Trimmed output of xreturns_mean_variance_cp.f90. The stock market crash in 2008 from 2008-09-15 to 2008-12-01 is apparent,
with very negative returns and annualized volatility of 78%.
read 4607 days and 1 columns from asset_class_etf_prices.csv
return scaling: 100.0000
changes in variance of SPY
Changepoints chosen by AIC, BIC: 75 46
BIC-selected model (46 changepoint(s)) -- SPY
start end n ann_ret% ann_vol% min% max% first% last%
2007-12-20 2008-09-12 184 -15.80 20.39 -3.19 4.15 0.63 0.46
2008-09-15 2008-12-01 55 -163.89 77.60 -9.84 14.52 -4.76 -8.86
2008-12-02 2009-04-20 95 15.66 38.53 -5.28 7.18 3.85 -4.19
2009-04-21 2009-07-15 60 51.89 23.49 -3.00 3.40 1.95 2.92
2009-07-16 2010-02-04 141 26.78 16.40 -3.09 2.28 -0.16 -3.09
2010-02-05 2010-04-26 55 62.47 10.22 -1.59 1.57 0.21 -0.38
2010-04-27 2010-09-01 90 -27.10 24.54 -3.78 4.40 -2.37 2.99
2010-09-02 2011-07-26 226 26.03 12.63 -2.25 2.13 0.93 -0.37
2011-07-27 2011-10-05 50 -67.47 37.26 -6.51 4.65 -2.05 1.85
2011-10-06 2011-12-20 53 44.61 27.03 -3.69 4.11 1.81 3.03
2011-12-21 2012-05-16 101 19.03 11.24 -1.68 1.80 0.19 -0.38
2012-05-17 2012-08-03 55 25.80 17.20 -2.52 2.49 -1.48 1.98
2012-08-06 2014-04-16 426 19.95 11.45 -2.48 2.56 0.19 1.05
2014-04-17 2014-07-15 61 26.14 6.91 -0.88 0.97 0.14 -0.19
2014-07-16 2014-09-24 50 8.68 9.02 -1.97 1.16 0.37 0.78
2014-09-25 2015-02-03 90 9.96 14.88 -1.98 2.47 -1.61 1.45
2015-02-04 2015-08-19 137 5.38 10.69 -2.10 1.34 -0.38 -0.79
2015-08-20 2015-10-29 50 6.64 23.62 -4.21 3.84 -2.09 -0.06
2015-10-30 2016-03-11 91 -4.89 18.09 -2.49 2.44 -0.43 1.61
2016-03-14 2016-06-22 71 13.31 9.14 -1.20 1.30 -0.13 -0.16
2016-06-23 2016-09-13 57 11.73 13.87 -3.59 1.80 1.30 -1.44
2016-09-14 2016-12-07 60 24.38 9.46 -1.26 2.21 -0.04 1.31
2016-12-08 2017-02-28 55 26.49 6.32 -0.83 0.87 0.24 -0.27
2017-03-01 2017-08-22 122 9.89 7.77 -1.77 1.40 1.40 1.05
2017-08-23 2018-01-25 107 36.34 6.19 -0.72 1.07 -0.36 0.04
2018-01-26 2018-04-10 51 -28.08 22.97 -4.18 2.74 1.16 1.59
2018-04-11 2018-07-12 65 22.50 10.09 -1.36 1.33 -0.52 0.91
2018-07-13 2018-10-09 62 13.57 6.51 -0.78 0.85 0.08 -0.15
2018-10-10 2019-01-04 59 -49.65 25.89 -3.24 5.05 -3.17 3.35
2019-01-07 2019-08-02 145 27.92 11.08 -2.51 2.17 0.79 -0.75
2019-08-05 2019-10-15 51 14.27 17.49 -3.01 1.96 -3.01 0.99
2019-10-16 2020-01-24 69 36.86 7.21 -0.89 0.94 -0.16 -0.89
2020-01-27 2020-04-06 50 -85.55 63.58 -10.94 9.06 -1.60 6.72
2020-04-07 2020-06-17 50 85.91 27.90 -5.76 3.36 0.10 -0.42
2020-06-18 2020-08-28 51 61.33 14.26 -2.55 1.54 0.04 0.65
2020-08-31 2020-11-09 50 10.18 22.20 -3.44 2.23 -0.36 1.26
2020-11-10 2021-01-26 52 41.10 11.37 -1.36 1.61 -0.15 -0.16
2021-01-27 2021-05-14 76 29.46 15.42 -2.44 2.42 -2.44 1.54
2021-05-17 2021-11-24 135 24.02 10.10 -2.02 1.68 -0.25 0.27
2021-11-26 2022-04-21 101 -13.59 20.10 -2.95 2.68 -2.23 -1.50
2022-04-22 2022-11-30 154 -6.86 26.53 -4.35 5.50 -2.74 3.15
2022-12-01 2023-05-05 107 6.15 16.33 -2.45 2.29 -0.07 1.85
2023-05-08 2024-07-23 304 26.47 11.17 -1.65 2.07 0.03 -0.16
2024-07-24 2025-03-13 160 1.45 14.88 -2.98 2.49 -2.27 -1.33
2025-03-14 2025-05-27 51 42.20 35.92 -5.85 10.50 2.07 2.08
2025-05-28 2025-10-09 94 35.97 8.99 -1.64 1.54 -0.58 -0.29
2025-10-10 2026-04-14 127 8.87 13.94 -2.70 2.91 -2.70 1.22
Summary: # variance changepoints chosen by AIC and BIC
Series AIC BIC
SPY 75 46
finished xreturns_mean_variance_cp.f90
wall time elapsed (s): 1.0794