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%	3.02%	2.69%	3.55%	3.71%	3.77%	41.62	44.82	40.10	46.52
Weekly	7.00%	7.60%	6.84%	8.36%	8.17%	8.30%	39.80	46.87	36.68	50.85
Monthly	14.39%	19.12%	13.68%	17.92%	17.00%	17.28%	36.44	51.19	30.74	60.68
Quarterly	24.70%	35.66%	24.20%	31.00%	29.45%	29.93%	32.17	57.98	23.97	77.83
Annual	—	—	—	—	58.89%	59.86%	23.97	77.83	13.30	140.26
Option Time Horizon	—	—	—	—	22.23%	22.60%	34.58	53.94	27.69	67.37

Calculation Notes: Computed at 2026-03-23T16:37 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $43.19 | Strike (K): $45.00 (first OTM call ≥ spot) | Observed Mid-Price: $3.2000 (Bid $3.1000 / Ask $3.3000) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 58.89% (CRR binomial tree, American, n=20 steps) | BS IV: 59.57% (European Black-Scholes) | Yahoo IV (Annual): 59.86% → 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 17.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.26%	43	0.59%	0.59%
-9.26% to -6.93%	73	1.00%	1.58%
-6.93% to -4.59%	182	2.48%	4.07%
-4.59% to -2.26%	789	10.77%	14.84%
-2.26% to 0.07%	2764	37.72%	52.56%
0.07% to 2.40%	2458	33.55%	86.11%
2.40% to 4.73%	667	9.10%	95.21%
4.73% to 7.06%	193	2.63%	97.84%
7.06% to 9.39%	77	1.05%	98.89%
Greater than 9.39%	81	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.04%	3.18%	81.23%	68.27%
±2σ	-6.15%	6.28%	95.26%	95.45%
±3σ	-9.26%	9.39%	98.31%	99.73%

Descriptive Statistics

Mean	0.067%
Standard Error	0.036%
Median	0.000%
Mode	0.000%
Standard Deviation	3.108%
Sample Variance	9.660%
Kurtosis	17.29
Skewness	0.94
Range	76.401%
Minimum	-28.125%
Maximum	48.276%
Count	7327

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.135%	3563	48.63%	1.038%
Negative	-2.004%	3551	48.47%	-0.971%
Zero	0.000%	213	2.91%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.67%
20	1 Month	4.24%
60	1 Quarter	4.44%
250	1 Year	4.01%
750	3 Years	3.39%
1,250	5 Years	3.55%
2,500	10 Years	3.19%
5,000	20 Years	3.30%
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 45.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.38%	0	0.00%	0.00%
-5.38% to -3.11%	0	0.00%	0.00%
-3.11% to -0.84%	0	0.00%	0.00%
-0.84% to 1.42%	713	9.73%	9.73%
1.42% to 3.69%	4131	56.37%	66.10%
3.69% to 5.96%	1467	20.02%	86.12%
5.96% to 8.23%	538	7.34%	93.46%
8.23% to 10.50%	251	3.43%	96.89%
10.50% to 12.77%	99	1.35%	98.24%
Greater than 12.77%	129	1.76%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.67%	6.72%	89.38%	68.27%
±2σ	-2.36%	9.74%	96.17%	95.45%
±3σ	-5.38%	12.77%	98.24%	99.73%

Descriptive Statistics

Mean	3.692%
Standard Error	0.035%
Median	2.816%
Mode	3.226%
Standard Deviation	3.025%
Sample Variance	9.148%
Kurtosis	45.17
Skewness	4.49
Range	61.446%
Minimum	0.402%
Maximum	61.848%
Count	7328

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.692%	7328	100.00%	3.692%
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 14.17 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.00%	60	0.82%	0.82%
-8.00% to -5.99%	71	0.97%	1.79%
-5.99% to -3.98%	225	3.07%	4.86%
-3.98% to -1.96%	750	10.23%	15.09%
-1.96% to 0.05%	2703	36.89%	51.98%
0.05% to 2.06%	2388	32.59%	84.57%
2.06% to 4.08%	743	10.14%	94.71%
4.08% to 6.09%	253	3.45%	98.16%
6.09% to 8.11%	74	1.01%	99.17%
Greater than 8.11%	61	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.63%	2.74%	79.67%	68.27%
±2σ	-5.32%	5.42%	94.92%	95.45%
±3σ	-8.00%	8.11%	98.35%	99.73%

Descriptive Statistics

Mean	0.051%
Standard Error	0.031%
Median	0.000%
Mode	0.000%
Standard Deviation	2.685%
Sample Variance	7.208%
Kurtosis	14.17
Skewness	0.58
Range	64.963%
Minimum	-25.833%
Maximum	39.130%
Count	7328

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.874%	3584	48.91%	0.917%
Negative	-1.811%	3502	47.79%	-0.865%
Zero	0.000%	242	3.30%	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 8.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.67%	8	0.53%	0.53%
-20.67% to -15.42%	16	1.05%	1.58%
-15.42% to -10.17%	56	3.69%	5.27%
-10.17% to -4.92%	168	11.06%	16.33%
-4.92% to 0.33%	540	35.55%	51.88%
0.33% to 5.58%	504	33.18%	85.06%
5.58% to 10.83%	136	8.95%	94.01%
10.83% to 16.08%	58	3.82%	97.83%
16.08% to 21.33%	18	1.18%	99.01%
Greater than 21.33%	15	0.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.67%	7.33%	77.68%	68.27%
±2σ	-13.67%	14.33%	94.40%	95.45%
±3σ	-20.67%	21.33%	98.49%	99.73%

Descriptive Statistics

Mean	0.331%
Standard Error	0.180%
Median	0.090%
Mode	0.000%
Standard Deviation	7.000%
Sample Variance	49.005%
Kurtosis	8.95
Skewness	0.99
Range	99.355%
Minimum	-30.000%
Maximum	69.355%
Count	1519

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.059%	771	50.76%	2.568%
Negative	-4.667%	728	47.93%	-2.237%
Zero	0.000%	20	1.32%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	7.95%
12	1 Quarter	10.14%
52	1 Year	9.31%
156	3 Years	7.97%
260	5 Years	8.36%
520	10 Years	7.55%
1,040	20 Years	7.78%
2,600	50 Years	9.22%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -13.07%	0	0.00%	0.00%
-13.07% to -7.37%	0	0.00%	0.00%
-7.37% to -1.66%	0	0.00%	0.00%
-1.66% to 4.04%	209	13.75%	13.75%
4.04% to 9.74%	791	52.04%	65.79%
9.74% to 15.44%	287	18.88%	84.67%
15.44% to 21.15%	133	8.75%	93.42%
21.15% to 26.85%	49	3.22%	96.64%
26.85% to 32.55%	22	1.45%	98.09%
Greater than 32.55%	29	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.14%	17.34%	88.22%	68.27%
±2σ	-5.46%	24.95%	95.86%	95.45%
±3σ	-13.07%	32.55%	98.09%	99.73%

Descriptive Statistics

Mean	9.742%
Standard Error	0.195%
Median	7.547%
Mode	14.286%
Standard Deviation	7.603%
Sample Variance	57.802%
Kurtosis	14.39
Skewness	2.97
Range	74.375%
Minimum	0.625%
Maximum	75.000%
Count	1520

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.742%	1520	100.00%	9.742%
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 4.92 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.35%	7	0.46%	0.46%
-20.35% to -15.22%	15	0.99%	1.45%
-15.22% to -10.09%	56	3.68%	5.13%
-10.09% to -4.95%	166	10.92%	16.05%
-4.95% to 0.18%	566	37.24%	53.29%
0.18% to 5.31%	478	31.45%	84.74%
5.31% to 10.44%	142	9.34%	94.08%
10.44% to 15.57%	50	3.29%	97.37%
15.57% to 20.71%	23	1.51%	98.88%
Greater than 20.71%	17	1.12%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.67%	7.02%	77.96%	68.27%
±2σ	-13.51%	13.86%	94.54%	95.45%
±3σ	-20.35%	20.71%	98.42%	99.73%

Descriptive Statistics

Mean	0.178%
Standard Error	0.176%
Median	-0.079%
Mode	0.000%
Standard Deviation	6.843%
Sample Variance	46.825%
Kurtosis	4.92
Skewness	0.55
Range	83.154%
Minimum	-40.952%
Maximum	42.202%
Count	1520

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.065%	735	48.35%	2.449%
Negative	-4.519%	764	50.26%	-2.271%
Zero	0.000%	21	1.38%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.50. Further, an Excess Kurtosis of 8.27 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -41.79%	0	0.00%	0.00%
-41.79% to -31.00%	3	0.86%	0.86%
-31.00% to -20.21%	12	3.44%	4.30%
-20.21% to -9.42%	48	13.75%	18.05%
-9.42% to 1.36%	122	34.96%	53.01%
1.36% to 12.15%	115	32.95%	85.96%
12.15% to 22.94%	30	8.60%	94.56%
22.94% to 33.73%	10	2.87%	97.42%
33.73% to 44.52%	4	1.15%	98.57%
Greater than 44.52%	5	1.43%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.02%	15.75%	77.36%	68.27%
±2σ	-27.41%	30.14%	95.42%	95.45%
±3σ	-41.79%	44.52%	98.57%	99.73%

Descriptive Statistics

Mean	1.365%
Standard Error	0.770%
Median	0.539%
Mode	-1.852%
Standard Deviation	14.386%
Sample Variance	206.949%
Kurtosis	8.27
Skewness	1.50
Range	142.192%
Minimum	-38.346%
Maximum	103.846%
Count	349

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.234%	180	51.58%	5.794%
Negative	-9.256%	167	47.85%	-4.429%
Zero	0.000%	2	0.57%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	20.99%
12	1 Year	20.08%
36	3 Years	17.44%
60	5 Years	17.92%
120	10 Years	16.64%
240	20 Years	16.84%
600	50 Years	20.46%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.79%	0	0.00%	0.00%
-33.79% to -19.45%	0	0.00%	0.00%
-19.45% to -5.10%	0	0.00%	0.00%
-5.10% to 9.24%	33	9.43%	9.43%
9.24% to 23.58%	202	57.71%	67.14%
23.58% to 37.93%	69	19.71%	86.86%
37.93% to 52.27%	29	8.29%	95.14%
52.27% to 66.61%	5	1.43%	96.57%
66.61% to 80.96%	4	1.14%	97.71%
Greater than 80.96%	8	2.29%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	4.46%	42.71%	90.00%	68.27%
±2σ	-14.66%	61.83%	96.29%	95.45%
±3σ	-33.79%	80.96%	97.71%	99.73%

Descriptive Statistics

Mean	23.584%
Standard Error	1.022%
Median	18.370%
Mode	50.000%
Standard Deviation	19.124%
Sample Variance	365.733%
Kurtosis	17.92
Skewness	3.49
Range	166.410%
Minimum	5.590%
Maximum	172.000%
Count	350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.584%	350	100.00%	23.584%
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 2.33 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -40.40%	1	0.29%	0.29%
-40.40% to -30.14%	5	1.43%	1.71%
-30.14% to -19.88%	10	2.86%	4.57%
-19.88% to -9.62%	47	13.43%	18.00%
-9.62% to 0.64%	124	35.43%	53.43%
0.64% to 10.89%	99	28.29%	81.71%
10.89% to 21.15%	45	12.86%	94.57%
21.15% to 31.41%	7	2.00%	96.57%
31.41% to 41.67%	9	2.57%	99.14%
Greater than 41.67%	3	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.04%	14.31%	75.14%	68.27%
±2σ	-26.72%	27.99%	94.00%	95.45%
±3σ	-40.40%	41.67%	98.86%	99.73%

Descriptive Statistics

Mean	0.636%
Standard Error	0.731%
Median	-0.021%
Mode	0.000%
Standard Deviation	13.679%
Sample Variance	187.110%
Kurtosis	2.33
Skewness	0.51
Range	113.120%
Minimum	-50.943%
Maximum	62.177%
Count	350

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	10.979%	171	48.86%	5.364%
Negative	-9.402%	176	50.29%	-4.728%
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 -69.83%	0	0.00%	0.00%
-69.83% to -51.30%	0	0.00%	0.00%
-51.30% to -32.78%	5	4.31%	4.31%
-32.78% to -14.25%	17	14.66%	18.97%
-14.25% to 4.28%	38	32.76%	51.72%
4.28% to 22.80%	36	31.03%	82.76%
22.80% to 41.33%	13	11.21%	93.97%
41.33% to 59.86%	3	2.59%	96.55%
59.86% 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	-20.43%	28.98%	71.55%	68.27%
±2σ	-45.13%	53.68%	94.83%	95.45%
±3σ	-69.83%	78.39%	99.14%	99.73%

Descriptive Statistics

Mean	4.278%
Standard Error	2.294%
Median	1.832%
Mode	-44.595%
Standard Deviation	24.703%
Sample Variance	610.222%
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	-15.222%	55	47.41%	-7.217%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	32.15%
12	3 Years	30.75%
20	5 Years	31.00%
40	10 Years	29.44%
80	20 Years	29.56%
200	50 Years	36.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.14. 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 -60.10%	0	0.00%	0.00%
-60.10% to -33.36%	0	0.00%	0.00%
-33.36% to -6.62%	0	0.00%	0.00%
-6.62% to 20.12%	10	8.55%	8.55%
20.12% to 46.87%	72	61.54%	70.09%
46.87% to 73.61%	16	13.68%	83.76%
73.61% to 100.35%	7	5.98%	89.74%
100.35% to 127.09%	5	4.27%	94.02%
127.09% to 153.84%	5	4.27%	98.29%
Greater than 153.84%	2	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	11.21%	82.52%	86.32%	68.27%
±2σ	-24.45%	118.18%	93.16%	95.45%
±3σ	-60.10%	153.84%	98.29%	99.73%

Descriptive Statistics

Mean	46.867%
Standard Error	3.296%
Median	32.727%
Mode	14.289%
Standard Deviation	35.657%
Sample Variance	1271.421%
Kurtosis	4.91
Skewness	2.14
Range	194.802%
Minimum	14.289%
Maximum	209.091%
Count	117

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	46.867%	117	100.00%	46.867%
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 0.84. Further, an Excess Kurtosis of 1.18 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -70.94%	0	0.00%	0.00%
-70.94% to -52.79%	1	0.85%	0.85%
-52.79% to -34.64%	5	4.27%	5.13%
-34.64% to -16.48%	18	15.38%	20.51%
-16.48% to 1.67%	40	34.19%	54.70%
1.67% to 19.82%	32	27.35%	82.05%
19.82% to 37.97%	12	10.26%	92.31%
37.97% to 56.12%	5	4.27%	96.58%
56.12% to 74.27%	2	1.71%	98.29%
Greater than 74.27%	2	1.71%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-22.54%	25.87%	71.79%	68.27%
±2σ	-46.74%	50.07%	94.87%	95.45%
±3σ	-70.94%	74.27%	98.29%	99.73%

Descriptive Statistics

Mean	1.666%
Standard Error	2.237%
Median	-0.891%
Mode	-52.970%
Standard Deviation	24.201%
Sample Variance	585.665%
Kurtosis	1.18
Skewness	0.84
Range	136.710%
Minimum	-52.970%
Maximum	83.740%
Count	117

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	20.578%	57	48.72%	10.025%
Negative	-16.301%	60	51.28%	-8.359%
Zero	0.000%	0	0.00%	0.000%

KMX Deep Analytical Report