XPO - 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	3.44%	3.46%	3.20%	3.99%	2.83%	3.00%	204.02	215.89	198.33	222.08
Weekly	7.56%	8.15%	7.33%	9.76%	6.22%	6.61%	197.21	223.35	185.31	237.69
Monthly	15.90%	17.28%	14.97%	20.56%	12.96%	13.75%	184.37	238.90	161.96	271.95
Quarterly	23.77%	31.69%	24.21%	33.36%	22.44%	23.82%	167.68	262.67	133.98	328.75
Annual	—	—	—	—	44.88%	47.63%	133.98	328.75	85.53	514.97
Option Time Horizon	—	—	—	—	17.26%	18.32%	176.59	249.42	148.60	296.41

Calculation Notes: Computed at 2026-02-22T13:04 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $209.87 | Strike (K): $210.00 (first OTM call ≥ spot) | Observed Mid-Price: $14.7500 (Bid $14.1000 / Ask $15.4000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 44.88% (CRR binomial tree, American, n=20 steps) | BS IV: 44.36% (European Black-Scholes) | Yahoo IV (Annual): 47.63% → 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 0.87. Further, an Excess Kurtosis of 11.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.17%	32	0.57%	0.57%
-10.17% to -7.59%	52	0.93%	1.50%
-7.59% to -5.01%	169	3.03%	4.53%
-5.01% to -2.43%	647	11.59%	16.12%
-2.43% to 0.14%	2111	37.81%	53.93%
0.14% to 2.72%	1708	30.59%	84.52%
2.72% to 5.30%	599	10.73%	95.25%
5.30% to 7.88%	151	2.70%	97.96%
7.88% to 10.46%	51	0.91%	98.87%
Greater than 10.46%	63	1.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.29%	3.58%	79.78%	68.27%
±2σ	-6.73%	7.02%	95.25%	95.45%
±3σ	-10.17%	10.46%	98.30%	99.73%

Descriptive Statistics

Mean	0.144%
Standard Error	0.046%
Median	0.000%
Mode	0.000%
Standard Deviation	3.438%
Sample Variance	11.818%
Kurtosis	11.53
Skewness	0.87
Range	64.166%
Minimum	-26.166%
Maximum	38.000%
Count	5583

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.576%	2651	47.48%	1.223%
Negative	-2.319%	2597	46.52%	-1.079%
Zero	0.000%	335	6.00%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	3.88%
20	1 Month	4.90%
60	1 Quarter	4.07%
250	1 Year	4.20%
750	3 Years	3.94%
1,250	5 Years	3.99%
2,500	10 Years	3.94%
5,000	20 Years	4.47%
12,500	50 Years	4.76%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.75%	0	0.00%	0.00%
-5.75% to -3.15%	0	0.00%	0.00%
-3.15% to -0.55%	0	0.00%	0.00%
-0.55% to 2.04%	694	12.43%	12.43%
2.04% to 4.64%	2937	52.60%	65.03%
4.64% to 7.24%	1176	21.06%	86.09%
7.24% to 9.84%	399	7.15%	93.23%
9.84% to 12.44%	190	3.40%	96.63%
12.44% to 15.04%	84	1.50%	98.14%
Greater than 15.04%	104	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.18%	8.11%	87.91%	68.27%
±2σ	-2.29%	11.57%	96.02%	95.45%
±3σ	-5.75%	15.04%	98.14%	99.73%

Descriptive Statistics

Mean	4.643%
Standard Error	0.046%
Median	3.680%
Mode	7.143%
Standard Deviation	3.465%
Sample Variance	12.006%
Kurtosis	22.99
Skewness	3.49
Range	50.924%
Minimum	0.392%
Maximum	51.316%
Count	5584

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.643%	5584	100.00%	4.643%
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 0.06. Further, an Excess Kurtosis of 7.26 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.62%	37	0.66%	0.66%
-9.62% to -7.22%	60	1.07%	1.74%
-7.22% to -4.82%	182	3.26%	5.00%
-4.82% to -2.42%	631	11.30%	16.30%
-2.42% to -0.02%	1747	31.29%	47.58%
-0.02% to 2.38%	2014	36.07%	83.65%
2.38% to 4.78%	637	11.41%	95.06%
4.78% to 7.18%	167	2.99%	98.05%
7.18% to 9.58%	62	1.11%	99.16%
Greater than 9.58%	47	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.22%	3.18%	77.56%	68.27%
±2σ	-6.42%	6.38%	94.99%	95.45%
±3σ	-9.62%	9.58%	98.50%	99.73%

Descriptive Statistics

Mean	-0.020%
Standard Error	0.043%
Median	0.000%
Mode	0.000%
Standard Deviation	3.200%
Sample Variance	10.241%
Kurtosis	7.26
Skewness	0.06
Range	55.647%
Minimum	-25.287%
Maximum	30.360%
Count	5584

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.319%	2614	46.81%	1.086%
Negative	-2.315%	2668	47.78%	-1.106%
Zero	0.000%	302	5.41%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.03. Further, an Excess Kurtosis of 10.42 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.00%	6	0.51%	0.51%
-22.00% to -16.33%	16	1.37%	1.89%
-16.33% to -10.66%	40	3.43%	5.32%
-10.66% to -4.99%	119	10.21%	15.52%
-4.99% to 0.68%	439	37.65%	53.17%
0.68% to 6.36%	354	30.36%	83.53%
6.36% to 12.03%	123	10.55%	94.08%
12.03% to 17.70%	50	4.29%	98.37%
17.70% to 23.37%	6	0.51%	98.89%
Greater than 23.37%	13	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-6.88%	8.25%	78.47%	68.27%
±2σ	-14.44%	15.81%	94.85%	95.45%
±3σ	-22.00%	23.37%	98.37%	99.73%

Descriptive Statistics

Mean	0.684%
Standard Error	0.221%
Median	0.346%
Mode	0.000%
Standard Deviation	7.563%
Sample Variance	57.194%
Kurtosis	10.42
Skewness	1.03
Range	106.128%
Minimum	-30.556%
Maximum	75.572%
Count	1166

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.669%	600	51.46%	2.917%
Negative	-4.988%	522	44.77%	-2.233%
Zero	0.000%	44	3.77%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	14.39%
12	1 Quarter	10.43%
52	1 Year	9.88%
156	3 Years	9.61%
260	5 Years	9.76%
520	10 Years	9.46%
1,040	20 Years	10.17%
2,600	50 Years	10.80%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.57. Further, an Excess Kurtosis of 25.37 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.91%	0	0.00%	0.00%
-12.91% to -6.80%	0	0.00%	0.00%
-6.80% to -0.69%	0	0.00%	0.00%
-0.69% to 5.42%	174	14.91%	14.91%
5.42% to 11.53%	576	49.36%	64.27%
11.53% to 17.64%	245	20.99%	85.26%
17.64% to 23.75%	99	8.48%	93.74%
23.75% to 29.86%	34	2.91%	96.66%
29.86% to 35.97%	22	1.89%	98.54%
Greater than 35.97%	17	1.46%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	3.38%	19.67%	87.15%	68.27%
±2σ	-4.77%	27.82%	95.89%	95.45%
±3σ	-12.91%	35.97%	98.54%	99.73%

Descriptive Statistics

Mean	11.527%
Standard Error	0.238%
Median	9.350%
Mode	16.667%
Standard Deviation	8.146%
Sample Variance	66.351%
Kurtosis	25.37
Skewness	3.57
Range	107.631%
Minimum	1.460%
Maximum	109.091%
Count	1167

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.527%	1167	100.00%	11.527%
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 Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 6.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -22.15%	5	0.43%	0.43%
-22.15% to -16.65%	10	0.86%	1.29%
-16.65% to -11.16%	36	3.08%	4.37%
-11.16% to -5.66%	158	13.54%	17.91%
-5.66% to -0.16%	385	32.99%	50.90%
-0.16% to 5.33%	395	33.85%	84.75%
5.33% to 10.83%	115	9.85%	94.60%
10.83% to 16.33%	36	3.08%	97.69%
16.33% to 21.82%	14	1.20%	98.89%
Greater than 21.82%	13	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.49%	7.17%	78.49%	68.27%
±2σ	-14.82%	14.49%	94.77%	95.45%
±3σ	-22.15%	21.82%	98.46%	99.73%

Descriptive Statistics

Mean	-0.163%
Standard Error	0.215%
Median	-0.313%
Mode	0.000%
Standard Deviation	7.329%
Sample Variance	53.717%
Kurtosis	6.02
Skewness	0.86
Range	85.566%
Minimum	-41.304%
Maximum	44.262%
Count	1167

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.314%	537	46.02%	2.445%
Negative	-5.056%	602	51.59%	-2.608%
Zero	0.000%	28	2.40%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.15. 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 -44.81%	0	0.00%	0.00%
-44.81% to -32.89%	2	0.75%	0.75%
-32.89% to -20.97%	11	4.10%	4.85%
-20.97% to -9.04%	38	14.18%	19.03%
-9.04% to 2.88%	93	34.70%	53.73%
2.88% to 14.80%	78	29.10%	82.84%
14.80% to 26.73%	32	11.94%	94.78%
26.73% to 38.65%	7	2.61%	97.39%
38.65% to 50.57%	5	1.87%	99.25%
Greater than 50.57%	2	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.02%	18.78%	74.63%	68.27%
±2σ	-28.92%	34.67%	94.78%	95.45%
±3σ	-44.82%	50.57%	99.25%	99.73%

Descriptive Statistics

Mean	2.879%
Standard Error	0.971%
Median	1.529%
Mode	0.000%
Standard Deviation	15.898%
Sample Variance	252.755%
Kurtosis	4.90
Skewness	1.15
Range	133.205%
Minimum	-36.083%
Maximum	97.122%
Count	268

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.403%	145	54.10%	7.252%
Negative	-10.017%	117	43.66%	-4.373%
Zero	0.000%	6	2.24%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	25.86%
12	1 Year	19.89%
36	3 Years	20.94%
60	5 Years	20.56%
120	10 Years	20.81%
240	20 Years	21.85%
600	50 Years	22.99%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.04. Further, an Excess Kurtosis of 16.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.26%	0	0.00%	0.00%
-25.26% to -12.30%	0	0.00%	0.00%
-12.30% to 0.65%	0	0.00%	0.00%
0.65% to 13.61%	40	14.87%	14.87%
13.61% to 26.57%	130	48.33%	63.20%
26.57% to 39.53%	59	21.93%	85.13%
39.53% to 52.49%	24	8.92%	94.05%
52.49% to 65.45%	8	2.97%	97.03%
65.45% to 78.41%	3	1.12%	98.14%
Greater than 78.41%	5	1.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	9.29%	43.85%	84.76%	68.27%
±2σ	-7.98%	61.13%	95.54%	95.45%
±3σ	-25.26%	78.41%	98.14%	99.73%

Descriptive Statistics

Mean	26.573%
Standard Error	1.054%
Median	21.845%
Mode	20.000%
Standard Deviation	17.279%
Sample Variance	298.570%
Kurtosis	16.02
Skewness	3.04
Range	156.023%
Minimum	5.795%
Maximum	161.818%
Count	269

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.573%	269	100.00%	26.573%
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 0.60. Further, an Excess Kurtosis of 1.79 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -45.55%	1	0.37%	0.37%
-45.55% to -34.32%	1	0.37%	0.74%
-34.32% to -23.09%	11	4.09%	4.83%
-23.09% to -11.85%	39	14.50%	19.33%
-11.85% to -0.62%	96	35.69%	55.02%
-0.62% to 10.61%	72	26.77%	81.78%
10.61% to 21.84%	30	11.15%	92.94%
21.84% to 33.07%	10	3.72%	96.65%
33.07% to 44.30%	7	2.60%	99.26%
Greater than 44.30%	2	0.74%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.60%	14.35%	75.46%	68.27%
±2σ	-30.57%	29.32%	94.05%	95.45%
±3σ	-45.55%	44.30%	98.88%	99.73%

Descriptive Statistics

Mean	-0.624%
Standard Error	0.913%
Median	-1.924%
Mode	0.000%
Standard Deviation	14.974%
Sample Variance	224.208%
Kurtosis	1.79
Skewness	0.60
Range	111.304%
Minimum	-49.635%
Maximum	61.669%
Count	269

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.400%	115	42.75%	5.301%
Negative	-10.555%	151	56.13%	-5.925%
Zero	0.000%	3	1.11%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.29. Further, an Excess Kurtosis of 0.59 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -63.42%	0	0.00%	0.00%
-63.42% to -45.59%	1	1.11%	1.11%
-45.59% to -27.76%	3	3.33%	4.44%
-27.76% to -9.93%	17	18.89%	23.33%
-9.93% to 7.89%	22	24.44%	47.78%
7.89% to 25.72%	30	33.33%	81.11%
25.72% to 43.55%	11	12.22%	93.33%
43.55% to 61.38%	3	3.33%	96.67%
61.38% to 79.21%	3	3.33%	100.00%
Greater than 79.21%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.88%	31.66%	68.89%	68.27%
±2σ	-39.65%	55.44%	94.44%	95.45%
±3σ	-63.42%	79.21%	100.00%	99.73%

Descriptive Statistics

Mean	7.894%
Standard Error	2.506%
Median	9.199%
Mode	-53.333%
Standard Deviation	23.771%
Sample Variance	565.076%
Kurtosis	0.59
Skewness	0.29
Range	130.107%
Minimum	-53.333%
Maximum	76.774%
Count	90

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	21.617%	57	63.33%	13.691%
Negative	-16.302%	32	35.56%	-5.796%
Zero	0.000%	1	1.11%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	31.28%
12	3 Years	35.72%
20	5 Years	33.36%
40	10 Years	35.01%
80	20 Years	37.86%
200	50 Years	39.93%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.84. Further, an Excess Kurtosis of 3.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.27%	0	0.00%	0.00%
-44.27% to -20.50%	0	0.00%	0.00%
-20.50% to 3.27%	0	0.00%	0.00%
3.27% to 27.04%	18	19.78%	19.78%
27.04% to 50.80%	39	42.86%	62.64%
50.80% to 74.57%	21	23.08%	85.71%
74.57% to 98.34%	5	5.49%	91.21%
98.34% to 122.11%	4	4.40%	95.60%
122.11% to 145.88%	1	1.10%	96.70%
Greater than 145.88%	3	3.30%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.11%	82.49%	84.62%	68.27%
±2σ	-12.58%	114.19%	93.41%	95.45%
±3σ	-44.27%	145.88%	96.70%	99.73%

Descriptive Statistics

Mean	50.803%
Standard Error	3.322%
Median	42.285%
Mode	66.667%
Standard Deviation	31.691%
Sample Variance	1004.348%
Kurtosis	3.44
Skewness	1.84
Range	146.459%
Minimum	15.359%
Maximum	161.818%
Count	91

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	50.803%	91	100.00%	50.803%
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 1.64. Further, an Excess Kurtosis of 5.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -75.13%	0	0.00%	0.00%
-75.13% to -56.97%	0	0.00%	0.00%
-56.97% to -38.81%	2	2.20%	2.20%
-38.81% to -20.65%	13	14.29%	16.48%
-20.65% to -2.49%	43	47.25%	63.74%
-2.49% to 15.67%	16	17.58%	81.32%
15.67% to 33.83%	11	12.09%	93.41%
33.83% to 51.99%	3	3.30%	96.70%
51.99% to 70.15%	2	2.20%	98.90%
Greater than 70.15%	1	1.10%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.70%	21.72%	75.82%	68.27%
±2σ	-50.92%	45.94%	96.70%	95.45%
±3σ	-75.13%	70.15%	98.90%	99.73%

Descriptive Statistics

Mean	-2.490%
Standard Error	2.538%
Median	-8.585%
Mode	0.000%
Standard Deviation	24.213%
Sample Variance	586.284%
Kurtosis	5.14
Skewness	1.64
Range	159.541%
Minimum	-45.255%
Maximum	114.286%
Count	91

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	23.963%	30	32.97%	7.900%
Negative	-16.026%	59	64.83%	-10.390%
Zero	0.000%	2	2.20%	0.000%

XPO Deep Analytical Report