PCAR - Detail Report

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.10. Further, an Excess Kurtosis of 5.49 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -6.00%	92	0.80%	0.80%
-6.00% to -4.48%	124	1.07%	1.87%
-4.48% to -2.96%	382	3.30%	5.17%
-2.96% to -1.44%	1263	10.92%	16.09%
-1.44% to 0.08%	4365	37.74%	53.83%
0.08% to 1.60%	3475	30.04%	83.87%
1.60% to 3.12%	1203	10.40%	94.27%
3.12% to 4.63%	422	3.65%	97.92%
4.63% to 6.15%	136	1.18%	99.09%
Greater than 6.15%	105	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.95%	2.10%	77.79%	68.27%
±2σ	-3.98%	4.13%	94.56%	95.45%
±3σ	-6.00%	6.15%	98.30%	99.73%

Descriptive Statistics

Mean	0.076%
Standard Error	0.019%
Median	0.000%
Mode	0.000%
Standard Deviation	2.026%
Sample Variance	4.105%
Kurtosis	5.49
Skewness	0.10
Range	32.553%
Minimum	-13.710%
Maximum	18.843%
Count	11567

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.536%	5479	47.37%	0.728%
Negative	-1.467%	5141	44.45%	-0.652%
Zero	0.000%	947	8.19%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.32. Further, an Excess Kurtosis of 9.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -2.78%	0	0.00%	0.00%
-2.78% to -1.47%	0	0.00%	0.00%
-1.47% to -0.16%	0	0.00%	0.00%
-0.16% to 1.15%	2247	19.42%	19.42%
1.15% to 2.46%	4980	43.05%	62.47%
2.46% to 3.77%	2492	21.54%	84.02%
3.77% to 5.08%	995	8.60%	92.62%
5.08% to 6.39%	450	3.89%	96.51%
6.39% to 7.71%	198	1.71%	98.22%
Greater than 7.71%	206	1.78%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	0.71%	4.21%	80.71%	68.27%
±2σ	-1.03%	5.96%	95.65%	95.45%
±3σ	-2.78%	7.71%	98.22%	99.73%

Descriptive Statistics

Mean	2.462%
Standard Error	0.016%
Median	2.027%
Mode	0.625%
Standard Deviation	1.748%
Sample Variance	3.054%
Kurtosis	9.47
Skewness	2.32
Range	19.882%
Minimum	0.219%
Maximum	20.101%
Count	11568

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	2.462%	11568	100.00%	2.462%
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 0.18. Further, an Excess Kurtosis of 5.69 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.43%	93	0.80%	0.80%
-5.43% to -4.08%	147	1.27%	2.07%
-4.08% to -2.72%	395	3.41%	5.49%
-2.72% to -1.37%	1244	10.75%	16.24%
-1.37% to -0.01%	3170	27.40%	43.65%
-0.01% to 1.34%	4730	40.89%	84.53%
1.34% to 2.69%	1178	10.18%	94.72%
2.69% to 4.05%	375	3.24%	97.96%
4.05% to 5.40%	145	1.25%	99.21%
Greater than 5.40%	91	0.79%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-1.82%	1.79%	78.07%	68.27%
±2σ	-3.62%	3.60%	94.38%	95.45%
±3σ	-5.43%	5.40%	98.41%	99.73%

Descriptive Statistics

Mean	-0.014%
Standard Error	0.017%
Median	0.000%
Mode	0.000%
Standard Deviation	1.805%
Sample Variance	3.258%
Kurtosis	5.69
Skewness	0.18
Range	27.987%
Minimum	-13.968%
Maximum	14.019%
Count	11568

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	1.362%	5072	43.84%	0.597%
Negative	-1.398%	5059	43.73%	-0.611%
Zero	0.000%	1437	12.42%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.04. Further, an Excess Kurtosis of 2.37 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.49%	13	0.54%	0.54%
-12.49% to -9.28%	23	0.96%	1.50%
-9.28% to -6.06%	104	4.34%	5.84%
-6.06% to -2.85%	310	12.94%	18.78%
-2.85% to 0.36%	763	31.84%	50.63%
0.36% to 3.58%	709	29.59%	80.22%
3.58% to 6.79%	331	13.81%	94.03%
6.79% to 10.00%	101	4.22%	98.25%
10.00% to 13.21%	28	1.17%	99.42%
Greater than 13.21%	14	0.58%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-3.92%	4.65%	73.66%	68.27%
±2σ	-8.21%	8.93%	95.33%	95.45%
±3σ	-12.49%	13.21%	98.87%	99.73%

Descriptive Statistics

Mean	0.363%
Standard Error	0.088%
Median	0.282%
Mode	0.000%
Standard Deviation	4.284%
Sample Variance	18.351%
Kurtosis	2.37
Skewness	0.04
Range	47.958%
Minimum	-21.978%
Maximum	25.980%
Count	2396

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.423%	1245	51.96%	1.779%
Negative	-3.111%	1090	45.49%	-1.415%
Zero	0.000%	61	2.55%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.24. Further, an Excess Kurtosis of 9.09 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -5.64%	0	0.00%	0.00%
-5.64% to -2.69%	0	0.00%	0.00%
-2.69% to 0.26%	0	0.00%	0.00%
0.26% to 3.21%	462	19.27%	19.27%
3.21% to 6.16%	992	41.39%	60.66%
6.16% to 9.11%	558	23.28%	83.94%
9.11% to 12.06%	220	9.18%	93.12%
12.06% to 15.01%	87	3.63%	96.75%
15.01% to 17.96%	39	1.63%	98.37%
Greater than 17.96%	39	1.63%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	2.23%	10.09%	80.43%	68.27%
±2σ	-1.70%	14.02%	96.12%	95.45%
±3σ	-5.64%	17.96%	98.37%	99.73%

Descriptive Statistics

Mean	6.160%
Standard Error	0.080%
Median	5.281%
Mode	3.571%
Standard Deviation	3.932%
Sample Variance	15.459%
Kurtosis	9.09
Skewness	2.24
Range	37.745%
Minimum	0.461%
Maximum	38.206%
Count	2397

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.160%	2397	100.00%	6.160%
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 0.46. Further, an Excess Kurtosis of 2.99 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.77%	5	0.21%	0.21%
-12.77% to -9.61%	27	1.13%	1.34%
-9.61% to -6.44%	99	4.13%	5.47%
-6.44% to -3.27%	344	14.35%	19.82%
-3.27% to -0.10%	745	31.08%	50.90%
-0.10% to 3.07%	723	30.16%	81.06%
3.07% to 6.24%	313	13.06%	94.12%
6.24% to 9.40%	95	3.96%	98.08%
9.40% to 12.57%	26	1.08%	99.17%
Greater than 12.57%	20	0.83%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-4.33%	4.12%	74.43%	68.27%
±2σ	-8.55%	8.35%	94.83%	95.45%
±3σ	-12.77%	12.57%	98.96%	99.73%

Descriptive Statistics

Mean	-0.101%
Standard Error	0.086%
Median	-0.234%
Mode	0.000%
Standard Deviation	4.224%
Sample Variance	17.842%
Kurtosis	2.99
Skewness	0.46
Range	48.145%
Minimum	-21.854%
Maximum	26.291%
Count	2397

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	3.282%	1101	45.93%	1.507%
Negative	-3.130%	1232	51.40%	-1.609%
Zero	0.000%	64	2.67%	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 1.68 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -24.15%	1	0.18%	0.18%
-24.15% to -17.73%	5	0.91%	1.09%
-17.73% to -11.30%	24	4.36%	5.44%
-11.30% to -4.88%	90	16.33%	21.78%
-4.88% to 1.55%	166	30.13%	51.91%
1.55% to 7.97%	159	28.86%	80.76%
7.97% to 14.39%	68	12.34%	93.10%
14.39% to 20.82%	25	4.54%	97.64%
20.82% to 27.24%	8	1.45%	99.09%
Greater than 27.24%	5	0.91%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-7.02%	10.11%	72.05%	68.27%
±2σ	-15.59%	18.68%	95.64%	95.45%
±3σ	-24.15%	27.24%	98.91%	99.73%

Descriptive Statistics

Mean	1.546%
Standard Error	0.365%
Median	1.228%
Mode	0.000%
Standard Deviation	8.566%
Sample Variance	73.384%
Kurtosis	1.68
Skewness	0.32
Range	73.222%
Minimum	-35.644%
Maximum	37.578%
Count	551

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	7.182%	310	56.26%	4.041%
Negative	-5.800%	237	43.01%	-2.495%
Zero	0.000%	4	0.73%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.84. Further, an Excess Kurtosis of 14.56 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -10.51%	0	0.00%	0.00%
-10.51% to -4.38%	0	0.00%	0.00%
-4.38% to 1.75%	0	0.00%	0.00%
1.75% to 7.88%	98	17.75%	17.75%
7.88% to 14.01%	227	41.12%	58.88%
14.01% to 20.14%	151	27.36%	86.23%
20.14% to 26.27%	45	8.15%	94.38%
26.27% to 32.39%	17	3.08%	97.46%
32.39% to 38.52%	3	0.54%	98.01%
Greater than 38.52%	11	1.99%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	5.83%	22.18%	83.33%	68.27%
±2σ	-2.34%	30.35%	96.92%	95.45%
±3σ	-10.51%	38.52%	98.01%	99.73%

Descriptive Statistics

Mean	14.007%
Standard Error	0.348%
Median	12.320%
Mode	12.500%
Standard Deviation	8.172%
Sample Variance	66.788%
Kurtosis	14.56
Skewness	2.84
Range	76.213%
Minimum	2.235%
Maximum	78.448%
Count	552

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	14.007%	552	100.00%	14.007%
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 0.69. Further, an Excess Kurtosis of 3.78 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -25.97%	2	0.36%	0.36%
-25.97% to -19.60%	4	0.72%	1.09%
-19.60% to -13.22%	20	3.62%	4.71%
-13.22% to -6.85%	88	15.94%	20.65%
-6.85% to -0.47%	177	32.07%	52.72%
-0.47% to 5.90%	150	27.17%	79.89%
5.90% to 12.28%	79	14.31%	94.20%
12.28% to 18.65%	23	4.17%	98.37%
18.65% to 25.03%	5	0.91%	99.28%
Greater than 25.03%	4	0.72%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-8.97%	8.03%	73.01%	68.27%
±2σ	-17.47%	16.53%	95.47%	95.45%
±3σ	-25.97%	25.03%	98.91%	99.73%

Descriptive Statistics

Mean	-0.471%
Standard Error	0.362%
Median	-0.965%
Mode	0.000%
Standard Deviation	8.500%
Sample Variance	72.255%
Kurtosis	3.78
Skewness	0.69
Range	82.394%
Minimum	-27.009%
Maximum	55.385%
Count	552

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	6.642%	245	44.38%	2.948%
Negative	-6.292%	300	54.35%	-3.420%
Zero	0.000%	7	1.27%	0.000%

Close-to-Close Returns

Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.05. Further, an Excess Kurtosis of -0.04 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -37.90%	0	0.00%	0.00%
-37.90% to -27.28%	2	1.09%	1.09%
-27.28% to -16.67%	13	7.07%	8.15%
-16.67% to -6.05%	26	14.13%	22.28%
-6.05% to 4.57%	55	29.89%	52.17%
4.57% to 15.18%	46	25.00%	77.17%
15.18% to 25.80%	30	16.30%	93.48%
25.80% to 36.41%	9	4.89%	98.37%
36.41% to 47.03%	3	1.63%	100.00%
Greater than 47.03%	0	0.00%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-9.59%	18.72%	72.28%	68.27%
±2σ	-23.74%	32.88%	92.93%	95.45%
±3σ	-37.90%	47.03%	100.00%	99.73%

Descriptive Statistics

Mean	4.565%
Standard Error	1.044%
Median	3.971%
Mode	-2.037%
Standard Deviation	14.155%
Sample Variance	200.358%
Kurtosis	-0.04
Skewness	0.05
Range	73.145%
Minimum	-33.489%
Maximum	39.656%
Count	184

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	13.067%	115	62.50%	8.167%
Negative	-9.747%	68	36.96%	-3.602%
Zero	0.000%	1	0.54%	0.000%

High-to-Low Returns

Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.55. Further, an Excess Kurtosis of 2.85 proves the distribution possesses Fat Tails (Higher Outlier Risk).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -12.01%	0	0.00%	0.00%
-12.01% to -2.44%	0	0.00%	0.00%
-2.44% to 7.13%	0	0.00%	0.00%
7.13% to 16.70%	41	22.16%	22.16%
16.70% to 26.27%	69	37.30%	59.46%
26.27% to 35.84%	45	24.32%	83.78%
35.84% to 45.41%	15	8.11%	91.89%
45.41% to 54.98%	6	3.24%	95.14%
54.98% to 64.56%	6	3.24%	98.38%
Greater than 64.56%	3	1.62%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	13.51%	39.03%	77.30%	68.27%
±2σ	0.75%	51.80%	94.05%	95.45%
±3σ	-12.01%	64.56%	98.38%	99.73%

Descriptive Statistics

Mean	26.275%
Standard Error	0.938%
Median	23.781%
Mode	26.344%
Standard Deviation	12.760%
Sample Variance	162.820%
Kurtosis	2.85
Skewness	1.55
Range	70.076%
Minimum	8.372%
Maximum	78.448%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	26.275%	185	100.00%	26.275%
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 0.78. Further, an Excess Kurtosis of 0.96 proves the distribution possesses Normal Tails (Mesokurtic).

Bin Distribution Over Raw Range

Bin / Range	Frequency	Prob	Cum. Prob
Less than -43.53%	0	0.00%	0.00%
-43.53% to -33.06%	0	0.00%	0.00%
-33.06% to -22.58%	9	4.86%	4.86%
-22.58% to -12.10%	34	18.38%	23.24%
-12.10% to -1.62%	58	31.35%	54.59%
-1.62% to 8.86%	47	25.41%	80.00%
8.86% to 19.33%	21	11.35%	91.35%
19.33% to 29.81%	10	5.41%	96.76%
29.81% to 40.29%	5	2.70%	99.46%
Greater than 40.29%	1	0.54%	100.00%

Standard Deviation Interval Analysis

SD	Lower Bnd	Upper Bnd	Actual %	Normal %
±1σ	-15.59%	12.35%	75.68%	68.27%
±2σ	-29.56%	26.32%	95.68%	95.45%
±3σ	-43.53%	40.29%	99.46%	99.73%

Descriptive Statistics

Mean	-1.622%
Standard Error	1.027%
Median	-3.509%
Mode	-8.025%
Standard Deviation	13.971%
Sample Variance	195.201%
Kurtosis	0.96
Skewness	0.78
Range	80.176%
Minimum	-28.668%
Maximum	51.508%
Count	185

Frequency Breakdown

Category	Avg Return	Count	Probability	Freq Adj Return
Positive	11.517%	76	41.08%	4.731%
Negative	-10.985%	107	57.84%	-6.354%
Zero	0.000%	2	1.08%	0.000%

PCAR Deep Analytical Report