KMX - 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	3.11%	3.03%	2.69%	3.53%	3.81%	3.87%	42.83	46.23	41.23	48.03
Weekly	7.01%	7.61%	6.85%	8.35%	8.40%	8.51%	40.92	48.40	37.62	52.64
Monthly	14.40%	19.15%	13.70%	17.95%	17.48%	17.73%	37.36	53.00	31.37	63.13
Quarterly	24.70%	35.67%	24.20%	30.95%	30.28%	30.70%	32.87	60.24	24.29	81.54
Annual	—	—	—	—	60.56%	61.40%	24.29	81.54	13.25	149.41
Option Time Horizon	—	—	—	—	23.29%	23.62%	35.25	56.17	27.93	70.91

Calculation Notes: Computed at 2026-02-22T14:21 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $44.50 | Strike (K): $45.00 (first OTM call ≥ spot) | Observed Mid-Price: $4.0000 (Bid $3.9000 / Ask $4.1000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 60.56% (CRR binomial tree, American, n=20 steps) | BS IV: 60.38% (European Black-Scholes) | Yahoo IV (Annual): 61.40% → 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 0.94. Further, an Excess Kurtosis of 17.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.27%	42	0.57%	0.57%
-9.27% to -6.93%	73	1.00%	1.57%
-6.93% to -4.60%	182	2.49%	4.07%
-4.60% to -2.27%	786	10.76%	14.82%
-2.27% to 0.07%	2759	37.76%	52.59%
0.07% to 2.40%	2449	33.52%	86.11%
2.40% to 4.73%	664	9.09%	95.20%
4.73% to 7.07%	193	2.64%	97.84%
7.07% to 9.40%	77	1.05%	98.89%
Greater than 9.40%	81	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.04%	3.18%	81.25%	68.27%
±2σ	-6.16%	6.29%	95.28%	95.45%
±3σ	-9.27%	9.40%	98.32%	99.73%

Descriptive Statistics

Mean	0.067%
Standard Error	0.036%
Median	0.000%
Mode	0.000%
Standard Deviation	3.111%
Sample Variance	9.676%
Kurtosis	17.28
Skewness	0.94
Range	76.401%
Minimum	-28.125%
Maximum	48.276%
Count	7306

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.138%	3551	48.60%	1.039%
Negative	-2.004%	3542	48.48%	-0.972%
Zero	0.000%	213	2.92%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	5.65%
20	1 Month	5.02%
60	1 Quarter	4.28%
250	1 Year	3.93%
750	3 Years	3.38%
1,250	5 Years	3.53%
2,500	10 Years	3.18%
5,000	20 Years	3.29%
12,500	50 Years	3.83%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 4.49. Further, an Excess Kurtosis of 45.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.39%	0	0.00%	0.00%
-5.39% to -3.12%	0	0.00%	0.00%
-3.12% to -0.85%	0	0.00%	0.00%
-0.85% to 1.42%	713	9.76%	9.76%
1.42% to 3.69%	4119	56.37%	66.13%
3.69% to 5.96%	1460	19.98%	86.11%
5.96% to 8.23%	537	7.35%	93.46%
8.23% to 10.50%	250	3.42%	96.88%
10.50% to 12.77%	99	1.35%	98.23%
Greater than 12.77%	129	1.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.66%	6.72%	89.38%	68.27%
±2σ	-2.36%	9.75%	96.15%	95.45%
±3σ	-5.39%	12.77%	98.23%	99.73%

Descriptive Statistics

Mean	3.691%
Standard Error	0.035%
Median	2.813%
Mode	3.226%
Standard Deviation	3.027%
Sample Variance	9.165%
Kurtosis	45.13
Skewness	4.49
Range	61.446%
Minimum	0.402%
Maximum	61.848%
Count	7307

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.691%	7307	100.00%	3.691%
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 0.58. Further, an Excess Kurtosis of 14.19 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.01%	60	0.82%	0.82%
-8.01% to -5.99%	71	0.97%	1.79%
-5.99% to -3.98%	225	3.08%	4.87%
-3.98% to -1.96%	745	10.20%	15.07%
-1.96% to 0.05%	2698	36.92%	51.99%
0.05% to 2.07%	2380	32.57%	84.56%
2.07% to 4.08%	742	10.15%	94.72%
4.08% to 6.09%	251	3.44%	98.15%
6.09% to 8.11%	75	1.03%	99.18%
Greater than 8.11%	60	0.82%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.63%	2.74%	79.70%	68.27%
±2σ	-5.32%	5.42%	94.92%	95.45%
±3σ	-8.01%	8.11%	98.36%	99.73%

Descriptive Statistics

Mean	0.052%
Standard Error	0.031%
Median	0.000%
Mode	0.000%
Standard Deviation	2.686%
Sample Variance	7.213%
Kurtosis	14.19
Skewness	0.58
Range	64.963%
Minimum	-25.833%
Maximum	39.130%
Count	7307

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.874%	3574	48.91%	0.917%
Negative	-1.811%	3491	47.78%	-0.865%
Zero	0.000%	242	3.31%	0.000%

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 8.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.70%	8	0.53%	0.53%
-20.70% to -15.44%	16	1.06%	1.58%
-15.44% to -10.18%	56	3.70%	5.28%
-10.18% to -4.92%	167	11.02%	16.30%
-4.92% to 0.33%	539	35.58%	51.88%
0.33% to 5.59%	501	33.07%	84.95%
5.59% to 10.85%	138	9.11%	94.06%
10.85% to 16.11%	57	3.76%	97.82%
16.11% to 21.37%	18	1.19%	99.01%
Greater than 21.37%	15	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.68%	7.34%	77.56%	68.27%
±2σ	-13.69%	14.36%	94.39%	95.45%
±3σ	-20.70%	21.37%	98.48%	99.73%

Descriptive Statistics

Mean	0.334%
Standard Error	0.180%
Median	0.090%
Mode	0.000%
Standard Deviation	7.011%
Sample Variance	49.152%
Kurtosis	8.91
Skewness	0.99
Range	99.355%
Minimum	-30.000%
Maximum	69.355%
Count	1515

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.072%	769	50.76%	2.574%
Negative	-4.675%	726	47.92%	-2.240%
Zero	0.000%	20	1.32%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	11.32%
12	1 Quarter	9.87%
52	1 Year	9.31%
156	3 Years	8.04%
260	5 Years	8.35%
520	10 Years	7.54%
1,040	20 Years	7.77%
2,600	50 Years	9.23%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.97. Further, an Excess Kurtosis of 14.35 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.09%	0	0.00%	0.00%
-13.09% to -7.38%	0	0.00%	0.00%
-7.38% to -1.67%	0	0.00%	0.00%
-1.67% to 4.04%	209	13.79%	13.79%
4.04% to 9.75%	788	51.98%	65.77%
9.75% to 15.46%	286	18.87%	84.63%
15.46% to 21.16%	133	8.77%	93.40%
21.16% to 26.87%	49	3.23%	96.64%
26.87% to 32.58%	22	1.45%	98.09%
Greater than 32.58%	29	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.13%	17.36%	88.19%	68.27%
±2σ	-5.48%	24.97%	95.84%	95.45%
±3σ	-13.09%	32.58%	98.09%	99.73%

Descriptive Statistics

Mean	9.746%
Standard Error	0.195%
Median	7.547%
Mode	14.286%
Standard Deviation	7.612%
Sample Variance	57.940%
Kurtosis	14.35
Skewness	2.97
Range	74.375%
Minimum	0.625%
Maximum	75.000%
Count	1516

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.746%	1516	100.00%	9.746%
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 0.55. Further, an Excess Kurtosis of 4.90 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.38%	7	0.46%	0.46%
-20.38% to -15.24%	15	0.99%	1.45%
-15.24% to -10.10%	56	3.69%	5.15%
-10.10% to -4.96%	167	11.02%	16.16%
-4.96% to 0.18%	563	37.14%	53.30%
0.18% to 5.32%	476	31.40%	84.70%
5.32% to 10.46%	143	9.43%	94.13%
10.46% to 15.59%	49	3.23%	97.36%
15.59% to 20.73%	23	1.52%	98.88%
Greater than 20.73%	17	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.68%	7.03%	77.97%	68.27%
±2σ	-13.53%	13.88%	94.53%	95.45%
±3σ	-20.38%	20.73%	98.42%	99.73%

Descriptive Statistics

Mean	0.177%
Standard Error	0.176%
Median	-0.079%
Mode	0.000%
Standard Deviation	6.852%
Sample Variance	46.950%
Kurtosis	4.90
Skewness	0.55
Range	83.154%
Minimum	-40.952%
Maximum	42.202%
Count	1516

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.073%	733	48.35%	2.453%
Negative	-4.529%	762	50.26%	-2.276%
Zero	0.000%	21	1.39%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.49. Further, an Excess Kurtosis of 8.24 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.84%	0	0.00%	0.00%
-41.84% to -31.03%	3	0.86%	0.86%
-31.03% to -20.23%	12	3.45%	4.31%
-20.23% to -9.43%	48	13.79%	18.10%
-9.43% to 1.38%	121	34.77%	52.87%
1.38% to 12.18%	115	33.05%	85.92%
12.18% to 22.98%	30	8.62%	94.54%
22.98% to 33.79%	10	2.87%	97.41%
33.79% to 44.59%	4	1.15%	98.56%
Greater than 44.59%	5	1.44%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.03%	15.78%	77.30%	68.27%
±2σ	-27.43%	30.19%	95.40%	95.45%
±3σ	-41.84%	44.59%	98.56%	99.73%

Descriptive Statistics

Mean	1.377%
Standard Error	0.772%
Median	0.696%
Mode	-1.852%
Standard Deviation	14.405%
Sample Variance	207.491%
Kurtosis	8.24
Skewness	1.49
Range	142.192%
Minimum	-38.346%
Maximum	103.846%
Count	348

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.296%	179	51.44%	5.810%
Negative	-9.238%	167	47.99%	-4.433%
Zero	0.000%	2	0.57%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.26%
12	1 Year	20.59%
36	3 Years	17.66%
60	5 Years	17.95%
120	10 Years	16.65%
240	20 Years	16.86%
600	50 Years	20.48%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.49. Further, an Excess Kurtosis of 17.86 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.83%	0	0.00%	0.00%
-33.83% to -19.47%	0	0.00%	0.00%
-19.47% to -5.11%	0	0.00%	0.00%
-5.11% to 9.25%	33	9.46%	9.46%
9.25% to 23.61%	201	57.59%	67.05%
23.61% to 37.97%	69	19.77%	86.82%
37.97% to 52.33%	29	8.31%	95.13%
52.33% to 66.69%	5	1.43%	96.56%
66.69% to 81.05%	4	1.15%	97.71%
Greater than 81.05%	8	2.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.46%	42.75%	89.97%	68.27%
±2σ	-14.69%	61.90%	96.28%	95.45%
±3σ	-33.83%	81.05%	97.71%	99.73%

Descriptive Statistics

Mean	23.607%
Standard Error	1.025%
Median	18.460%
Mode	50.000%
Standard Deviation	19.147%
Sample Variance	366.594%
Kurtosis	17.86
Skewness	3.49
Range	166.410%
Minimum	5.590%
Maximum	172.000%
Count	349

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.607%	349	100.00%	23.607%
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 2.32 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.45%	1	0.29%	0.29%
-40.45% to -30.18%	5	1.43%	1.72%
-30.18% to -19.91%	10	2.87%	4.58%
-19.91% to -9.64%	47	13.47%	18.05%
-9.64% to 0.64%	124	35.53%	53.58%
0.64% to 10.91%	99	28.37%	81.95%
10.91% to 21.18%	44	12.61%	94.56%
21.18% to 31.45%	7	2.01%	96.56%
31.45% to 41.73%	9	2.58%	99.14%
Greater than 41.73%	3	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.06%	14.33%	75.07%	68.27%
±2σ	-26.76%	28.03%	93.98%	95.45%
±3σ	-40.45%	41.73%	98.85%	99.73%

Descriptive Statistics

Mean	0.636%
Standard Error	0.733%
Median	-0.032%
Mode	0.000%
Standard Deviation	13.697%
Sample Variance	187.618%
Kurtosis	2.32
Skewness	0.51
Range	113.120%
Minimum	-50.943%
Maximum	62.177%
Count	349

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.029%	170	48.71%	5.372%
Negative	-9.393%	176	50.43%	-4.737%
Zero	0.000%	3	0.86%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.92. Further, an Excess Kurtosis of 2.28 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -69.79%	0	0.00%	0.00%
-69.79% to -51.27%	0	0.00%	0.00%
-51.27% to -32.74%	5	4.31%	4.31%
-32.74% to -14.22%	17	14.66%	18.97%
-14.22% to 4.30%	38	32.76%	51.72%
4.30% to 22.82%	36	31.03%	82.76%
22.82% to 41.35%	13	11.21%	93.97%
41.35% to 59.87%	3	2.59%	96.55%
59.87% to 78.39%	3	2.59%	99.14%
Greater than 78.39%	1	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-20.39%	29.00%	70.69%	68.27%
±2σ	-45.09%	53.70%	94.83%	95.45%
±3σ	-69.79%	78.39%	99.14%	99.73%

Descriptive Statistics

Mean	4.302%
Standard Error	2.293%
Median	1.832%
Mode	-44.595%
Standard Deviation	24.697%
Sample Variance	609.932%
Kurtosis	2.28
Skewness	0.92
Range	152.842%
Minimum	-44.595%
Maximum	108.247%
Count	116

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.859%	61	52.59%	11.495%
Negative	-15.170%	55	47.41%	-7.193%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.89%
12	3 Years	30.67%
20	5 Years	30.95%
40	10 Years	29.41%
80	20 Years	29.54%
200	50 Years	36.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.13. Further, an Excess Kurtosis of 4.91 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -60.14%	0	0.00%	0.00%
-60.14% to -33.39%	0	0.00%	0.00%
-33.39% to -6.64%	0	0.00%	0.00%
-6.64% to 20.11%	10	8.55%	8.55%
20.11% to 46.85%	72	61.54%	70.09%
46.85% to 73.60%	16	13.68%	83.76%
73.60% to 100.35%	7	5.98%	89.74%
100.35% to 127.10%	5	4.27%	94.02%
127.10% to 153.85%	5	4.27%	98.29%
Greater than 153.85%	2	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.19%	82.52%	86.32%	68.27%
±2σ	-24.48%	118.19%	93.16%	95.45%
±3σ	-60.14%	153.85%	98.29%	99.73%

Descriptive Statistics

Mean	46.855%
Standard Error	3.297%
Median	32.727%
Mode	14.289%
Standard Deviation	35.666%
Sample Variance	1272.030%
Kurtosis	4.91
Skewness	2.13
Range	194.802%
Minimum	14.289%
Maximum	209.091%
Count	117

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.855%	117	100.00%	46.855%
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 0.85. Further, an Excess Kurtosis of 1.19 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -70.96%	0	0.00%	0.00%
-70.96% to -52.81%	1	0.85%	0.85%
-52.81% to -34.66%	5	4.27%	5.13%
-34.66% to -16.51%	18	15.38%	20.51%
-16.51% to 1.64%	41	35.04%	55.56%
1.64% to 19.79%	31	26.50%	82.05%
19.79% to 37.94%	12	10.26%	92.31%
37.94% to 56.09%	5	4.27%	96.58%
56.09% to 74.24%	2	1.71%	98.29%
Greater than 74.24%	2	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.56%	25.84%	71.79%	68.27%
±2σ	-46.76%	50.04%	94.87%	95.45%
±3σ	-70.96%	74.24%	98.29%	99.73%

Descriptive Statistics

Mean	1.641%
Standard Error	2.237%
Median	-0.891%
Mode	-52.970%
Standard Deviation	24.201%
Sample Variance	585.709%
Kurtosis	1.19
Skewness	0.85
Range	136.710%
Minimum	-52.970%
Maximum	83.740%
Count	117

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.905%	56	47.86%	10.006%
Negative	-16.044%	61	52.14%	-8.365%
Zero	0.000%	0	0.00%	0.000%

KMX Deep Analytical Report