4.758%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	15.64%
12	1 Quarter	12.16%
52	1 Year	14.26%
156	3 Years	16.13%
260	5 Years	19.14%
520	10 Years	19.14%
1,040	20 Years	19.14%
2,600	50 Years	19.14%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.00. Further, an Excess Kurtosis of 6.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.17%	0	0.00%	0.00%
-17.17% to -7.52%	0	0.00%	0.00%
-7.52% to 2.14%	0	0.00%	0.00%
2.14% to 11.80%	53	19.85%	19.85%
11.80% to 21.45%	117	43.82%	63.67%
21.45% to 31.11%	49	18.35%	82.02%
31.11% to 40.77%	25	9.36%	91.39%
40.77% to 50.42%	14	5.24%	96.63%
50.42% to 60.08%	6	2.25%	98.88%
Greater than 60.08%	3	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.58%	34.33%	80.15%	68.27%
±2σ	-4.30%	47.20%	95.88%	95.45%
±3σ	-17.17%	60.08%	98.88%	99.73%

Descriptive Statistics

Mean	21.453%
Standard Error	0.788%
Median	17.843%
Mode	21.356%
Standard Deviation	12.875%
Sample Variance	165.764%
Kurtosis	6.11
Skewness	2.00
Range	87.617%
Minimum	5.653%
Maximum	93.270%
Count	267

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.453%	267	100.00%	21.453%
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 0.47. Further, an Excess Kurtosis of 0.75 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.94%	0	0.00%	0.00%
-38.94% to -28.96%	2	0.75%	0.75%
-28.96% to -18.99%	11	4.12%	4.87%
-18.99% to -9.01%	41	15.36%	20.22%
-9.01% to 0.97%	92	34.46%	54.68%
0.97% to 10.94%	71	26.59%	81.27%
10.94% to 20.92%	28	10.49%	91.76%
20.92% to 30.89%	16	5.99%	97.75%
30.89% to 40.87%	3	1.12%	98.88%
Greater than 40.87%	3	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.34%	14.27%	69.66%	68.27%
±2σ	-25.64%	27.57%	94.76%	95.45%
±3σ	-38.94%	40.87%	98.88%	99.73%

Descriptive Statistics

Mean	0.966%
Standard Error	0.814%
Median	-0.348%
Mode	-8.985%
Standard Deviation	13.301%
Sample Variance	176.918%
Kurtosis	0.75
Skewness	0.47
Range	82.726%
Minimum	-36.296%
Maximum	46.430%
Count	267

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.189%	132	49.44%	5.532%
Negative	-9.030%	135	50.56%	-4.566%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.17. Further, an Excess Kurtosis of 1.17 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.37%	0	0.00%	0.00%
-84.37% to -62.66%	0	0.00%	0.00%
-62.66% to -40.96%	0	0.00%	0.00%
-40.96% to -19.25%	11	18.03%	18.03%
-19.25% to 2.46%	26	42.62%	60.66%
2.46% to 24.16%	12	19.67%	80.33%
24.16% to 45.87%	5	8.20%	88.52%
45.87% to 67.58%	5	8.20%	96.72%
67.58% to 89.28%	1	1.64%	98.36%
Greater than 89.28%	1	1.64%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.48%	31.40%	72.13%	68.27%
±2σ	-55.43%	60.34%	95.08%	95.45%
±3σ	-84.37%	89.28%	98.36%	99.73%

Descriptive Statistics

Mean	2.457%
Standard Error	3.706%
Median	-1.294%
Mode	-37.986%
Standard Deviation	28.942%
Sample Variance	837.625%
Kurtosis	1.17
Skewness	1.17
Range	133.386%
Minimum	-37.986%
Maximum	95.400%
Count	61

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.552%	26	42.62%	11.743%
Negative	-16.185%	35	57.38%	-9.286%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	26.80%
12	1 Year	30.97%
36	3 Years	36.65%
60	5 Years	41.54%
120	10 Years	41.79%
240	20 Years	41.79%
600	50 Years	41.79%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.26. Further, an Excess Kurtosis of 1.73 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.26%	0	0.00%	0.00%
-35.26% to -12.94%	0	0.00%	0.00%
-12.94% to 9.38%	0	0.00%	0.00%
9.38% to 31.70%	15	24.19%	24.19%
31.70% to 54.02%	21	33.87%	58.06%
54.02% to 76.34%	13	20.97%	79.03%
76.34% to 98.66%	8	12.90%	91.94%
98.66% to 120.98%	3	4.84%	96.77%
120.98% to 143.30%	1	1.61%	98.39%
Greater than 143.30%	1	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	24.26%	83.78%	74.19%	68.27%
±2σ	-5.50%	113.54%	96.77%	95.45%
±3σ	-35.26%	143.30%	98.39%	99.73%

Descriptive Statistics

Mean	54.020%
Standard Error	3.779%
Median	48.007%
Mode	17.573%
Standard Deviation	29.759%
Sample Variance	885.578%
Kurtosis	1.73
Skewness	1.26
Range	141.238%
Minimum	17.573%
Maximum	158.811%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	54.020%	62	100.00%	54.020%
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 0.24. Further, an Excess Kurtosis of -0.18 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.19%	0	0.00%	0.00%
-74.19% to -54.52%	0	0.00%	0.00%
-54.52% to -34.84%	5	8.06%	8.06%
-34.84% to -15.17%	8	12.90%	20.97%
-15.17% to 4.50%	19	30.65%	51.61%
4.50% to 24.18%	19	30.65%	82.26%
24.18% to 43.85%	4	6.45%	88.71%
43.85% to 63.52%	7	11.29%	100.00%
63.52% to 83.20%	0	0.00%	100.00%
Greater than 83.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.73%	30.73%	69.35%	68.27%
±2σ	-47.96%	56.97%	93.55%	95.45%
±3σ	-74.19%	83.20%	100.00%	99.73%

Descriptive Statistics

Mean	4.503%
Standard Error	3.331%
Median	2.722%
Mode	-48.561%
Standard Deviation	26.231%
Sample Variance	688.090%
Kurtosis	-0.18
Skewness	0.24
Range	110.965%
Minimum	-48.561%
Maximum	62.404%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.140%	35	56.45%	12.498%
Negative	-18.360%	27	43.55%	-7.995%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.65. Further, an Excess Kurtosis of 2.50 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -177.41%	0	0.00%	0.00%
-177.41% to -130.62%	0	0.00%	0.00%
-130.62% to -83.82%	0	0.00%	0.00%
-83.82% to -37.02%	3	14.29%	14.29%
-37.02% to 9.77%	12	57.14%	71.43%
9.77% to 56.57%	3	14.29%	85.71%
56.57% to 103.37%	1	4.76%	90.48%
103.37% to 150.16%	1	4.76%	95.24%
150.16% to 196.96%	1	4.76%	100.00%
Greater than 196.96%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-52.62%	72.17%	76.19%	68.27%
±2σ	-115.02%	134.56%	95.24%	95.45%
±3σ	-177.41%	196.96%	100.00%	99.73%

Descriptive Statistics

Mean	9.773%
Standard Error	13.616%
Median	-15.274%
Mode	-60.572%
Standard Deviation	62.395%
Sample Variance	3893.193%
Kurtosis	2.50
Skewness	1.65
Range	249.102%
Minimum	-60.572%
Maximum	188.530%
Count	21

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	78.874%	7	33.33%	26.291%
Negative	-24.777%	14	66.67%	-16.518%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	43.17%
12	3 Years	74.87%
20	5 Years	79.71%
40	10 Years	79.91%
80	20 Years	79.91%
200	50 Years	79.91%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.60. Further, an Excess Kurtosis of -0.46 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -78.53%	0	0.00%	0.00%
-78.53% to -29.29%	0	0.00%	0.00%
-29.29% to 19.95%	0	0.00%	0.00%
19.95% to 69.19%	8	36.36%	36.36%
69.19% to 118.43%	2	9.09%	45.45%
118.43% to 167.67%	8	36.36%	81.82%
167.67% to 216.91%	2	9.09%	90.91%
216.91% to 266.15%	1	4.55%	95.45%
266.15% to 315.39%	1	4.55%	100.00%
Greater than 315.39%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	52.78%	184.09%	68.18%	68.27%
±2σ	-12.87%	249.74%	95.45%	95.45%
±3σ	-78.53%	315.39%	100.00%	99.73%

Descriptive Statistics

Mean	118.432%
Standard Error	13.997%
Median	123.812%
Mode	33.100%
Standard Deviation	65.653%
Sample Variance	4310.291%
Kurtosis	-0.46
Skewness	0.60
Range	233.630%
Minimum	33.100%
Maximum	266.730%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	118.432%	22	100.00%	118.432%
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 1.06. Further, an Excess Kurtosis of 1.82 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -143.70%	0	0.00%	0.00%
-143.70% to -104.36%	0	0.00%	0.00%
-104.36% to -65.02%	0	0.00%	0.00%
-65.02% to -25.68%	5	22.73%	22.73%
-25.68% to 13.65%	6	27.27%	50.00%
13.65% to 52.99%	8	36.36%	86.36%
52.99% to 92.33%	1	4.55%	90.91%
92.33% to 131.67%	1	4.55%	95.45%
131.67% to 171.01%	1	4.55%	100.00%
Greater than 171.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-38.80%	66.11%	77.27%	68.27%
±2σ	-91.25%	118.56%	90.91%	95.45%
±3σ	-143.70%	171.01%	100.00%	99.73%

Descriptive Statistics

Mean	13.654%
Standard Error	11.183%
Median	12.925%
Mode	-64.382%
Standard Deviation	52.452%
Sample Variance	2751.252%
Kurtosis	1.82
Skewness	1.06
Range	218.791%
Minimum	-64.382%
Maximum	154.409%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	41.181%	14	63.64%	26.206%
Negative	-34.516%	8	36.36%	-12.551%
Zero	0.000%	0	0.00%	0.000%

AFRM Deep Analytical Report