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	6.09%	4.38%	4.98%	7.81%	5.30%	5.33%	43.12	47.94	40.90	50.55
Weekly	13.19%	12.79%	13.23%	19.08%	11.67%	11.74%	40.46	51.10	36.01	57.42
Monthly	28.79%	29.70%	26.13%	41.42%	24.29%	24.43%	35.67	57.97	27.98	73.90
Quarterly	62.61%	64.65%	52.57%	80.20%	42.06%	42.32%	29.86	69.25	19.61	105.46
Annual	—	—	—	—	84.13%	84.64%	19.61	105.46	8.45	244.59
Option Time Horizon	—	—	—	—	31.75%	31.95%	33.10	62.46	24.09	85.81

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $45.47 | Strike (K): $47.50 (first OTM call ≥ spot) | Observed Mid-Price: $5.0500 (Bid $4.9500 / Ask $5.1500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 84.13% (CRR binomial tree, American, n=20 steps) | BS IV: 84.84% (European Black-Scholes) | Yahoo IV (Annual): 84.64% → 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 5.79 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -18.16%	6	0.46%	0.46%
-18.16% to -13.59%	12	0.92%	1.38%
-13.59% to -9.02%	39	3.00%	4.38%
-9.02% to -4.45%	168	12.90%	17.28%
-4.45% to 0.12%	452	34.72%	52.00%
0.12% to 4.69%	407	31.26%	83.26%
4.69% to 9.27%	142	10.91%	94.16%
9.27% to 13.84%	46	3.53%	97.70%
13.84% to 18.41%	14	1.08%	98.77%
Greater than 18.41%	16	1.23%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.97%	6.22%	78.34%	68.27%
±2σ	-12.07%	12.31%	95.01%	95.45%
±3σ	-18.16%	18.41%	98.31%	99.73%

Descriptive Statistics

Mean	0.123%
Standard Error	0.169%
Median	-0.124%
Mode	-2.491%
Standard Deviation	6.095%
Sample Variance	37.150%
Kurtosis	5.79
Skewness	0.99
Range	69.306%
Minimum	-22.634%
Maximum	46.672%
Count	1302

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.496%	640	49.16%	2.210%
Negative	-4.123%	659	50.61%	-2.087%
Zero	0.000%	3	0.23%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.11%
20	1 Month	6.11%
60	1 Quarter	5.78%
250	1 Year	5.91%
750	3 Years	6.68%
1,250	5 Years	7.81%
2,500	10 Years	7.88%
5,000	20 Years	7.88%
12,500	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 3.54. Further, an Excess Kurtosis of 31.34 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.48%	0	0.00%	0.00%
-5.48% to -2.20%	0	0.00%	0.00%
-2.20% to 1.09%	0	0.00%	0.00%
1.09% to 4.37%	227	17.42%	17.42%
4.37% to 7.66%	574	44.05%	61.47%
7.66% to 10.94%	300	23.02%	84.50%
10.94% to 14.22%	115	8.83%	93.32%
14.22% to 17.51%	46	3.53%	96.85%
17.51% to 20.79%	23	1.77%	98.62%
Greater than 20.79%	18	1.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.28%	12.03%	82.04%	68.27%
±2σ	-1.10%	16.41%	96.16%	95.45%
±3σ	-5.48%	20.79%	98.62%	99.73%

Descriptive Statistics

Mean	7.655%
Standard Error	0.121%
Median	6.535%
Mode	6.443%
Standard Deviation	4.378%
Sample Variance	19.166%
Kurtosis	31.34
Skewness	3.54
Range	65.425%
Minimum	1.715%
Maximum	67.140%
Count	1303

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.655%	1303	100.00%	7.655%
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 1.86 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -14.74%	7	0.54%	0.54%
-14.74% to -11.01%	12	0.92%	1.46%
-11.01% to -7.28%	52	3.99%	5.45%
-7.28% to -3.54%	183	14.04%	19.49%
-3.54% to 0.19%	412	31.62%	51.11%
0.19% to 3.92%	385	29.55%	80.66%
3.92% to 7.66%	165	12.66%	93.32%
7.66% to 11.39%	64	4.91%	98.23%
11.39% to 15.12%	18	1.38%	99.62%
Greater than 15.12%	5	0.38%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.79%	5.17%	73.37%	68.27%
±2σ	-9.76%	10.15%	94.55%	95.45%
±3σ	-14.74%	15.12%	99.08%	99.73%

Descriptive Statistics

Mean	0.191%
Standard Error	0.138%
Median	0.047%
Mode	0.000%
Standard Deviation	4.978%
Sample Variance	24.779%
Kurtosis	1.86
Skewness	0.16
Range	49.840%
Minimum	-21.619%
Maximum	28.221%
Count	1303

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.913%	654	50.19%	1.964%
Negative	-3.587%	644	49.42%	-1.773%
Zero	0.000%	5	0.38%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.63. Further, an Excess Kurtosis of 1.65 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.09%	0	0.00%	0.00%
-39.09% to -29.19%	2	0.74%	0.74%
-29.19% to -19.30%	13	4.81%	5.56%
-19.30% to -9.40%	41	15.19%	20.74%
-9.40% to 0.49%	87	32.22%	52.96%
0.49% to 10.39%	77	28.52%	81.48%
10.39% to 20.28%	32	11.85%	93.33%
20.28% to 30.18%	12	4.44%	97.78%
30.18% to 40.07%	4	1.48%	99.26%
Greater than 40.07%	2	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.70%	13.69%	71.48%	68.27%
±2σ	-25.89%	26.88%	95.56%	95.45%
±3σ	-39.09%	40.07%	99.26%	99.73%

Descriptive Statistics

Mean	0.493%
Standard Error	0.803%
Median	-0.877%
Mode	-32.181%
Standard Deviation	13.193%
Sample Variance	174.061%
Kurtosis	1.65
Skewness	0.63
Range	92.212%
Minimum	-32.181%
Maximum	60.031%
Count	270

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.973%	129	47.78%	5.243%
Negative	-9.096%	141	52.22%	-4.750%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	14.20%
12	1 Quarter	13.65%
52	1 Year	13.93%
156	3 Years	16.00%
260	5 Years	19.08%
520	10 Years	19.08%
1,040	20 Years	19.08%
2,600	50 Years	19.08%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.03. 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 -16.99%	0	0.00%	0.00%
-16.99% to -7.40%	0	0.00%	0.00%
-7.40% to 2.19%	0	0.00%	0.00%
2.19% to 11.79%	53	19.56%	19.56%
11.79% to 21.38%	120	44.28%	63.84%
21.38% to 30.98%	50	18.45%	82.29%
30.98% to 40.57%	25	9.23%	91.51%
40.57% to 50.16%	14	5.17%	96.68%
50.16% to 59.76%	6	2.21%	98.89%
Greater than 59.76%	3	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.59%	34.17%	80.81%	68.27%
±2σ	-4.20%	46.96%	95.20%	95.45%
±3σ	-16.99%	59.76%	98.89%	99.73%

Descriptive Statistics

Mean	21.382%
Standard Error	0.777%
Median	17.803%
Mode	21.356%
Standard Deviation	12.791%
Sample Variance	163.613%
Kurtosis	6.25
Skewness	2.03
Range	87.617%
Minimum	5.653%
Maximum	93.270%
Count	271

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.382%	271	100.00%	21.382%
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 0.77 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.70%	0	0.00%	0.00%
-38.70% to -28.78%	2	0.74%	0.74%
-28.78% to -18.85%	11	4.06%	4.80%
-18.85% to -8.93%	44	16.24%	21.03%
-8.93% to 0.99%	90	33.21%	54.24%
0.99% to 10.92%	74	27.31%	81.55%
10.92% to 20.84%	28	10.33%	91.88%
20.84% to 30.76%	16	5.90%	97.79%
30.76% to 40.69%	3	1.11%	98.89%
Greater than 40.69%	3	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.24%	14.22%	70.11%	68.27%
±2σ	-25.47%	27.45%	94.46%	95.45%
±3σ	-38.70%	40.69%	98.89%	99.73%

Descriptive Statistics

Mean	0.993%
Standard Error	0.804%
Median	0.109%
Mode	-8.985%
Standard Deviation	13.231%
Sample Variance	175.068%
Kurtosis	0.77
Skewness	0.47
Range	82.726%
Minimum	-36.296%
Maximum	46.430%
Count	271

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.002%	136	50.19%	5.521%
Negative	-9.091%	135	49.81%	-4.529%
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 1.18. Further, an Excess Kurtosis of 1.22 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -84.12%	0	0.00%	0.00%
-84.12% to -62.53%	0	0.00%	0.00%
-62.53% to -40.93%	0	0.00%	0.00%
-40.93% to -19.34%	12	19.35%	19.35%
-19.34% to 2.26%	26	41.94%	61.29%
2.26% to 23.85%	12	19.35%	80.65%
23.85% to 45.45%	5	8.06%	88.71%
45.45% to 67.04%	4	6.45%	95.16%
67.04% to 88.64%	2	3.23%	98.39%
Greater than 88.64%	1	1.61%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.54%	31.05%	72.58%	68.27%
±2σ	-55.33%	59.85%	95.16%	95.45%
±3σ	-84.12%	88.64%	98.39%	99.73%

Descriptive Statistics

Mean	2.258%
Standard Error	3.657%
Median	-1.468%
Mode	-37.986%
Standard Deviation	28.794%
Sample Variance	829.073%
Kurtosis	1.22
Skewness	1.18
Range	133.386%
Minimum	-37.986%
Maximum	95.400%
Count	62

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.552%	26	41.94%	11.554%
Negative	-16.009%	36	58.06%	-9.296%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	29.00%
12	1 Year	30.01%
36	3 Years	36.30%
60	5 Years	41.42%
120	10 Years	41.55%
240	20 Years	41.55%
600	50 Years	41.55%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.27. Further, an Excess Kurtosis of 1.77 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -35.43%	0	0.00%	0.00%
-35.43% to -13.15%	0	0.00%	0.00%
-13.15% to 9.12%	0	0.00%	0.00%
9.12% to 31.39%	15	23.81%	23.81%
31.39% to 53.66%	22	34.92%	58.73%
53.66% to 75.93%	13	20.63%	79.37%
75.93% to 98.20%	8	12.70%	92.06%
98.20% to 120.48%	3	4.76%	96.83%
120.48% to 142.75%	1	1.59%	98.41%
Greater than 142.75%	1	1.59%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	23.96%	83.36%	74.60%	68.27%
±2σ	-5.73%	113.05%	96.83%	95.45%
±3σ	-35.43%	142.75%	98.41%	99.73%

Descriptive Statistics

Mean	53.661%
Standard Error	3.741%
Median	47.391%
Mode	17.573%
Standard Deviation	29.696%
Sample Variance	881.843%
Kurtosis	1.77
Skewness	1.27
Range	141.238%
Minimum	17.573%
Maximum	158.811%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	53.661%	63	100.00%	53.661%
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 0.23. 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 -73.80%	0	0.00%	0.00%
-73.80% to -54.20%	0	0.00%	0.00%
-54.20% to -34.60%	5	7.94%	7.94%
-34.60% to -15.00%	8	12.70%	20.63%
-15.00% to 4.59%	20	31.75%	52.38%
4.59% to 24.19%	18	28.57%	80.95%
24.19% to 43.79%	5	7.94%	88.89%
43.79% to 63.39%	7	11.11%	100.00%
63.39% to 82.98%	0	0.00%	100.00%
Greater than 82.98%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-21.54%	30.72%	69.84%	68.27%
±2σ	-47.67%	56.85%	93.65%	95.45%
±3σ	-73.80%	82.98%	100.00%	99.73%

Descriptive Statistics

Mean	4.594%
Standard Error	3.292%
Median	1.899%
Mode	-48.561%
Standard Deviation	26.130%
Sample Variance	682.761%
Kurtosis	-0.18
Skewness	0.23
Range	110.965%
Minimum	-48.561%
Maximum	62.404%
Count	63

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.810%	36	57.14%	12.463%
Negative	-18.360%	27	42.86%	-7.869%
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 2.48 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -178.50%	0	0.00%	0.00%
-178.50% to -131.54%	0	0.00%	0.00%
-131.54% to -84.58%	0	0.00%	0.00%
-84.58% to -37.62%	3	14.29%	14.29%
-37.62% to 9.34%	12	57.14%	71.43%
9.34% to 56.30%	3	14.29%	85.71%
56.30% to 103.25%	1	4.76%	90.48%
103.25% to 150.21%	1	4.76%	95.24%
150.21% to 197.17%	1	4.76%	100.00%
Greater than 197.17%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-53.28%	71.95%	76.19%	68.27%
±2σ	-115.89%	134.56%	95.24%	95.45%
±3σ	-178.50%	197.17%	100.00%	99.73%

Descriptive Statistics

Mean	9.336%
Standard Error	13.663%
Median	-16.110%
Mode	-60.572%
Standard Deviation	62.612%
Sample Variance	3920.223%
Kurtosis	2.48
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	-25.434%	14	66.67%	-16.956%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	45.60%
12	3 Years	75.68%
20	5 Years	80.20%
40	10 Years	80.37%
80	20 Years	80.37%
200	50 Years	80.37%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.65. Further, an Excess Kurtosis of -0.43 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -74.69%	0	0.00%	0.00%
-74.69% to -26.20%	0	0.00%	0.00%
-26.20% to 22.28%	0	0.00%	0.00%
22.28% to 70.76%	8	36.36%	36.36%
70.76% to 119.25%	2	9.09%	45.45%
119.25% to 167.73%	8	36.36%	81.82%
167.73% to 216.22%	2	9.09%	90.91%
216.22% to 264.70%	1	4.55%	95.45%
264.70% to 313.19%	1	4.55%	100.00%
Greater than 313.19%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	54.60%	183.89%	59.09%	68.27%
±2σ	-10.04%	248.54%	95.45%	95.45%
±3σ	-74.69%	313.19%	100.00%	99.73%

Descriptive Statistics

Mean	119.248%
Standard Error	13.783%
Median	123.812%
Mode	41.816%
Standard Deviation	64.646%
Sample Variance	4179.072%
Kurtosis	-0.43
Skewness	0.65
Range	224.914%
Minimum	41.816%
Maximum	266.730%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	119.248%	22	100.00%	119.248%
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 1.02. Further, an Excess Kurtosis of 1.72 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -143.41%	0	0.00%	0.00%
-143.41% to -103.99%	0	0.00%	0.00%
-103.99% to -64.56%	0	0.00%	0.00%
-64.56% to -25.13%	5	22.73%	22.73%
-25.13% to 14.30%	6	27.27%	50.00%
14.30% to 53.72%	8	36.36%	86.36%
53.72% to 93.15%	1	4.55%	90.91%
93.15% to 132.58%	1	4.55%	95.45%
132.58% to 172.01%	1	4.55%	100.00%
Greater than 172.01%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-38.27%	66.87%	77.27%	68.27%
±2σ	-90.84%	119.44%	90.91%	95.45%
±3σ	-143.41%	172.01%	100.00%	99.73%

Descriptive Statistics

Mean	14.296%
Standard Error	11.208%
Median	12.925%
Mode	-64.382%
Standard Deviation	52.570%
Sample Variance	2763.618%
Kurtosis	1.72
Skewness	1.02
Range	218.791%
Minimum	-64.382%
Maximum	154.409%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	42.189%	14	63.64%	26.847%
Negative	-34.516%	8	36.36%	-12.551%
Zero	0.000%	0	0.00%	0.000%

AFRM Deep Analytical Report