This is a follow-up / continuation of the last post. In that one we look at the monthly return for 1 month. In this one we look at all of them. For each month we look at the distribution of the 1 month return, calculating the mean (mu), median, standard deviation (stddev), skew, kurtosis (kurt), and maximum value. Below is a summary of each of these variables for the 154 months.
summary(ystats)## mu median stddev skew
## Min. :-22.1700 Min. :-21.790 Min. : 4.010 Min. :-0.9000
## 1st Qu.: -2.1950 1st Qu.: -1.465 1st Qu.: 9.180 1st Qu.: 0.0625
## Median : 1.1200 Median : 0.825 Median : 9.655 Median : 0.5400
## Mean : 0.7871 Mean : 0.498 Mean :10.269 Mean : 0.9528
## 3rd Qu.: 3.8375 3rd Qu.: 3.265 3rd Qu.:10.758 3rd Qu.: 0.9950
## Max. : 15.7700 Max. : 12.490 Max. :20.900 Max. :30.0600
## kurt max
## Min. : 0.87 Min. : 35.29
## 1st Qu.: 5.27 1st Qu.: 71.39
## Median : 7.79 Median : 86.84
## Mean : 23.71 Mean :106.64
## 3rd Qu.: 11.97 3rd Qu.:117.30
## Max. :1313.57 Max. :933.33
We note that the mean and median are not stationary. That is the value moves around a lot. No surprise. We see more evidence of the non-normality of the cross-section of returns. In over 75% of the months, the skewness is above 0 (a normal distribution has a value of 0). A normal distribution would have a kurtosis of 3.0 and these values are generally higher. The standard deviation is close to 10 for about one-half of the months. Finally, we note an outlier maximum return near 1000%. We examined this value which was for the now delisted company Biocoral Inc (BCRA). While the return is computationally correct, it turns out this stock did not trade on many days. It is so illiquid that I plan to add a new filter for the data to screen out stocks will low trading volumes. What follows are time series plots of each variable.
## mu median stddev skew kurt max
## 2003-01-03 -2.27 -2.35 10.60 0.73 12.66 131.00
## 2003-01-31 -2.75 -2.00 9.67 -0.87 6.69 44.64
## 2003-02-28 0.47 0.45 9.54 -0.09 5.52 57.37
## 2003-04-04 9.22 8.07 11.49 1.00 5.97 109.64
## 2003-05-02 9.79 7.39 20.90 30.06 1313.57 933.33
## 2003-05-30 2.50 1.51 9.78 1.29 7.08 88.78
## 2003-07-03 5.10 3.89 12.49 1.44 8.42 135.14
## 2003-08-01 4.38 3.03 9.47 0.56 6.58 73.51
## 2003-08-29 -0.73 -0.92 9.37 0.76 5.40 71.55
## 2003-10-03 8.09 6.68 12.16 1.36 8.98 131.71
## 2003-10-31 3.14 2.56 9.29 0.43 7.79 69.62
## 2003-11-28 3.46 2.76 9.90 0.57 6.17 76.44
## 2004-01-02 3.69 2.59 11.14 1.21 6.27 114.89
## 2004-01-30 1.66 1.37 9.35 0.52 4.65 67.67
## 2004-02-27 0.08 -0.26 9.40 1.12 11.68 113.36
## 2004-04-02 -4.48 -3.97 10.78 0.07 5.08 92.19
## 2004-04-30 1.20 0.68 10.44 4.10 75.04 211.26
## 2004-06-04 3.46 3.33 9.38 0.34 4.99 69.00
## 2004-07-02 -5.53 -4.21 10.25 -0.76 2.28 36.29
## 2004-07-30 -0.37 0.13 9.68 0.01 16.62 129.68
## 2004-09-03 4.62 3.55 9.32 1.22 7.92 96.25
## 2004-09-30 2.26 1.91 10.32 0.31 12.42 124.49
## 2004-10-29 1.22 1.11 4.01 0.19 12.01 35.29
## 2004-12-03 3.54 2.83 9.60 4.51 116.11 246.37
## 2004-12-31 -3.36 -3.14 9.41 0.66 14.58 121.88
## 2005-01-31 2.23 1.41 9.67 0.46 6.27 98.78
## 2005-02-28 -2.85 -2.65 8.65 -0.29 5.38 56.48
## 2005-03-31 -4.69 -4.26 9.21 -0.36 2.46 40.09
## 2005-04-29 4.92 4.00 9.85 0.81 11.60 118.68
## 2005-05-31 3.42 2.96 8.89 0.41 7.21 73.27
## 2005-06-30 5.75 4.95 9.31 0.67 4.14 76.58
## 2005-07-29 -1.17 -1.48 9.69 0.90 9.17 89.60
## 2005-08-31 0.93 0.26 9.59 -0.25 7.95 54.43
## 2005-09-30 -3.25 -3.06 9.25 -0.16 4.79 51.12
## 2005-10-31 4.35 3.54 9.64 0.11 8.03 73.34
## 2005-11-30 0.62 0.11 8.45 0.54 8.57 57.27
## 2005-12-30 6.97 5.33 10.98 1.11 4.50 97.66
## 2006-01-31 -0.16 0.00 9.34 0.15 5.98 79.35
## 2006-02-28 3.36 2.79 9.55 0.43 4.78 64.51
## 2006-03-31 0.87 0.40 9.49 0.43 8.55 96.73
## 2006-04-28 -5.02 -4.48 9.48 -0.17 6.47 82.36
## 2006-05-31 -0.57 -0.48 8.91 -0.32 9.00 80.31
## 2006-06-30 -2.32 -1.42 9.64 -0.56 3.13 47.14
## 2006-07-31 2.77 2.44 9.64 0.12 6.25 71.06
## 2006-08-31 1.01 0.76 8.53 0.06 7.45 82.08
## 2006-09-29 4.94 4.43 9.57 0.83 13.67 126.75
## 2006-10-31 3.16 2.39 9.42 1.00 5.80 78.00
## 2006-11-30 1.16 0.88 8.28 0.20 15.20 71.41
## 2006-12-29 1.81 1.38 8.53 0.41 4.46 73.68
## 2007-01-31 -0.46 -0.77 8.67 0.80 16.42 121.52
## 2007-02-28 1.08 0.77 8.83 0.14 16.93 115.80
## 2007-03-30 2.77 2.22 8.54 0.52 4.59 57.71
## 2007-04-30 3.54 2.60 9.78 0.70 11.17 108.40
## 2007-05-31 -0.91 -1.39 8.35 0.36 4.31 50.16
## 2007-06-29 -5.42 -5.52 10.49 0.16 5.46 59.03
## 2007-07-31 0.20 0.24 10.89 0.01 6.06 93.16
## 2007-08-31 2.57 1.97 10.64 2.02 38.63 202.34
## 2007-09-28 2.50 2.14 12.07 -0.16 4.65 65.00
## 2007-10-31 -7.43 -6.38 10.99 -0.23 4.72 87.94
## 2007-11-30 -0.78 -1.20 11.86 3.77 67.79 254.61
## 2007-12-31 -6.37 -6.25 12.69 -0.01 3.38 88.89
## 2008-01-31 -2.67 -3.00 12.70 0.39 5.18 102.19
## 2008-02-29 -1.75 -0.87 11.90 -0.90 4.95 55.68
## 2008-03-31 4.46 4.14 12.68 0.09 4.14 79.00
## 2008-04-30 3.75 2.74 12.07 0.62 4.08 94.78
## 2008-05-30 -9.57 -9.74 12.81 0.58 5.74 107.54
## 2008-06-30 0.88 0.59 14.78 0.18 1.84 76.37
## 2008-07-31 1.86 1.45 11.60 1.19 17.16 173.52
## 2008-08-29 -10.23 -9.31 14.84 -0.27 2.51 71.39
## 2008-09-30 -22.17 -21.79 16.93 0.00 0.87 73.91
## 2008-10-31 -11.24 -10.35 16.96 -0.33 1.52 69.39
## 2008-11-28 5.42 4.31 15.77 0.63 3.71 106.61
## 2008-12-31 -8.57 -8.74 16.06 1.33 19.97 232.38
## 2009-01-30 -11.05 -10.24 13.86 -0.29 1.64 50.09
## 2009-02-27 8.74 8.11 13.82 0.35 3.13 91.95
## 2009-03-31 15.77 12.40 19.82 1.46 5.95 180.03
## 2009-04-30 6.27 4.56 15.60 1.10 4.87 129.92
## 2009-05-29 0.73 0.39 11.74 0.81 7.79 117.80
## 2009-06-30 9.40 8.27 12.26 0.73 3.94 90.06
## 2009-07-31 2.97 1.99 11.98 3.45 59.20 244.98
## 2009-08-31 6.35 5.11 10.82 0.77 5.31 78.38
## 2009-09-30 -4.97 -4.33 9.82 -0.28 2.80 49.92
## 2009-10-30 4.10 3.39 10.93 1.31 11.44 114.71
## 2009-11-30 6.11 5.35 9.34 0.80 4.79 80.06
## 2009-12-31 -3.53 -3.96 9.31 0.93 6.29 89.65
## 2010-01-29 3.84 3.15 9.34 0.90 6.88 82.88
## 2010-02-26 7.05 6.38 10.55 3.26 62.25 224.38
## 2010-03-31 4.27 3.29 10.04 1.05 5.59 89.01
## 2010-04-30 -8.15 -8.02 8.67 0.54 10.10 83.33
## 2010-05-28 -5.84 -5.39 9.29 -0.05 4.12 66.93
## 2010-06-30 7.27 6.93 9.86 0.55 6.71 86.75
## 2010-07-30 -5.71 -5.75 10.47 3.25 70.47 218.02
## 2010-08-31 11.06 9.99 9.91 0.77 10.38 100.82
## 2010-09-30 4.04 3.54 9.30 -0.06 9.17 64.48
## 2010-10-29 1.88 0.91 9.75 0.50 4.65 58.19
## 2010-11-30 7.38 6.52 9.83 2.53 42.78 189.81
## 2010-12-31 0.31 0.23 9.12 0.59 5.94 86.93
## 2011-01-31 4.07 3.19 9.49 0.70 7.02 71.51
## 2011-02-28 1.52 1.03 9.21 0.54 6.29 68.80
## 2011-03-31 2.66 2.31 9.35 1.67 22.78 119.18
## 2011-04-29 -2.24 -2.09 8.77 0.41 8.49 78.53
## 2011-05-31 -2.34 -2.11 7.70 -0.19 5.63 47.88
## 2011-06-30 -3.40 -3.39 8.80 0.38 5.46 67.07
## 2011-07-29 -8.02 -7.23 10.69 -0.52 4.77 68.54
## 2011-08-31 -11.02 -10.13 10.67 -0.03 6.89 105.30
## 2011-09-30 13.50 12.49 12.09 0.57 4.08 122.52
## 2011-10-31 -1.53 -0.78 10.17 0.98 27.93 167.46
## 2011-11-30 -0.38 -0.05 8.60 0.35 9.35 73.29
## 2011-12-30 7.33 6.09 10.62 1.55 10.93 133.27
## 2012-01-31 3.04 2.43 9.05 0.32 9.99 88.60
## 2012-02-29 1.44 1.35 8.69 0.76 9.64 84.45
## 2012-03-30 -1.26 -0.67 8.38 0.21 8.73 78.52
## 2012-04-30 -7.73 -6.92 10.08 -0.12 5.27 77.32
## 2012-05-31 3.88 3.51 8.33 0.61 7.52 73.81
## 2012-06-29 -0.54 0.45 9.85 -0.39 8.79 85.04
## 2012-07-31 2.74 1.96 9.12 1.30 15.81 115.27
## 2012-08-31 3.03 2.50 7.35 0.69 16.04 100.00
## 2012-09-28 -1.50 -1.12 8.67 -0.17 7.83 56.07
## 2012-10-31 0.62 0.50 8.31 0.13 5.25 51.65
## 2012-11-30 2.23 1.63 7.36 1.46 16.48 88.16
## 2012-12-31 5.81 5.41 8.22 0.45 9.52 78.46
## 2013-01-31 0.50 0.53 7.85 -0.07 9.76 55.28
## 2013-02-28 3.83 3.50 8.06 0.93 9.77 89.17
## 2013-03-29 0.39 0.44 8.69 0.29 8.14 72.70
## 2013-04-30 2.88 2.22 10.63 2.03 18.07 134.74
## 2013-05-31 -0.78 -0.92 8.48 0.32 12.18 83.11
## 2013-06-28 6.15 5.48 9.48 2.00 21.59 147.85
## 2013-07-31 -2.60 -3.34 9.39 3.02 44.54 175.82
## 2013-08-30 5.61 4.88 9.39 1.62 16.81 106.17
## 2013-09-30 2.72 3.15 9.94 -0.48 8.45 67.79
## 2013-10-31 3.01 2.47 9.77 0.55 5.71 69.31
## 2013-11-29 2.21 1.58 8.95 2.06 28.32 119.32
## 2013-12-31 -2.26 -3.36 11.69 8.01 212.58 340.66
## 2014-01-31 4.65 4.04 9.42 1.31 14.24 125.02
## 2014-02-28 -0.16 0.33 8.99 -0.43 9.94 80.79
## 2014-03-31 -2.66 -1.86 9.30 -0.36 4.49 58.98
## 2014-04-30 0.90 1.07 8.70 -0.10 8.37 81.01
## 2014-05-30 4.49 3.44 9.55 8.06 211.95 284.37
## 2014-06-30 -4.67 -4.34 9.17 4.58 135.29 235.94
## 2014-07-31 4.14 3.62 8.98 0.67 10.30 84.72
## 2014-08-29 -5.07 -4.97 9.09 0.72 14.10 91.64
## 2014-09-30 3.49 3.84 12.33 0.51 20.64 192.24
## 2014-10-31 -0.15 0.57 10.02 -0.27 6.20 67.68
## 2014-11-28 0.71 0.76 10.55 1.39 16.13 122.46
## 2014-12-31 -3.14 -3.30 10.35 0.50 8.98 114.49
## 2015-01-30 5.83 5.42 9.92 0.80 5.27 84.17
## 2015-02-27 0.26 0.13 9.47 0.84 11.87 112.53
## 2015-03-31 0.21 -0.91 10.60 0.77 11.15 91.30
## 2015-04-30 0.92 0.46 10.33 2.03 21.15 132.07
## 2015-05-29 -0.70 -1.41 9.14 0.67 7.70 68.04
## 2015-06-30 -2.06 -1.27 10.90 -0.28 5.31 92.68
## 2015-07-31 -6.18 -5.77 10.04 -0.37 8.95 83.30
## 2015-08-31 -5.78 -4.24 10.91 -0.60 5.25 77.63
## 2015-09-30 6.24 6.22 12.08 0.52 10.40 141.07
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