DBX - 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	2.42%	1.93%	2.10%	2.68%	2.46%	2.85%	24.04	25.25	23.46	25.88
Weekly	5.39%	4.98%	5.45%	6.19%	5.42%	6.28%	23.34	26.01	22.11	27.46
Monthly	8.64%	8.78%	9.25%	13.00%	11.27%	13.08%	22.01	27.58	19.67	30.87
Quarterly	15.04%	13.46%	14.95%	24.39%	19.53%	22.66%	20.27	29.95	16.67	36.41
Annual	—	—	—	—	39.06%	45.31%	16.67	36.41	11.28	53.81
Option Time Horizon	—	—	—	—	14.74%	17.10%	21.26	28.55	18.35	33.09

Calculation Notes: Computed at 2026-03-23T16:35 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $24.64 | Strike (K): $25.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.3500 (Bid $1.1500 / Ask $1.5500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 39.06% (CRR binomial tree, American, n=20 steps) | BS IV: 39.23% (European Black-Scholes) | Yahoo IV (Annual): 45.31% → 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 Fairly Symmetrical with a Skewness factor of -0.26. Further, an Excess Kurtosis of 10.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.25%	16	0.80%	0.80%
-7.25% to -5.43%	22	1.10%	1.89%
-5.43% to -3.61%	54	2.69%	4.58%
-3.61% to -1.80%	236	11.75%	16.33%
-1.80% to 0.02%	648	32.25%	48.58%
0.02% to 1.84%	703	34.99%	83.57%
1.84% to 3.66%	249	12.39%	95.97%
3.66% to 5.48%	50	2.49%	98.46%
5.48% to 7.30%	16	0.80%	99.25%
Greater than 7.30%	15	0.75%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.40%	2.45%	78.25%	68.27%
±2σ	-4.83%	4.87%	95.62%	95.45%
±3σ	-7.25%	7.30%	98.46%	99.73%

Descriptive Statistics

Mean	0.023%
Standard Error	0.054%
Median	0.099%
Mode	0.000%
Standard Deviation	2.425%
Sample Variance	5.880%
Kurtosis	10.95
Skewness	-0.26
Range	42.883%
Minimum	-22.926%
Maximum	19.957%
Count	2009

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.636%	1033	51.42%	0.841%
Negative	-1.726%	953	47.44%	-0.819%
Zero	0.000%	23	1.15%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	2.72%
20	1 Month	3.15%
60	1 Quarter	2.74%
250	1 Year	2.61%
750	3 Years	2.45%
1,250	5 Years	2.68%
2,500	10 Years	3.22%
5,000	20 Years	3.22%
12,500	50 Years	3.22%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.66. Further, an Excess Kurtosis of 10.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.68%	0	0.00%	0.00%
-2.68% to -1.23%	0	0.00%	0.00%
-1.23% to 0.21%	0	0.00%	0.00%
0.21% to 1.66%	299	14.88%	14.88%
1.66% to 3.10%	986	49.05%	63.93%
3.10% to 4.55%	431	21.44%	85.37%
4.55% to 6.00%	164	8.16%	93.53%
6.00% to 7.44%	55	2.74%	96.27%
7.44% to 8.89%	32	1.59%	97.86%
Greater than 8.89%	43	2.14%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	1.18%	5.03%	86.22%	68.27%
±2σ	-0.75%	6.96%	95.57%	95.45%
±3σ	-2.68%	8.89%	97.86%	99.73%

Descriptive Statistics

Mean	3.105%
Standard Error	0.043%
Median	2.585%
Mode	1.557%
Standard Deviation	1.928%
Sample Variance	3.716%
Kurtosis	10.56
Skewness	2.66
Range	17.524%
Minimum	0.750%
Maximum	18.274%
Count	2010

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.105%	2010	100.00%	3.105%
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 0.24. Further, an Excess Kurtosis of 4.21 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.29%	15	0.75%	0.75%
-6.29% to -4.72%	25	1.24%	1.99%
-4.72% to -3.15%	56	2.79%	4.78%
-3.15% to -1.58%	264	13.13%	17.91%
-1.58% to -0.01%	651	32.39%	50.30%
-0.01% to 1.57%	655	32.59%	82.89%
1.57% to 3.14%	227	11.29%	94.18%
3.14% to 4.71%	82	4.08%	98.26%
4.71% to 6.28%	21	1.04%	99.30%
Greater than 6.28%	14	0.70%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.10%	2.09%	76.62%	68.27%
±2σ	-4.20%	4.19%	94.88%	95.45%
±3σ	-6.29%	6.28%	98.56%	99.73%

Descriptive Statistics

Mean	-0.005%
Standard Error	0.047%
Median	-0.042%
Mode	0.000%
Standard Deviation	2.095%
Sample Variance	4.390%
Kurtosis	4.21
Skewness	0.24
Range	23.239%
Minimum	-10.078%
Maximum	13.161%
Count	2010

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.536%	977	48.61%	0.747%
Negative	-1.494%	1011	50.30%	-0.751%
Zero	0.000%	22	1.09%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.49. Further, an Excess Kurtosis of 8.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.08%	4	0.96%	0.96%
-16.08% to -12.04%	3	0.72%	1.68%
-12.04% to -7.99%	17	4.08%	5.76%
-7.99% to -3.95%	51	12.23%	17.99%
-3.95% to 0.09%	125	29.98%	47.96%
0.09% to 4.14%	148	35.49%	83.45%
4.14% to 8.18%	52	12.47%	95.92%
8.18% to 12.22%	11	2.64%	98.56%
12.22% to 16.27%	3	0.72%	99.28%
Greater than 16.27%	3	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.30%	5.49%	77.70%	68.27%
±2σ	-10.69%	10.88%	95.92%	95.45%
±3σ	-16.08%	16.27%	98.32%	99.73%

Descriptive Statistics

Mean	0.094%
Standard Error	0.264%
Median	0.260%
Mode	-2.782%
Standard Deviation	5.391%
Sample Variance	29.060%
Kurtosis	8.44
Skewness	0.49
Range	62.223%
Minimum	-22.688%
Maximum	39.535%
Count	417

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.636%	219	52.52%	1.910%
Negative	-3.862%	196	47.00%	-1.815%
Zero	0.000%	2	0.48%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	6.61%
12	1 Quarter	5.87%
52	1 Year	5.69%
156	3 Years	5.72%
260	5 Years	6.19%
520	10 Years	7.45%
1,040	20 Years	7.45%
2,600	50 Years	7.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.93. Further, an Excess Kurtosis of 13.28 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.14%	0	0.00%	0.00%
-7.14% to -3.41%	0	0.00%	0.00%
-3.41% to 0.33%	0	0.00%	0.00%
0.33% to 4.06%	66	15.79%	15.79%
4.06% to 7.80%	192	45.93%	61.72%
7.80% to 11.53%	104	24.88%	86.60%
11.53% to 15.27%	33	7.89%	94.50%
15.27% to 19.00%	7	1.67%	96.17%
19.00% to 22.73%	7	1.67%	97.85%
Greater than 22.73%	9	2.15%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.82%	12.78%	87.32%	68.27%
±2σ	-2.16%	17.75%	95.69%	95.45%
±3σ	-7.14%	22.73%	97.85%	99.73%

Descriptive Statistics

Mean	7.797%
Standard Error	0.244%
Median	6.617%
Mode	3.974%
Standard Deviation	4.979%
Sample Variance	24.790%
Kurtosis	13.28
Skewness	2.93
Range	43.118%
Minimum	2.270%
Maximum	45.388%
Count	418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.797%	418	100.00%	7.797%
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 0.75. Further, an Excess Kurtosis of 5.45 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.13%	1	0.24%	0.24%
-16.13% to -12.04%	5	1.20%	1.44%
-12.04% to -7.96%	7	1.67%	3.11%
-7.96% to -3.87%	57	13.64%	16.75%
-3.87% to 0.22%	160	38.28%	55.02%
0.22% to 4.30%	118	28.23%	83.25%
4.30% to 8.39%	48	11.48%	94.74%
8.39% to 12.48%	13	3.11%	97.85%
12.48% to 16.57%	4	0.96%	98.80%
Greater than 16.57%	5	1.20%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.23%	5.67%	76.56%	68.27%
±2σ	-10.68%	11.12%	95.45%	95.45%
±3σ	-16.13%	16.57%	98.56%	99.73%

Descriptive Statistics

Mean	0.218%
Standard Error	0.267%
Median	-0.149%
Mode	0.000%
Standard Deviation	5.449%
Sample Variance	29.693%
Kurtosis	5.45
Skewness	0.75
Range	55.201%
Minimum	-28.048%
Maximum	27.153%
Count	418

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.229%	198	47.37%	2.003%
Negative	-3.455%	216	51.67%	-1.785%
Zero	0.000%	4	0.96%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.32. Further, an Excess Kurtosis of 0.62 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.77%	0	0.00%	0.00%
-25.77% to -19.30%	2	2.08%	2.08%
-19.30% to -12.82%	3	3.12%	5.21%
-12.82% to -6.34%	14	14.58%	19.79%
-6.34% to 0.14%	29	30.21%	50.00%
0.14% to 6.61%	25	26.04%	76.04%
6.61% to 13.09%	17	17.71%	93.75%
13.09% to 19.57%	5	5.21%	98.96%
19.57% to 26.04%	1	1.04%	100.00%
Greater than 26.04%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.50%	8.77%	77.08%	68.27%
±2σ	-17.14%	17.41%	92.71%	95.45%
±3σ	-25.77%	26.04%	100.00%	99.73%

Descriptive Statistics

Mean	0.135%
Standard Error	0.881%
Median	0.112%
Mode	-24.400%
Standard Deviation	8.636%
Sample Variance	74.574%
Kurtosis	0.62
Skewness	-0.32
Range	45.350%
Minimum	-24.400%
Maximum	20.950%
Count	96

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.787%	48	50.00%	3.394%
Negative	-6.518%	48	50.00%	-3.259%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	9.10%
12	1 Year	10.54%
36	3 Years	12.32%
60	5 Years	13.00%
120	10 Years	15.71%
240	20 Years	15.71%
600	50 Years	15.71%

High-to-Low 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 2.07 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.99%	0	0.00%	0.00%
-8.99% to -2.40%	0	0.00%	0.00%
-2.40% to 4.19%	0	0.00%	0.00%
4.19% to 10.77%	22	22.68%	22.68%
10.77% to 17.36%	40	41.24%	63.92%
17.36% to 23.95%	18	18.56%	82.47%
23.95% to 30.53%	9	9.28%	91.75%
30.53% to 37.12%	2	2.06%	93.81%
37.12% to 43.71%	4	4.12%	97.94%
Greater than 43.71%	2	2.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.58%	26.14%	76.29%	68.27%
±2σ	-0.21%	34.93%	93.81%	95.45%
±3σ	-8.99%	43.71%	97.94%	99.73%

Descriptive Statistics

Mean	17.360%
Standard Error	0.892%
Median	14.928%
Mode	5.501%
Standard Deviation	8.783%
Sample Variance	77.144%
Kurtosis	2.07
Skewness	1.49
Range	42.358%
Minimum	5.501%
Maximum	47.859%
Count	97

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	17.360%	97	100.00%	17.360%
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 0.93. Further, an Excess Kurtosis of 1.96 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.13%	0	0.00%	0.00%
-27.13% to -20.19%	0	0.00%	0.00%
-20.19% to -13.25%	4	4.12%	4.12%
-13.25% to -6.31%	18	18.56%	22.68%
-6.31% to 0.63%	31	31.96%	54.64%
0.63% to 7.57%	28	28.87%	83.51%
7.57% to 14.50%	10	10.31%	93.81%
14.50% to 21.44%	2	2.06%	95.88%
21.44% to 28.38%	2	2.06%	97.94%
Greater than 28.38%	2	2.06%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.62%	9.88%	78.35%	68.27%
±2σ	-17.88%	19.13%	93.81%	95.45%
±3σ	-27.13%	28.38%	97.94%	99.73%

Descriptive Statistics

Mean	0.627%
Standard Error	0.939%
Median	-0.048%
Mode	-19.223%
Standard Deviation	9.251%
Sample Variance	85.588%
Kurtosis	1.96
Skewness	0.93
Range	52.250%
Minimum	-19.223%
Maximum	33.027%
Count	97

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.719%	47	48.45%	3.740%
Negative	-6.162%	49	50.52%	-3.113%
Zero	0.000%	1	1.03%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.40. Further, an Excess Kurtosis of -0.61 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.66%	0	0.00%	0.00%
-44.66% to -33.39%	0	0.00%	0.00%
-33.39% to -22.11%	1	3.12%	3.12%
-22.11% to -10.83%	10	31.25%	34.38%
-10.83% to 0.45%	7	21.88%	56.25%
0.45% to 11.73%	7	21.88%	78.12%
11.73% to 23.01%	3	9.38%	87.50%
23.01% to 34.29%	4	12.50%	100.00%
34.29% to 45.57%	0	0.00%	100.00%
Greater than 45.57%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.59%	15.49%	68.75%	68.27%
±2σ	-29.63%	30.53%	96.88%	95.45%
±3σ	-44.66%	45.57%	100.00%	99.73%

Descriptive Statistics

Mean	0.452%
Standard Error	2.659%
Median	-2.756%
Mode	-26.894%
Standard Deviation	15.039%
Sample Variance	226.184%
Kurtosis	-0.61
Skewness	0.40
Range	59.392%
Minimum	-26.894%
Maximum	32.498%
Count	32

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.558%	14	43.75%	6.369%
Negative	-10.519%	18	56.25%	-5.917%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	18.53%
12	3 Years	24.79%
20	5 Years	24.39%
40	10 Years	28.26%
80	20 Years	28.26%
200	50 Years	28.26%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Right Skewed (Positive Asymmetry) with a Skewness factor of 0.86. Further, an Excess Kurtosis of 0.53 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.54%	0	0.00%	0.00%
-7.54% to 2.55%	0	0.00%	0.00%
2.55% to 12.64%	1	3.03%	3.03%
12.64% to 22.74%	5	15.15%	18.18%
22.74% to 32.83%	14	42.42%	60.61%
32.83% to 42.92%	7	21.21%	81.82%
42.92% to 53.01%	3	9.09%	90.91%
53.01% to 63.10%	1	3.03%	93.94%
63.10% to 73.20%	2	6.06%	100.00%
Greater than 73.20%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	19.37%	46.28%	63.64%	68.27%
±2σ	5.92%	59.74%	90.91%	95.45%
±3σ	-7.54%	73.20%	100.00%	99.73%

Descriptive Statistics

Mean	32.829%
Standard Error	2.342%
Median	30.976%
Mode	11.471%
Standard Deviation	13.456%
Sample Variance	181.067%
Kurtosis	0.53
Skewness	0.86
Range	52.153%
Minimum	11.471%
Maximum	63.624%
Count	33

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	32.829%	33	100.00%	32.829%
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 0.24. Further, an Excess Kurtosis of -0.38 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.24%	0	0.00%	0.00%
-43.24% to -32.03%	0	0.00%	0.00%
-32.03% to -20.82%	1	3.03%	3.03%
-20.82% to -9.61%	7	21.21%	24.24%
-9.61% to 1.60%	8	24.24%	48.48%
1.60% to 12.81%	7	21.21%	69.70%
12.81% to 24.02%	8	24.24%	93.94%
24.02% to 35.23%	1	3.03%	96.97%
35.23% to 46.44%	1	3.03%	100.00%
Greater than 46.44%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-13.35%	16.55%	63.64%	68.27%
±2σ	-28.30%	31.50%	96.97%	95.45%
±3σ	-43.25%	46.44%	100.00%	99.73%

Descriptive Statistics

Mean	1.599%
Standard Error	2.602%
Median	2.053%
Mode	-24.972%
Standard Deviation	14.948%
Sample Variance	223.431%
Kurtosis	-0.38
Skewness	0.24
Range	62.537%
Minimum	-24.972%
Maximum	37.565%
Count	33

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.648%	18	54.55%	6.899%
Negative	-11.660%	15	45.45%	-5.300%
Zero	0.000%	0	0.00%	0.000%

DBX Deep Analytical Report