TRVG - 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	4.16%	5.33%	3.69%	5.61%	8.46%	8.46%	2.68	3.18	2.47	3.46
Weekly	8.90%	12.07%	8.70%	12.56%	18.63%	18.63%	2.42	3.52	2.01	4.24
Monthly	17.89%	25.99%	21.09%	24.72%	38.78%	38.79%	1.98	4.30	1.34	6.34
Quarterly	35.29%	63.02%	45.22%	44.68%	67.17%	67.19%	1.49	5.72	0.76	11.19
Annual	—	—	—	—	134.33%	134.38%	0.76	11.19	0.20	42.87
Option Time Horizon	—	—	—	—	48.20%	48.22%	1.80	4.73	1.11	7.66

Calculation Notes: Computed at 2026-03-01T12:16 UTC | Reference Contract: Call option expiring 2026-04-17 (47 days) | Spot Price (S): $2.92 | Strike (K): $5.00 (first OTM call ≥ spot) | Observed Mid-Price: $0.1250 (Bid $0.0000 / Ask $0.2500) | Risk-Free Rate (r): 3.74% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 134.33% (CRR binomial tree, American, n=20 steps) | BS IV: 135.27% (European Black-Scholes) | Yahoo IV (Annual): 134.38% → period-scaled as σ_period = σ_annual·√h | Price bands: Upper = S·e^+σ√h, Lower = S·e^−σ√h

Historical Dividend Payouts

Ex-Dividend Date	Amount
2023-11-14	$2.8250

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.33. Further, an Excess Kurtosis of 17.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.50%	11	0.47%	0.47%
-12.50% to -9.38%	11	0.47%	0.95%
-9.38% to -6.26%	51	2.19%	3.14%
-6.26% to -3.14%	282	12.12%	15.26%
-3.14% to -0.02%	851	36.59%	51.85%
-0.02% to 3.11%	768	33.02%	84.87%
3.11% to 6.23%	242	10.40%	95.27%
6.23% to 9.35%	58	2.49%	97.76%
9.35% to 12.47%	23	0.99%	98.75%
Greater than 12.47%	29	1.25%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.18%	4.15%	80.74%	68.27%
±2σ	-8.34%	8.31%	96.04%	95.45%
±3σ	-12.50%	12.47%	98.28%	99.73%

Descriptive Statistics

Mean	-0.016%
Standard Error	0.086%
Median	-0.294%
Mode	0.000%
Standard Deviation	4.162%
Sample Variance	17.324%
Kurtosis	17.01
Skewness	1.33
Range	79.769%
Minimum	-27.864%
Maximum	51.905%
Count	2326

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.239%	966	41.53%	1.345%
Negative	-2.624%	1206	51.85%	-1.361%
Zero	0.000%	154	6.62%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	1.81%
20	1 Month	2.24%
60	1 Quarter	2.96%
250	1 Year	5.21%
750	3 Years	5.46%
1,250	5 Years	5.61%
2,500	10 Years	6.00%
5,000	20 Years	6.00%
12,500	50 Years	6.00%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 16.97. Further, an Excess Kurtosis of 537.29 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.01%	0	0.00%	0.00%
-10.01% to -6.01%	0	0.00%	0.00%
-6.01% to -2.01%	0	0.00%	0.00%
-2.01% to 1.99%	117	5.03%	5.03%
1.99% to 5.98%	1387	59.60%	64.63%
5.98% to 9.98%	579	24.88%	89.51%
9.98% to 13.98%	138	5.93%	95.44%
13.98% to 17.98%	64	2.75%	98.20%
17.98% to 21.98%	24	1.03%	99.23%
Greater than 21.98%	18	0.77%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.65%	11.32%	92.48%	68.27%
±2σ	-4.68%	16.65%	97.51%	95.45%
±3σ	-10.01%	21.98%	99.23%	99.73%

Descriptive Statistics

Mean	5.984%
Standard Error	0.111%
Median	4.959%
Mode	4.167%
Standard Deviation	5.332%
Sample Variance	28.429%
Kurtosis	537.29
Skewness	16.97
Range	183.681%
Minimum	0.377%
Maximum	184.058%
Count	2327

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.984%	2327	100.00%	5.984%
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 -0.29. Further, an Excess Kurtosis of 6.52 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.86%	20	0.86%	0.86%
-10.86% to -8.10%	31	1.33%	2.19%
-8.10% to -5.33%	68	2.92%	5.11%
-5.33% to -2.57%	274	11.77%	16.89%
-2.57% to 0.19%	777	33.39%	50.28%
0.19% to 2.96%	765	32.87%	83.15%
2.96% to 5.72%	270	11.60%	94.76%
5.72% to 8.49%	84	3.61%	98.37%
8.49% to 11.25%	22	0.95%	99.31%
Greater than 11.25%	16	0.69%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.49%	3.88%	77.65%	68.27%
±2σ	-7.18%	7.57%	94.84%	95.45%
±3σ	-10.86%	11.25%	98.45%	99.73%

Descriptive Statistics

Mean	0.194%
Standard Error	0.076%
Median	0.171%
Mode	0.000%
Standard Deviation	3.686%
Sample Variance	13.583%
Kurtosis	6.52
Skewness	-0.29
Range	55.137%
Minimum	-32.915%
Maximum	22.222%
Count	2327

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.710%	1178	50.62%	1.372%
Negative	-2.720%	1008	43.32%	-1.178%
Zero	0.000%	141	6.06%	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 6.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -26.80%	2	0.41%	0.41%
-26.80% to -20.12%	7	1.45%	1.86%
-20.12% to -13.45%	13	2.69%	4.55%
-13.45% to -6.78%	56	11.59%	16.15%
-6.78% to -0.10%	179	37.06%	53.21%
-0.10% to 6.57%	149	30.85%	84.06%
6.57% to 13.24%	48	9.94%	94.00%
13.24% to 19.92%	15	3.11%	97.10%
19.92% to 26.59%	8	1.66%	98.76%
Greater than 26.59%	6	1.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.00%	8.79%	79.71%	68.27%
±2σ	-17.90%	17.69%	94.00%	95.45%
±3σ	-26.80%	26.59%	98.34%	99.73%

Descriptive Statistics

Mean	-0.104%
Standard Error	0.405%
Median	-0.676%
Mode	0.000%
Standard Deviation	8.898%
Sample Variance	79.179%
Kurtosis	6.49
Skewness	1.03
Range	93.038%
Minimum	-31.908%
Maximum	61.130%
Count	483

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.040%	206	42.65%	3.003%
Negative	-5.839%	257	53.21%	-3.107%
Zero	0.000%	20	4.14%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	4.83%
12	1 Quarter	6.37%
52	1 Year	11.92%
156	3 Years	12.44%
260	5 Years	12.56%
520	10 Years	13.55%
1,040	20 Years	13.55%
2,600	50 Years	13.55%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.85. Further, an Excess Kurtosis of 82.67 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -21.72%	0	0.00%	0.00%
-21.72% to -12.66%	0	0.00%	0.00%
-12.66% to -3.61%	0	0.00%	0.00%
-3.61% to 5.45%	27	5.58%	5.58%
5.45% to 14.50%	290	59.92%	65.50%
14.50% to 23.56%	111	22.93%	88.43%
23.56% to 32.61%	32	6.61%	95.04%
32.61% to 41.67%	11	2.27%	97.31%
41.67% to 50.73%	6	1.24%	98.55%
Greater than 50.73%	7	1.45%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.43%	26.58%	91.94%	68.27%
±2σ	-9.64%	38.65%	97.11%	95.45%
±3σ	-21.72%	50.73%	98.55%	99.73%

Descriptive Statistics

Mean	14.503%
Standard Error	0.549%
Median	11.564%
Mode	9.091%
Standard Deviation	12.074%
Sample Variance	145.781%
Kurtosis	82.67
Skewness	6.85
Range	181.392%
Minimum	2.666%
Maximum	184.058%
Count	484

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.503%	484	100.00%	14.503%
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 0.62. Further, an Excess Kurtosis of 4.14 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.07%	2	0.41%	0.41%
-25.07% to -18.55%	5	1.03%	1.45%
-18.55% to -12.02%	15	3.10%	4.55%
-12.02% to -5.50%	68	14.05%	18.60%
-5.50% to 1.02%	159	32.85%	51.45%
1.02% to 7.55%	158	32.64%	84.09%
7.55% to 14.07%	53	10.95%	95.04%
14.07% to 20.60%	12	2.48%	97.52%
20.60% to 27.12%	6	1.24%	98.76%
Greater than 27.12%	6	1.24%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.67%	9.72%	76.03%	68.27%
±2σ	-16.37%	18.42%	95.04%	95.45%
±3σ	-25.07%	27.12%	98.35%	99.73%

Descriptive Statistics

Mean	1.024%
Standard Error	0.395%
Median	0.829%
Mode	0.000%
Standard Deviation	8.699%
Sample Variance	75.675%
Kurtosis	4.14
Skewness	0.62
Range	83.957%
Minimum	-37.320%
Maximum	46.637%
Count	484

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.612%	263	54.34%	3.593%
Negative	-5.977%	208	42.98%	-2.569%
Zero	0.000%	13	2.69%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.25. Further, an Excess Kurtosis of 3.15 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -54.28%	0	0.00%	0.00%
-54.28% to -40.87%	0	0.00%	0.00%
-40.87% to -27.45%	5	4.50%	4.50%
-27.45% to -14.03%	16	14.41%	18.92%
-14.03% to -0.61%	43	38.74%	57.66%
-0.61% to 12.81%	30	27.03%	84.68%
12.81% to 26.23%	8	7.21%	91.89%
26.23% to 39.65%	6	5.41%	97.30%
39.65% to 53.07%	1	0.90%	98.20%
Greater than 53.07%	2	1.80%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-18.50%	17.28%	78.38%	68.27%
±2σ	-36.39%	35.17%	96.40%	95.45%
±3σ	-54.29%	53.07%	98.20%	99.73%

Descriptive Statistics

Mean	-0.609%
Standard Error	1.698%
Median	-2.878%
Mode	-35.827%
Standard Deviation	17.892%
Sample Variance	320.119%
Kurtosis	3.15
Skewness	1.25
Range	108.049%
Minimum	-35.827%
Maximum	72.222%
Count	111

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.673%	46	41.44%	6.081%
Negative	-11.423%	65	58.56%	-6.689%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	10.17%
12	1 Year	21.46%
36	3 Years	24.43%
60	5 Years	24.72%
120	10 Years	29.00%
240	20 Years	29.00%
600	50 Years	29.00%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.09. Further, an Excess Kurtosis of 13.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.32%	0	0.00%	0.00%
-43.32% to -23.82%	0	0.00%	0.00%
-23.82% to -4.33%	0	0.00%	0.00%
-4.33% to 15.16%	16	14.29%	14.29%
15.16% to 34.66%	62	55.36%	69.64%
34.66% to 54.15%	17	15.18%	84.82%
54.15% to 73.64%	11	9.82%	94.64%
73.64% to 93.14%	2	1.79%	96.43%
93.14% to 112.63%	1	0.89%	97.32%
Greater than 112.63%	3	2.68%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	8.66%	60.65%	90.18%	68.27%
±2σ	-17.33%	86.64%	96.43%	95.45%
±3σ	-43.32%	112.63%	97.32%	99.73%

Descriptive Statistics

Mean	34.657%
Standard Error	2.456%
Median	27.507%
Mode	20.172%
Standard Deviation	25.992%
Sample Variance	675.585%
Kurtosis	13.10
Skewness	3.09
Range	180.284%
Minimum	6.545%
Maximum	186.829%
Count	112

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	34.657%	112	100.00%	34.657%
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 2.19. Further, an Excess Kurtosis of 12.13 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -58.42%	0	0.00%	0.00%
-58.42% to -42.60%	0	0.00%	0.00%
-42.60% to -26.78%	3	2.68%	2.68%
-26.78% to -10.96%	14	12.50%	15.18%
-10.96% to 4.86%	45	40.18%	55.36%
4.86% to 20.68%	37	33.04%	88.39%
20.68% to 36.50%	6	5.36%	93.75%
36.50% to 52.33%	5	4.46%	98.21%
52.33% to 68.15%	1	0.89%	99.11%
Greater than 68.15%	1	0.89%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-16.23%	25.96%	81.25%	68.27%
±2σ	-37.33%	47.05%	94.64%	95.45%
±3σ	-58.42%	68.15%	99.11%	99.73%

Descriptive Statistics

Mean	4.861%
Standard Error	1.993%
Median	3.189%
Mode	0.000%
Standard Deviation	21.095%
Sample Variance	445.017%
Kurtosis	12.13
Skewness	2.19
Range	173.444%
Minimum	-39.401%
Maximum	134.043%
Count	112

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	15.706%	67	59.82%	9.395%
Negative	-11.810%	43	38.39%	-4.534%
Zero	0.000%	2	1.79%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.02. Further, an Excess Kurtosis of 0.55 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -106.38%	0	0.00%	0.00%
-106.38% to -79.91%	0	0.00%	0.00%
-79.91% to -53.44%	1	2.70%	2.70%
-53.44% to -26.97%	5	13.51%	16.22%
-26.97% to -0.50%	20	54.05%	70.27%
-0.50% to 25.97%	4	10.81%	81.08%
25.97% to 52.44%	3	8.11%	89.19%
52.44% to 78.91%	3	8.11%	97.30%
78.91% to 105.38%	1	2.70%	100.00%
Greater than 105.38%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-35.79%	34.79%	75.68%	68.27%
±2σ	-71.09%	70.08%	91.89%	95.45%
±3σ	-106.38%	105.38%	100.00%	99.73%

Descriptive Statistics

Mean	-0.501%
Standard Error	5.802%
Median	-10.204%
Mode	-65.632%
Standard Deviation	35.293%
Sample Variance	1245.580%
Kurtosis	0.55
Skewness	1.02
Range	152.299%
Minimum	-65.632%
Maximum	86.667%
Count	37

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	43.944%	11	29.73%	13.065%
Negative	-19.304%	26	70.27%	-13.565%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	34.46%
12	3 Years	44.64%
20	5 Years	44.68%
40	10 Years	57.44%
80	20 Years	57.44%
200	50 Years	57.44%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.13. Further, an Excess Kurtosis of 12.72 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -113.49%	0	0.00%	0.00%
-113.49% to -66.22%	0	0.00%	0.00%
-66.22% to -18.95%	0	0.00%	0.00%
-18.95% to 28.31%	3	7.89%	7.89%
28.31% to 75.58%	23	60.53%	68.42%
75.58% to 122.85%	7	18.42%	86.84%
122.85% to 170.12%	3	7.89%	94.74%
170.12% to 217.38%	1	2.63%	97.37%
217.38% to 264.65%	0	0.00%	97.37%
Greater than 264.65%	1	2.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	12.56%	138.60%	89.47%	68.27%
±2σ	-50.47%	201.63%	94.74%	95.45%
±3σ	-113.49%	264.65%	97.37%	99.73%

Descriptive Statistics

Mean	75.581%
Standard Error	10.224%
Median	57.015%
Mode	15.901%
Standard Deviation	63.023%
Sample Variance	3971.935%
Kurtosis	12.72
Skewness	3.13
Range	354.499%
Minimum	15.901%
Maximum	370.400%
Count	38

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	75.581%	38	100.00%	75.581%
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 1.81. Further, an Excess Kurtosis of 5.65 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -119.97%	0	0.00%	0.00%
-119.97% to -86.05%	0	0.00%	0.00%
-86.05% to -52.13%	0	0.00%	0.00%
-52.13% to -18.22%	7	18.42%	18.42%
-18.22% to 15.70%	13	34.21%	52.63%
15.70% to 49.62%	15	39.47%	92.11%
49.62% to 83.53%	1	2.63%	94.74%
83.53% to 117.45%	0	0.00%	94.74%
117.45% to 151.37%	1	2.63%	97.37%
Greater than 151.37%	1	2.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-29.52%	60.92%	76.32%	68.27%
±2σ	-74.74%	106.14%	94.74%	95.45%
±3σ	-119.97%	151.37%	97.37%	99.73%

Descriptive Statistics

Mean	15.700%
Standard Error	7.336%
Median	11.466%
Mode	-45.635%
Standard Deviation	45.222%
Sample Variance	2045.005%
Kurtosis	5.65
Skewness	1.81
Range	237.701%
Minimum	-45.635%
Maximum	192.066%
Count	38

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	36.403%	25	65.79%	23.949%
Negative	-24.114%	13	34.21%	-8.250%
Zero	0.000%	0	0.00%	0.000%

TRVG Deep Analytical Report