DLTR - 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	2.61%	2.25%	2.25%	2.98%	2.80%	3.01%	130.80	138.33	127.19	142.25
Weekly	5.64%	5.58%	5.67%	6.96%	6.16%	6.62%	126.48	143.05	118.92	152.14
Monthly	10.58%	13.02%	11.06%	15.92%	12.82%	13.77%	118.33	152.91	104.09	173.82
Quarterly	17.19%	21.07%	16.98%	29.20%	22.21%	23.85%	107.73	167.95	86.27	209.71
Annual	—	—	—	—	44.41%	47.71%	86.27	209.71	55.34	326.96
Option Time Horizon	—	—	—	—	17.08%	18.35%	113.39	159.57	95.58	189.29

Calculation Notes: Computed at 2026-02-22T14:21 UTC | Reference Contract: Call option expiring 2026-04-17 (54 days) | Spot Price (S): $134.51 | Strike (K): $135.00 (first OTM call ≥ spot) | Observed Mid-Price: $9.2000 (Bid $8.7000 / Ask $9.7000) | Risk-Free Rate (r): 3.72% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 44.41% (CRR binomial tree, American, n=20 steps) | BS IV: 44.06% (European Black-Scholes) | Yahoo IV (Annual): 47.71% → 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 -0.51. Further, an Excess Kurtosis of 17.80 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.73%	57	0.73%	0.73%
-7.73% to -5.77%	67	0.86%	1.59%
-5.77% to -3.82%	219	2.81%	4.40%
-3.82% to -1.86%	793	10.18%	14.59%
-1.86% to 0.10%	2908	37.34%	51.93%
0.10% to 2.05%	2602	33.41%	85.34%
2.05% to 4.01%	742	9.53%	94.86%
4.01% to 5.97%	231	2.97%	97.83%
5.97% to 7.92%	88	1.13%	98.96%
Greater than 7.92%	81	1.04%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.51%	2.71%	80.56%	68.27%
±2σ	-5.12%	5.31%	94.93%	95.45%
±3σ	-7.73%	7.92%	98.23%	99.73%

Descriptive Statistics

Mean	0.096%
Standard Error	0.030%
Median	0.000%
Mode	0.000%
Standard Deviation	2.609%
Sample Variance	6.809%
Kurtosis	17.80
Skewness	-0.51
Range	65.679%
Minimum	-43.814%
Maximum	21.865%
Count	7788

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.805%	3893	49.99%	0.902%
Negative	-1.670%	3763	48.32%	-0.807%
Zero	0.000%	132	1.70%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	4.39%
20	1 Month	3.48%
60	1 Quarter	3.52%
250	1 Year	3.64%
750	3 Years	3.10%
1,250	5 Years	2.98%
2,500	10 Years	2.75%
5,000	20 Years	2.72%
12,500	50 Years	3.30%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.81. Further, an Excess Kurtosis of 14.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -3.56%	0	0.00%	0.00%
-3.56% to -1.87%	0	0.00%	0.00%
-1.87% to -0.18%	0	0.00%	0.00%
-0.18% to 1.51%	1177	15.11%	15.11%
1.51% to 3.20%	3921	50.34%	65.45%
3.20% to 4.89%	1510	19.39%	84.84%
4.89% to 6.58%	612	7.86%	92.69%
6.58% to 8.27%	267	3.43%	96.12%
8.27% to 9.96%	153	1.96%	98.09%
Greater than 9.96%	149	1.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.95%	5.46%	86.35%	68.27%
±2σ	-1.31%	7.71%	95.02%	95.45%
±3σ	-3.56%	9.96%	98.10%	99.73%

Descriptive Statistics

Mean	3.201%
Standard Error	0.026%
Median	2.546%
Mode	4.167%
Standard Deviation	2.254%
Sample Variance	5.080%
Kurtosis	14.69
Skewness	2.81
Range	29.241%
Minimum	0.420%
Maximum	29.661%
Count	7789

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.201%	7789	100.00%	3.201%
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 4.11 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.76%	80	1.03%	1.03%
-6.76% to -5.07%	88	1.13%	2.16%
-5.07% to -3.38%	259	3.33%	5.48%
-3.38% to -1.70%	838	10.76%	16.24%
-1.70% to -0.01%	2563	32.91%	49.15%
-0.01% to 1.68%	2699	34.65%	83.80%
1.68% to 3.36%	834	10.71%	94.51%
3.36% to 5.05%	267	3.43%	97.93%
5.05% to 6.74%	94	1.21%	99.14%
Greater than 6.74%	67	0.86%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-2.26%	2.24%	78.07%	68.27%
±2σ	-4.51%	4.49%	94.38%	95.45%
±3σ	-6.76%	6.74%	98.11%	99.73%

Descriptive Statistics

Mean	-0.011%
Standard Error	0.025%
Median	0.000%
Mode	0.000%
Standard Deviation	2.249%
Sample Variance	5.056%
Kurtosis	4.11
Skewness	-0.06
Range	28.888%
Minimum	-14.366%
Maximum	14.522%
Count	7789

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.586%	3815	48.98%	0.777%
Negative	-1.599%	3836	49.25%	-0.787%
Zero	0.000%	138	1.77%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.12. Further, an Excess Kurtosis of 3.59 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -16.48%	13	0.80%	0.80%
-16.48% to -12.24%	20	1.24%	2.04%
-12.24% to -8.01%	63	3.90%	5.94%
-8.01% to -3.78%	162	10.03%	15.98%
-3.78% to 0.46%	575	35.60%	51.58%
0.46% to 4.69%	517	32.01%	83.59%
4.69% to 8.92%	165	10.22%	93.81%
8.92% to 13.16%	62	3.84%	97.65%
13.16% to 17.39%	24	1.49%	99.13%
Greater than 17.39%	14	0.87%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.19%	6.10%	77.89%	68.27%
±2σ	-10.83%	11.75%	93.31%	95.45%
±3σ	-16.48%	17.39%	98.33%	99.73%

Descriptive Statistics

Mean	0.456%
Standard Error	0.140%
Median	0.286%
Mode	0.000%
Standard Deviation	5.645%
Sample Variance	31.863%
Kurtosis	3.59
Skewness	-0.12
Range	62.730%
Minimum	-35.797%
Maximum	26.933%
Count	1615

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.121%	858	53.13%	2.189%
Negative	-3.728%	751	46.50%	-1.734%
Zero	0.000%	6	0.37%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	8.18%
12	1 Quarter	8.54%
52	1 Year	8.08%
156	3 Years	7.16%
260	5 Years	6.96%
520	10 Years	6.41%
1,040	20 Years	6.24%
2,600	50 Years	7.69%

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

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -8.74%	0	0.00%	0.00%
-8.74% to -4.56%	0	0.00%	0.00%
-4.56% to -0.37%	0	0.00%	0.00%
-0.37% to 3.82%	303	18.75%	18.75%
3.82% to 8.01%	729	45.11%	63.86%
8.01% to 12.20%	322	19.93%	83.79%
12.20% to 16.38%	129	7.98%	91.77%
16.38% to 20.57%	76	4.70%	96.47%
20.57% to 24.76%	29	1.79%	98.27%
Greater than 24.76%	28	1.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.42%	13.59%	84.53%	68.27%
±2σ	-3.16%	19.18%	95.36%	95.45%
±3σ	-8.74%	24.76%	98.27%	99.73%

Descriptive Statistics

Mean	8.008%
Standard Error	0.139%
Median	6.288%
Mode	3.231%
Standard Deviation	5.584%
Sample Variance	31.185%
Kurtosis	9.46
Skewness	2.38
Range	56.127%
Minimum	1.537%
Maximum	57.664%
Count	1616

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.008%	1616	100.00%	8.008%
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 1.11. Further, an Excess Kurtosis of 8.54 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -17.11%	6	0.37%	0.37%
-17.11% to -12.86%	19	1.18%	1.55%
-12.86% to -8.61%	63	3.90%	5.45%
-8.61% to -4.36%	176	10.89%	16.34%
-4.36% to -0.11%	587	36.32%	52.66%
-0.11% to 4.14%	524	32.43%	85.09%
4.14% to 8.38%	148	9.16%	94.25%
8.38% to 12.63%	52	3.22%	97.46%
12.63% to 16.88%	23	1.42%	98.89%
Greater than 16.88%	18	1.11%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-5.78%	5.55%	78.65%	68.27%
±2σ	-11.44%	11.22%	93.94%	95.45%
±3σ	-17.11%	16.88%	98.51%	99.73%

Descriptive Statistics

Mean	-0.113%
Standard Error	0.141%
Median	-0.336%
Mode	0.000%
Standard Deviation	5.665%
Sample Variance	32.097%
Kurtosis	8.54
Skewness	1.11
Range	77.699%
Minimum	-22.303%
Maximum	55.396%
Count	1616

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.086%	741	45.85%	1.874%
Negative	-3.702%	867	53.65%	-1.986%
Zero	0.000%	8	0.49%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.08. Further, an Excess Kurtosis of 1.24 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.93%	3	0.81%	0.81%
-29.93% to -22.00%	4	1.08%	1.89%
-22.00% to -14.06%	16	4.31%	6.20%
-14.06% to -6.12%	45	12.13%	18.33%
-6.12% to 1.81%	109	29.38%	47.71%
1.81% to 9.75%	122	32.88%	80.59%
9.75% to 17.68%	50	13.48%	94.07%
17.68% to 25.62%	17	4.58%	98.65%
25.62% to 33.55%	3	0.81%	99.46%
Greater than 33.55%	2	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.77%	12.39%	71.97%	68.27%
±2σ	-19.35%	22.97%	93.80%	95.45%
±3σ	-29.93%	33.55%	98.65%	99.73%

Descriptive Statistics

Mean	1.811%
Standard Error	0.549%
Median	2.118%
Mode	0.000%
Standard Deviation	10.581%
Sample Variance	111.954%
Kurtosis	1.24
Skewness	-0.08
Range	78.512%
Minimum	-36.088%
Maximum	42.424%
Count	371

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	8.541%	216	58.22%	4.973%
Negative	-7.717%	152	40.97%	-3.162%
Zero	0.000%	3	0.81%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	21.20%
12	1 Year	19.10%
36	3 Years	16.35%
60	5 Years	15.92%
120	10 Years	14.55%
240	20 Years	13.63%
600	50 Years	16.70%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.20. Further, an Excess Kurtosis of 19.64 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -20.17%	0	0.00%	0.00%
-20.17% to -10.41%	0	0.00%	0.00%
-10.41% to -0.65%	0	0.00%	0.00%
-0.65% to 9.12%	60	16.13%	16.13%
9.12% to 18.88%	176	47.31%	63.44%
18.88% to 28.64%	82	22.04%	85.48%
28.64% to 38.40%	29	7.80%	93.28%
38.40% to 48.17%	12	3.23%	96.51%
48.17% to 57.93%	9	2.42%	98.92%
Greater than 57.93%	4	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.86%	31.90%	86.83%	68.27%
±2σ	-7.15%	44.91%	95.97%	95.45%
±3σ	-20.17%	57.93%	98.92%	99.73%

Descriptive Statistics

Mean	18.879%
Standard Error	0.675%
Median	15.376%
Mode	14.925%
Standard Deviation	13.017%
Sample Variance	169.434%
Kurtosis	19.64
Skewness	3.20
Range	131.940%
Minimum	3.511%
Maximum	135.451%
Count	372

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	18.879%	372	100.00%	18.879%
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 1.19. Further, an Excess Kurtosis of 3.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -33.78%	0	0.00%	0.00%
-33.78% to -25.49%	1	0.27%	0.27%
-25.49% to -17.19%	15	4.03%	4.30%
-17.19% to -8.90%	56	15.05%	19.35%
-8.90% to -0.61%	134	36.02%	55.38%
-0.61% to 7.68%	104	27.96%	83.33%
7.68% to 15.97%	38	10.22%	93.55%
15.97% to 24.27%	12	3.23%	96.77%
24.27% to 32.56%	8	2.15%	98.92%
Greater than 32.56%	4	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.67%	10.45%	75.00%	68.27%
±2σ	-22.72%	21.50%	94.89%	95.45%
±3σ	-33.78%	32.56%	98.92%	99.73%

Descriptive Statistics

Mean	-0.610%
Standard Error	0.573%
Median	-1.873%
Mode	-12.500%
Standard Deviation	11.056%
Sample Variance	122.245%
Kurtosis	3.74
Skewness	1.19
Range	84.404%
Minimum	-28.369%
Maximum	56.035%
Count	372

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	9.131%	153	41.13%	3.755%
Negative	-7.484%	217	58.33%	-4.366%
Zero	0.000%	2	0.54%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.21. Further, an Excess Kurtosis of 0.20 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -46.46%	0	0.00%	0.00%
-46.46% to -33.57%	1	0.81%	0.81%
-33.57% to -20.68%	7	5.65%	6.45%
-20.68% to -7.78%	23	18.55%	25.00%
-7.78% to 5.11%	32	25.81%	50.81%
5.11% to 18.01%	36	29.03%	79.84%
18.01% to 30.90%	18	14.52%	94.35%
30.90% to 43.80%	4	3.23%	97.58%
43.80% to 56.69%	2	1.61%	99.19%
Greater than 56.69%	1	0.81%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-12.08%	22.30%	66.13%	68.27%
±2σ	-29.27%	39.50%	95.16%	95.45%
±3σ	-46.46%	56.69%	99.19%	99.73%

Descriptive Statistics

Mean	5.113%
Standard Error	1.544%
Median	4.851%
Mode	-38.049%
Standard Deviation	17.192%
Sample Variance	295.563%
Kurtosis	0.20
Skewness	0.21
Range	96.593%
Minimum	-38.049%
Maximum	58.544%
Count	124

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.392%	78	62.90%	9.682%
Negative	-12.317%	46	37.10%	-4.569%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	34.54%
12	3 Years	31.05%
20	5 Years	29.20%
40	10 Years	27.04%
80	20 Years	24.79%
200	50 Years	29.61%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.89. Further, an Excess Kurtosis of 4.75 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -27.18%	0	0.00%	0.00%
-27.18% to -11.38%	0	0.00%	0.00%
-11.38% to 4.42%	0	0.00%	0.00%
4.42% to 20.22%	27	21.60%	21.60%
20.22% to 36.02%	49	39.20%	60.80%
36.02% to 51.82%	28	22.40%	83.20%
51.82% to 67.62%	11	8.80%	92.00%
67.62% to 83.42%	4	3.20%	95.20%
83.42% to 99.22%	4	3.20%	98.40%
Greater than 99.22%	2	1.60%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	14.96%	57.09%	81.60%	68.27%
±2σ	-6.11%	78.16%	95.20%	95.45%
±3σ	-27.18%	99.22%	98.40%	99.73%

Descriptive Statistics

Mean	36.024%
Standard Error	1.884%
Median	30.988%
Mode	10.965%
Standard Deviation	21.067%
Sample Variance	443.838%
Kurtosis	4.75
Skewness	1.89
Range	124.486%
Minimum	10.965%
Maximum	135.451%
Count	125

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.024%	125	100.00%	36.024%
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 0.79. Further, an Excess Kurtosis of 1.07 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -53.20%	0	0.00%	0.00%
-53.20% to -40.46%	0	0.00%	0.00%
-40.46% to -27.73%	5	4.00%	4.00%
-27.73% to -14.99%	22	17.60%	21.60%
-14.99% to -2.26%	41	32.80%	54.40%
-2.26% to 10.48%	29	23.20%	77.60%
10.48% to 23.22%	20	16.00%	93.60%
23.22% to 35.95%	5	4.00%	97.60%
35.95% to 48.69%	2	1.60%	99.20%
Greater than 48.69%	1	0.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-19.24%	14.73%	67.20%	68.27%
±2σ	-36.22%	31.71%	96.00%	95.45%
±3σ	-53.20%	48.69%	99.20%	99.73%

Descriptive Statistics

Mean	-2.256%
Standard Error	1.519%
Median	-3.970%
Mode	-37.525%
Standard Deviation	16.981%
Sample Variance	288.351%
Kurtosis	1.07
Skewness	0.79
Range	98.787%
Minimum	-37.525%
Maximum	61.262%
Count	125

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.512%	46	36.80%	5.708%
Negative	-12.601%	79	63.20%	-7.964%
Zero	0.000%	0	0.00%	0.000%

DLTR Deep Analytical Report