PLAY - 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	4.19%	4.02%	3.38%	4.89%	5.81%	5.86%	11.48	12.90	10.83	13.67
Weekly	8.22%	13.71%	12.28%	11.45%	12.80%	12.89%	10.71	13.83	9.42	15.72
Monthly	15.04%	54.66%	19.01%	24.90%	26.64%	26.84%	9.32	15.88	7.14	20.73
Quarterly	29.72%	131.64%	39.85%	44.16%	46.13%	46.48%	7.67	19.30	4.84	30.62
Annual	—	—	—	—	92.27%	92.97%	4.84	30.62	1.92	77.04
Option Time Horizon	—	—	—	—	34.83%	35.09%	8.59	17.24	6.06	24.42

Calculation Notes: Computed at 2026-03-23T16:37 UTC | Reference Contract: Call option expiring 2026-05-15 (52 days) | Spot Price (S): $12.17 | Strike (K): $13.00 (first OTM call ≥ spot) | Observed Mid-Price: $1.4000 (Bid $1.3500 / Ask $1.4500) | Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury) | Dividend Yield (q): 0.00% | Binomial IV (Annual): 92.27% (CRR binomial tree, American, n=20 steps) | BS IV: 93.34% (European Black-Scholes) | Yahoo IV (Annual): 92.97% → 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
2020-01-09	$0.1600
2019-10-10	$0.1600
2019-06-24	$0.1500
2019-03-25	$0.1500
2018-12-24	$0.1500
2018-09-24	$0.1500

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.74. Further, an Excess Kurtosis of 61.14 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%	18	0.63%	0.63%
-12.50% to -9.35%	18	0.63%	1.25%
-9.35% to -6.21%	56	1.95%	3.20%
-6.21% to -3.07%	246	8.55%	11.75%
-3.07% to 0.07%	1135	39.45%	51.20%
0.07% to 3.22%	1072	37.26%	88.46%
3.22% to 6.36%	224	7.79%	96.25%
6.36% to 9.50%	66	2.29%	98.54%
9.50% to 12.64%	16	0.56%	99.10%
Greater than 12.64%	26	0.90%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.12%	4.26%	84.85%	68.27%
±2σ	-8.31%	8.45%	96.42%	95.45%
±3σ	-12.50%	12.64%	98.47%	99.73%

Descriptive Statistics

Mean	0.074%
Standard Error	0.078%
Median	0.000%
Mode	0.000%
Standard Deviation	4.190%
Sample Variance	17.558%
Kurtosis	61.14
Skewness	2.74
Range	122.333%
Minimum	-45.742%
Maximum	76.591%
Count	2877

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.531%	1432	49.77%	1.260%
Negative	-2.391%	1427	49.60%	-1.186%
Zero	0.000%	18	0.63%	0.000%

Average True Range Percentage (ATRP)

Trading Days	Horizon	Average Daily True Range %
5	1 Week	7.10%
20	1 Month	6.47%
60	1 Quarter	6.11%
250	1 Year	5.99%
750	3 Years	4.87%
1,250	5 Years	4.89%
2,500	10 Years	4.77%
5,000	20 Years	4.66%
12,500	50 Years	4.66%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 8.04. Further, an Excess Kurtosis of 125.44 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -7.52%	0	0.00%	0.00%
-7.52% to -4.50%	0	0.00%	0.00%
-4.50% to -1.49%	0	0.00%	0.00%
-1.49% to 1.52%	103	3.58%	3.58%
1.52% to 4.53%	1804	62.68%	66.26%
4.53% to 7.55%	672	23.35%	89.61%
7.55% to 10.56%	176	6.12%	95.73%
10.56% to 13.57%	56	1.95%	97.67%
13.57% to 16.59%	32	1.11%	98.78%
Greater than 16.59%	35	1.22%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.52%	8.55%	92.70%	68.27%
±2σ	-3.50%	12.57%	97.08%	95.45%
±3σ	-7.52%	16.59%	98.78%	99.73%

Descriptive Statistics

Mean	4.534%
Standard Error	0.075%
Median	3.668%
Mode	1.914%
Standard Deviation	4.017%
Sample Variance	16.136%
Kurtosis	125.44
Skewness	8.04
Range	95.212%
Minimum	0.788%
Maximum	96.000%
Count	2878

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	4.534%	2878	100.00%	4.534%
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 0.81. Further, an Excess Kurtosis of 20.38 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -9.98%	16	0.56%	0.56%
-9.98% to -7.45%	22	0.76%	1.32%
-7.45% to -4.92%	75	2.61%	3.93%
-4.92% to -2.38%	318	11.05%	14.98%
-2.38% to 0.15%	1074	37.32%	52.29%
0.15% to 2.68%	962	33.43%	85.72%
2.68% to 5.22%	283	9.83%	95.55%
5.22% to 7.75%	79	2.74%	98.30%
7.75% to 10.28%	18	0.63%	98.92%
Greater than 10.28%	31	1.08%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.23%	3.53%	80.85%	68.27%
±2σ	-6.61%	6.91%	96.04%	95.45%
±3σ	-9.99%	10.28%	98.37%	99.73%

Descriptive Statistics

Mean	0.149%
Standard Error	0.063%
Median	0.033%
Mode	0.000%
Standard Deviation	3.378%
Sample Variance	11.411%
Kurtosis	20.38
Skewness	0.81
Range	79.364%
Minimum	-37.558%
Maximum	41.806%
Count	2878

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.319%	1449	50.35%	1.168%
Negative	-2.068%	1417	49.24%	-1.018%
Zero	0.000%	12	0.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.16. Further, an Excess Kurtosis of 13.53 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.36%	3	0.50%	0.50%
-24.36% to -18.19%	9	1.51%	2.01%
-18.19% to -12.02%	16	2.68%	4.69%
-12.02% to -5.85%	56	9.38%	14.07%
-5.85% to 0.31%	228	38.19%	52.26%
0.31% to 6.48%	194	32.50%	84.76%
6.48% to 12.65%	66	11.06%	95.81%
12.65% to 18.82%	15	2.51%	98.32%
18.82% to 24.98%	5	0.84%	99.16%
Greater than 24.98%	5	0.84%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.91%	8.54%	80.90%	68.27%
±2σ	-16.13%	16.76%	95.14%	95.45%
±3σ	-24.36%	24.98%	98.66%	99.73%

Descriptive Statistics

Mean	0.313%
Standard Error	0.337%
Median	0.029%
Mode	0.000%
Standard Deviation	8.223%
Sample Variance	67.617%
Kurtosis	13.53
Skewness	-0.16
Range	120.796%
Minimum	-69.059%
Maximum	51.737%
Count	597

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	5.641%	299	50.08%	2.825%
Negative	-5.084%	295	49.41%	-2.512%
Zero	0.000%	3	0.50%	0.000%

Average True Range Percentage (ATRP)

Weeks	Horizon	Average Weekly True Range %
4	1 Month	13.92%
12	1 Quarter	14.70%
52	1 Year	14.12%
156	3 Years	11.55%
260	5 Years	11.45%
520	10 Years	11.04%
1,040	20 Years	10.78%
2,600	50 Years	10.78%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 10.39. Further, an Excess Kurtosis of 162.10 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -29.28%	0	0.00%	0.00%
-29.28% to -19.00%	0	0.00%	0.00%
-19.00% to -8.72%	0	0.00%	0.00%
-8.72% to 1.56%	0	0.00%	0.00%
1.56% to 11.84%	405	67.73%	67.73%
11.84% to 22.12%	145	24.25%	91.97%
22.12% to 32.40%	28	4.68%	96.66%
32.40% to 42.67%	9	1.51%	98.16%
42.67% to 52.95%	4	0.67%	98.83%
Greater than 52.95%	7	1.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.87%	25.54%	94.82%	68.27%
±2σ	-15.57%	39.25%	97.66%	95.45%
±3σ	-29.28%	52.95%	98.83%	99.73%

Descriptive Statistics

Mean	11.838%
Standard Error	0.560%
Median	8.953%
Mode	5.391%
Standard Deviation	13.705%
Sample Variance	187.822%
Kurtosis	162.10
Skewness	10.39
Range	248.983%
Minimum	1.931%
Maximum	250.914%
Count	598

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.838%	598	100.00%	11.838%
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 12.51. Further, an Excess Kurtosis of 240.77 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -36.12%	0	0.00%	0.00%
-36.12% to -26.91%	2	0.33%	0.33%
-26.91% to -17.70%	4	0.67%	1.00%
-17.70% to -8.49%	41	6.86%	7.86%
-8.49% to 0.72%	292	48.83%	56.69%
0.72% to 9.93%	213	35.62%	92.31%
9.93% to 19.14%	31	5.18%	97.49%
19.14% to 28.35%	12	2.01%	99.50%
28.35% to 37.56%	1	0.17%	99.67%
Greater than 37.56%	2	0.33%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-11.56%	13.00%	90.97%	68.27%
±2σ	-23.84%	25.28%	98.66%	95.45%
±3σ	-36.12%	37.56%	99.67%	99.73%

Descriptive Statistics

Mean	0.719%
Standard Error	0.502%
Median	-0.028%
Mode	0.000%
Standard Deviation	12.280%
Sample Variance	150.799%
Kurtosis	240.77
Skewness	12.51
Range	272.578%
Minimum	-32.856%
Maximum	239.722%
Count	598

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.205%	295	49.33%	3.061%
Negative	-4.669%	300	50.17%	-2.342%
Zero	0.000%	3	0.50%	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 1.73 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -44.25%	1	0.73%	0.73%
-44.25% to -32.97%	0	0.00%	0.73%
-32.97% to -21.69%	5	3.65%	4.38%
-21.69% to -10.41%	21	15.33%	19.71%
-10.41% to 0.86%	44	32.12%	51.82%
0.86% to 12.14%	33	24.09%	75.91%
12.14% to 23.42%	27	19.71%	95.62%
23.42% to 34.70%	2	1.46%	97.08%
34.70% to 45.98%	3	2.19%	99.27%
Greater than 45.98%	1	0.73%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-14.17%	15.90%	71.53%	68.27%
±2σ	-29.21%	30.94%	94.89%	95.45%
±3σ	-44.25%	45.98%	98.54%	99.73%

Descriptive Statistics

Mean	0.865%
Standard Error	1.285%
Median	0.349%
Mode	-60.376%
Standard Deviation	15.039%
Sample Variance	226.169%
Kurtosis	1.73
Skewness	-0.08
Range	107.928%
Minimum	-60.376%
Maximum	47.552%
Count	137

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	12.310%	69	50.37%	6.200%
Negative	-10.749%	68	49.63%	-5.335%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Months	Horizon	Average Monthly True Range %
3	1 Quarter	31.34%
12	1 Year	31.21%
36	3 Years	25.40%
60	5 Years	24.90%
120	10 Years	24.04%
240	20 Years	23.43%
600	50 Years	23.43%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 10.37. Further, an Excess Kurtosis of 116.04 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -133.19%	0	0.00%	0.00%
-133.19% to -92.19%	0	0.00%	0.00%
-92.19% to -51.19%	0	0.00%	0.00%
-51.19% to -10.20%	0	0.00%	0.00%
-10.20% to 30.80%	100	72.46%	72.46%
30.80% to 71.79%	34	24.64%	97.10%
71.79% to 112.79%	3	2.17%	99.28%
112.79% to 153.78%	0	0.00%	99.28%
153.78% to 194.78%	0	0.00%	99.28%
Greater than 194.78%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-23.86%	85.46%	98.55%	68.27%
±2σ	-78.52%	140.12%	99.28%	95.45%
±3σ	-133.19%	194.78%	99.28%	99.73%

Descriptive Statistics

Mean	30.798%
Standard Error	4.653%
Median	23.127%
Mode	7.244%
Standard Deviation	54.661%
Sample Variance	2987.789%
Kurtosis	116.04
Skewness	10.37
Range	634.558%
Minimum	7.244%
Maximum	641.802%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.798%	138	100.00%	30.798%
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 3.84. Further, an Excess Kurtosis of 29.06 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -55.33%	0	0.00%	0.00%
-55.33% to -41.07%	0	0.00%	0.00%
-41.07% to -26.81%	3	2.17%	2.17%
-26.81% to -12.55%	20	14.49%	16.67%
-12.55% to 1.71%	55	39.86%	56.52%
1.71% to 15.97%	40	28.99%	85.51%
15.97% to 30.23%	15	10.87%	96.38%
30.23% to 44.49%	4	2.90%	99.28%
44.49% to 58.75%	0	0.00%	99.28%
Greater than 58.75%	1	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-17.30%	20.72%	84.78%	68.27%
±2σ	-36.32%	39.74%	99.28%	95.45%
±3σ	-55.33%	58.75%	99.28%	99.73%

Descriptive Statistics

Mean	1.709%
Standard Error	1.619%
Median	-0.101%
Mode	-1.725%
Standard Deviation	19.014%
Sample Variance	361.520%
Kurtosis	29.06
Skewness	3.84
Range	185.266%
Minimum	-31.367%
Maximum	153.899%
Count	138

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.168%	67	48.55%	6.879%
Negative	-10.048%	71	51.45%	-5.170%
Zero	0.000%	0	0.00%	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 1.41 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -85.72%	0	0.00%	0.00%
-85.72% to -63.43%	1	2.17%	2.17%
-63.43% to -41.14%	1	2.17%	4.35%
-41.14% to -18.85%	8	17.39%	21.74%
-18.85% to 3.44%	14	30.43%	52.17%
3.44% to 25.73%	12	26.09%	78.26%
25.73% to 48.02%	7	15.22%	93.48%
48.02% to 70.31%	2	4.35%	97.83%
70.31% to 92.60%	0	0.00%	97.83%
Greater than 92.60%	1	2.17%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-26.28%	33.16%	69.57%	68.27%
±2σ	-56.00%	62.88%	95.65%	95.45%
±3σ	-85.72%	92.60%	97.83%	99.73%

Descriptive Statistics

Mean	3.440%
Standard Error	4.382%
Median	-0.405%
Mode	-66.848%
Standard Deviation	29.719%
Sample Variance	883.207%
Kurtosis	1.41
Skewness	0.49
Range	165.100%
Minimum	-66.848%
Maximum	98.252%
Count	46

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	27.157%	22	47.83%	12.988%
Negative	-18.301%	24	52.17%	-9.548%
Zero	0.000%	0	0.00%	0.000%

Average True Range Percentage (ATRP)

Quarters	Horizon	Average Quarterly True Range %
4	1 Year	61.52%
12	3 Years	49.71%
20	5 Years	44.16%
40	10 Years	44.82%
80	20 Years	43.45%
200	50 Years	43.45%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 6.33. Further, an Excess Kurtosis of 41.95 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -324.19%	0	0.00%	0.00%
-324.19% to -225.46%	0	0.00%	0.00%
-225.46% to -126.73%	0	0.00%	0.00%
-126.73% to -28.00%	0	0.00%	0.00%
-28.00% to 70.74%	39	82.98%	82.98%
70.74% to 169.47%	6	12.77%	95.74%
169.47% to 268.20%	1	2.13%	97.87%
268.20% to 366.93%	0	0.00%	97.87%
366.93% to 465.66%	0	0.00%	97.87%
Greater than 465.66%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-60.90%	202.38%	97.87%	68.27%
±2σ	-192.55%	334.02%	97.87%	95.45%
±3σ	-324.19%	465.66%	97.87%	99.73%

Descriptive Statistics

Mean	70.736%
Standard Error	19.202%
Median	42.586%
Mode	18.853%
Standard Deviation	131.641%
Sample Variance	17329.349%
Kurtosis	41.95
Skewness	6.33
Range	911.983%
Minimum	18.853%
Maximum	930.836%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	70.736%	47	100.00%	70.736%
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 2.83. Further, an Excess Kurtosis of 12.01 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -113.59%	0	0.00%	0.00%
-113.59% to -83.70%	0	0.00%	0.00%
-83.70% to -53.81%	0	0.00%	0.00%
-53.81% to -23.92%	7	14.89%	14.89%
-23.92% to 5.97%	23	48.94%	63.83%
5.97% to 35.85%	10	21.28%	85.11%
35.85% to 65.74%	5	10.64%	95.74%
65.74% to 95.63%	0	0.00%	95.74%
95.63% to 125.52%	1	2.13%	97.87%
Greater than 125.52%	1	2.13%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-33.89%	45.82%	89.36%	68.27%
±2σ	-73.74%	85.67%	95.74%	95.45%
±3σ	-113.59%	125.52%	97.87%	99.73%

Descriptive Statistics

Mean	5.966%
Standard Error	5.813%
Median	0.655%
Mode	-48.918%
Standard Deviation	39.852%
Sample Variance	1588.208%
Kurtosis	12.01
Skewness	2.83
Range	250.011%
Minimum	-48.918%
Maximum	201.093%
Count	47

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	30.018%	24	51.06%	15.328%
Negative	-19.131%	23	48.94%	-9.362%
Zero	0.000%	0	0.00%	0.000%

PLAY Deep Analytical Report