HRMY - 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	3.34%	2.76%	2.88%	4.57%	5.05%	5.12%	27.72	30.67	26.36	32.26
Weekly	7.26%	6.99%	7.10%	10.16%	11.12%	11.26%	26.09	32.59	23.35	36.42
Monthly	13.01%	12.49%	13.70%	21.39%	23.15%	23.44%	23.13	36.75	18.35	46.33
Quarterly	23.36%	20.46%	23.75%	37.80%	40.09%	40.60%	19.53	43.54	13.08	65.01
Annual	—	—	—	—	80.18%	81.20%	13.08	65.01	5.87	144.95
Option Time Horizon	—	—	—	—	30.84%	31.23%	21.42	39.69	15.74	54.03

Calculation Notes: Computed at 2026-02-22T12:59 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $29.16 | Strike (K): $30.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.3000 (Bid $2.0000 / Ask $4.6000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 80.18% (CRR binomial tree, American, n=20 steps) | BS IV: 80.47% (European Black-Scholes) | Yahoo IV (Annual): 81.20% → 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 Left Skewed (Negative Asymmetry) with a Skewness factor of -0.88. Further, an Excess Kurtosis of 11.39 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.99%	11	0.80%	0.80%
-9.99% to -7.48%	11	0.80%	1.59%
-7.48% to -4.97%	26	1.88%	3.47%
-4.97% to -2.47%	156	11.29%	14.76%
-2.47% to 0.04%	518	37.48%	52.24%
0.04% to 2.55%	432	31.26%	83.50%
2.55% to 5.05%	171	12.37%	95.88%
5.05% to 7.56%	33	2.39%	98.26%
7.56% to 10.07%	13	0.94%	99.20%
Greater than 10.07%	11	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.30%	3.38%	79.81%	68.27%
±2σ	-6.65%	6.73%	95.44%	95.45%
±3σ	-9.99%	10.07%	98.41%	99.73%

Descriptive Statistics

Mean	0.040%
Standard Error	0.090%
Median	-0.085%
Mode	0.000%
Standard Deviation	3.343%
Sample Variance	11.175%
Kurtosis	11.39
Skewness	-0.88
Range	49.681%
Minimum	-30.249%
Maximum	19.432%
Count	1382

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.362%	670	48.48%	1.145%
Negative	-2.175%	702	50.80%	-1.105%
Zero	0.000%	10	0.72%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.68%
20	1 Month	4.59%
60	1 Quarter	3.76%
250	1 Year	3.74%
750	3 Years	4.13%
1,250	5 Years	4.57%
2,500	10 Years	4.83%
5,000	20 Years	4.83%
12,500	50 Years	4.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.38. Further, an Excess Kurtosis of 9.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.48%	0	0.00%	0.00%
-3.48% to -1.41%	0	0.00%	0.00%
-1.41% to 0.66%	0	0.00%	0.00%
0.66% to 2.73%	244	17.64%	17.64%
2.73% to 4.80%	622	44.97%	62.62%
4.80% to 6.87%	304	21.98%	84.60%
6.87% to 8.94%	119	8.60%	93.20%
8.94% to 11.01%	43	3.11%	96.31%
11.01% to 13.08%	22	1.59%	97.90%
Greater than 13.08%	29	2.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.04%	7.56%	84.09%	68.27%
±2σ	-0.72%	10.32%	95.30%	95.45%
±3σ	-3.48%	13.08%	97.90%	99.73%

Descriptive Statistics

Mean	4.800%
Standard Error	0.074%
Median	4.058%
Mode	2.859%
Standard Deviation	2.760%
Sample Variance	7.617%
Kurtosis	9.01
Skewness	2.38
Range	26.404%
Minimum	1.155%
Maximum	27.559%
Count	1383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.800%	1383	100.00%	4.800%
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 0.51. Further, an Excess Kurtosis of 3.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.46%	7	0.51%	0.51%
-8.46% to -6.30%	12	0.87%	1.37%
-6.30% to -4.14%	53	3.83%	5.21%
-4.14% to -1.98%	183	13.23%	18.44%
-1.98% to 0.19%	458	33.12%	51.55%
0.19% to 2.35%	416	30.08%	81.63%
2.35% to 4.51%	190	13.74%	95.37%
4.51% to 6.67%	35	2.53%	97.90%
6.67% to 8.83%	11	0.80%	98.70%
Greater than 8.83%	18	1.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.70%	3.07%	75.42%	68.27%
±2σ	-5.58%	5.95%	95.30%	95.45%
±3σ	-8.46%	8.83%	98.19%	99.73%

Descriptive Statistics

Mean	0.187%
Standard Error	0.077%
Median	0.081%
Mode	0.000%
Standard Deviation	2.882%
Sample Variance	8.306%
Kurtosis	3.54
Skewness	0.51
Range	29.443%
Minimum	-13.222%
Maximum	16.221%
Count	1383

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.190%	719	51.99%	1.139%
Negative	-2.018%	652	47.14%	-0.951%
Zero	0.000%	12	0.87%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.07. Further, an Excess Kurtosis of 2.33 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.56%	3	1.05%	1.05%
-21.56% to -16.11%	5	1.74%	2.79%
-16.11% to -10.67%	8	2.79%	5.57%
-10.67% to -5.23%	29	10.10%	15.68%
-5.23% to 0.21%	111	38.68%	54.36%
0.21% to 5.66%	83	28.92%	83.28%
5.66% to 11.10%	31	10.80%	94.08%
11.10% to 16.54%	11	3.83%	97.91%
16.54% to 21.98%	4	1.39%	99.30%
Greater than 21.98%	2	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.04%	7.47%	75.96%	68.27%
±2σ	-14.30%	14.73%	92.68%	95.45%
±3σ	-21.56%	21.98%	98.26%	99.73%

Descriptive Statistics

Mean	0.213%
Standard Error	0.428%
Median	-0.230%
Mode	-0.224%
Standard Deviation	7.257%
Sample Variance	52.665%
Kurtosis	2.33
Skewness	-0.07
Range	53.206%
Minimum	-26.676%
Maximum	26.530%
Count	287

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.784%	133	46.34%	2.680%
Negative	-4.629%	153	53.31%	-2.468%
Zero	0.000%	1	0.35%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.16%
12	1 Quarter	9.08%
52	1 Year	8.76%
156	3 Years	9.41%
260	5 Years	10.16%
520	10 Years	10.66%
1,040	20 Years	10.66%
2,600	50 Years	10.66%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.77. Further, an Excess Kurtosis of 27.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.60%	0	0.00%	0.00%
-9.60% to -4.36%	0	0.00%	0.00%
-4.36% to 0.88%	0	0.00%	0.00%
0.88% to 6.12%	43	14.93%	14.93%
6.12% to 11.36%	142	49.31%	64.24%
11.36% to 16.59%	59	20.49%	84.72%
16.59% to 21.83%	29	10.07%	94.79%
21.83% to 27.07%	6	2.08%	96.88%
27.07% to 32.31%	4	1.39%	98.26%
Greater than 32.31%	5	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.37%	18.34%	85.42%	68.27%
±2σ	-2.62%	25.33%	95.83%	95.45%
±3σ	-9.60%	32.31%	98.26%	99.73%

Descriptive Statistics

Mean	11.355%
Standard Error	0.412%
Median	9.450%
Mode	6.626%
Standard Deviation	6.985%
Sample Variance	48.786%
Kurtosis	27.56
Skewness	3.77
Range	73.350%
Minimum	3.696%
Maximum	77.046%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.355%	288	100.00%	11.355%
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 1.07. Further, an Excess Kurtosis of 3.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.64%	0	0.00%	0.00%
-20.64% to -15.31%	1	0.35%	0.35%
-15.31% to -9.98%	14	4.86%	5.21%
-9.98% to -4.66%	38	13.19%	18.40%
-4.66% to 0.67%	102	35.42%	53.82%
0.67% to 6.00%	92	31.94%	85.76%
6.00% to 11.32%	22	7.64%	93.40%
11.32% to 16.65%	9	3.12%	96.53%
16.65% to 21.98%	5	1.74%	98.26%
Greater than 21.98%	5	1.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.43%	7.77%	78.12%	68.27%
±2σ	-13.54%	14.88%	94.79%	95.45%
±3σ	-20.64%	21.98%	98.26%	99.73%

Descriptive Statistics

Mean	0.670%
Standard Error	0.419%
Median	0.260%
Mode	-3.189%
Standard Deviation	7.103%
Sample Variance	50.451%
Kurtosis	3.61
Skewness	1.07
Range	56.645%
Minimum	-20.578%
Maximum	36.067%
Count	288

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.458%	149	51.74%	2.824%
Negative	-4.494%	138	47.92%	-2.153%
Zero	0.000%	1	0.35%	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 -0.39 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -38.47%	0	0.00%	0.00%
-38.47% to -28.71%	0	0.00%	0.00%
-28.71% to -18.96%	5	7.58%	7.58%
-18.96% to -9.20%	10	15.15%	22.73%
-9.20% to 0.55%	18	27.27%	50.00%
0.55% to 10.31%	15	22.73%	72.73%
10.31% to 20.06%	13	19.70%	92.42%
20.06% to 29.82%	5	7.58%	100.00%
29.82% to 39.57%	0	0.00%	100.00%
Greater than 39.57%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.45%	13.56%	69.70%	68.27%
±2σ	-25.46%	26.56%	95.45%	95.45%
±3σ	-38.47%	39.57%	100.00%	99.73%

Descriptive Statistics

Mean	0.552%
Standard Error	1.601%
Median	0.688%
Mode	-28.166%
Standard Deviation	13.006%
Sample Variance	169.162%
Kurtosis	-0.39
Skewness	-0.05
Range	57.715%
Minimum	-28.166%
Maximum	29.549%
Count	66

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.752%	34	51.52%	5.539%
Negative	-10.284%	32	48.48%	-4.986%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	18.90%
12	1 Year	20.40%
36	3 Years	19.71%
60	5 Years	21.39%
120	10 Years	22.41%
240	20 Years	22.41%
600	50 Years	22.41%

High-to-Low 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 3.85 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -11.47%	0	0.00%	0.00%
-11.47% to -2.10%	0	0.00%	0.00%
-2.10% to 7.26%	0	0.00%	0.00%
7.26% to 16.63%	15	22.39%	22.39%
16.63% to 25.99%	27	40.30%	62.69%
25.99% to 35.36%	12	17.91%	80.60%
35.36% to 44.73%	8	11.94%	92.54%
44.73% to 54.09%	3	4.48%	97.01%
54.09% to 63.46%	1	1.49%	98.51%
Greater than 63.46%	1	1.49%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.50%	38.48%	73.13%	68.27%
±2σ	1.02%	50.97%	95.52%	95.45%
±3σ	-11.47%	63.46%	98.51%	99.73%

Descriptive Statistics

Mean	25.993%
Standard Error	1.526%
Median	21.317%
Mode	10.999%
Standard Deviation	12.488%
Sample Variance	155.939%
Kurtosis	3.85
Skewness	1.65
Range	67.820%
Minimum	10.999%
Maximum	78.819%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	25.993%	67	100.00%	25.993%
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 0.69. Further, an Excess Kurtosis of 0.21 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -39.26%	0	0.00%	0.00%
-39.26% to -28.98%	0	0.00%	0.00%
-28.98% to -18.70%	2	2.99%	2.99%
-18.70% to -8.43%	16	23.88%	26.87%
-8.43% to 1.85%	18	26.87%	53.73%
1.85% to 12.12%	18	26.87%	80.60%
12.12% to 22.40%	7	10.45%	91.04%
22.40% to 32.67%	3	4.48%	95.52%
32.67% to 42.95%	3	4.48%	100.00%
Greater than 42.95%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.85%	15.55%	76.12%	68.27%
±2σ	-25.55%	29.25%	95.52%	95.45%
±3σ	-39.26%	42.95%	100.00%	99.73%

Descriptive Statistics

Mean	1.848%
Standard Error	1.674%
Median	-1.016%
Mode	-22.130%
Standard Deviation	13.701%
Sample Variance	187.712%
Kurtosis	0.21
Skewness	0.69
Range	61.085%
Minimum	-22.130%
Maximum	38.955%
Count	67

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.841%	33	49.25%	6.325%
Negative	-8.822%	34	50.75%	-4.477%
Zero	0.000%	0	0.00%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.59. Further, an Excess Kurtosis of 0.12 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -68.89%	0	0.00%	0.00%
-68.89% to -51.37%	0	0.00%	0.00%
-51.37% to -33.85%	0	0.00%	0.00%
-33.85% to -16.33%	6	27.27%	27.27%
-16.33% to 1.19%	6	27.27%	54.55%
1.19% to 18.70%	4	18.18%	72.73%
18.70% to 36.22%	5	22.73%	95.45%
36.22% to 53.74%	0	0.00%	95.45%
53.74% to 71.26%	1	4.55%	100.00%
Greater than 71.26%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.17%	24.54%	68.18%	68.27%
±2σ	-45.53%	47.90%	95.45%	95.45%
±3σ	-68.89%	71.26%	100.00%	99.73%

Descriptive Statistics

Mean	1.186%
Standard Error	4.980%
Median	-3.553%
Mode	-33.446%
Standard Deviation	23.358%
Sample Variance	545.581%
Kurtosis	0.12
Skewness	0.59
Range	91.970%
Minimum	-33.446%
Maximum	58.524%
Count	22

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	22.036%	10	45.45%	10.016%
Negative	-16.189%	12	54.55%	-8.830%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	35.04%
12	3 Years	33.78%
20	5 Years	37.80%
40	10 Years	38.29%
80	20 Years	38.29%
200	50 Years	38.29%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.20. Further, an Excess Kurtosis of 2.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.84%	0	0.00%	0.00%
-12.84% to 2.50%	0	0.00%	0.00%
2.50% to 17.84%	0	0.00%	0.00%
17.84% to 33.19%	5	21.74%	21.74%
33.19% to 48.53%	7	30.43%	52.17%
48.53% to 63.87%	7	30.43%	82.61%
63.87% to 79.21%	3	13.04%	95.65%
79.21% to 94.55%	0	0.00%	95.65%
94.55% to 109.89%	0	0.00%	95.65%
Greater than 109.89%	1	4.35%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	28.07%	68.98%	69.57%	68.27%
±2σ	7.62%	89.44%	95.65%	95.45%
±3σ	-12.84%	109.89%	95.65%	99.73%

Descriptive Statistics

Mean	48.527%
Standard Error	4.265%
Median	47.758%
Mode	18.020%
Standard Deviation	20.456%
Sample Variance	418.428%
Kurtosis	2.68
Skewness	1.20
Range	92.957%
Minimum	18.020%
Maximum	110.977%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	48.527%	23	100.00%	48.527%
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 0.50. Further, an Excess Kurtosis of -0.03 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -66.76%	0	0.00%	0.00%
-66.76% to -48.94%	0	0.00%	0.00%
-48.94% to -31.13%	1	4.35%	4.35%
-31.13% to -13.31%	5	21.74%	26.09%
-13.31% to 4.50%	6	26.09%	52.17%
4.50% to 22.32%	5	21.74%	73.91%
22.32% to 40.14%	4	17.39%	91.30%
40.14% to 57.95%	1	4.35%	95.65%
57.95% to 75.77%	1	4.35%	100.00%
Greater than 75.77%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.25%	28.26%	69.57%	68.27%
±2σ	-43.00%	52.01%	95.65%	95.45%
±3σ	-66.76%	75.77%	100.00%	99.73%

Descriptive Statistics

Mean	4.505%
Standard Error	4.953%
Median	2.802%
Mode	-36.364%
Standard Deviation	23.754%
Sample Variance	564.252%
Kurtosis	-0.03
Skewness	0.50
Range	95.030%
Minimum	-36.364%
Maximum	58.666%
Count	23

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.983%	13	56.52%	11.860%
Negative	-16.918%	10	43.48%	-7.356%
Zero	0.000%	0	0.00%	0.000%

HRMY Deep Analytical Report