From: Stressed portfolio optimization with semiparametric method
Period | Markowitz model | ||||||||
---|---|---|---|---|---|---|---|---|---|
VOO | TLT | LQD | IAU | VNQ | Volatility | Return | SR | VaR | |
2016.01 | 0.177457 | 0.236393 | 0.237593 | 0.251497 | 0.097060 | 0.004943 | 0.031138 | 0.310756 | 0.006319 |
2016.02 | 0.191533 | 0.189183 | 0.330781 | 0.151453 | 0.137050 | 0.003019 | − 0.005552 | − 0.098852 | 0.007427 |
2016.03 | 0.194609 | 0.355099 | 0.082842 | 0.298886 | 0.068564 | 0.004389 | 0.005317 | 0.055825 | 0.006111 |
2016.04 | 0.260998 | 0.075808 | 0.533044 | 0.054747 | 0.070539 | 0.002226 | 0.008347 | 0.178130 | 0.003372 |
2016.05 | 0.438323 | 0.064790 | 0.067393 | 0.369232 | 0.060262 | 0.002141 | 0.035697 | 0.823922 | 0.001026 |
2016.06 | 0.390102 | 0.240234 | 0.210918 | 0.075207 | 0.083540 | 0.002005 | 0.012844 | 0.309909 | 0.002488 |
2016.07 | 0.479150 | 0.070969 | 0.089529 | 0.298833 | 0.061519 | 0.002885 | 0.007432 | 0.121583 | 0.004865 |
2016.08 | 0.738519 | 0.068578 | 0.061201 | 0.072736 | 0.054747 | 0.002956 | 0.016902 | 0.278845 | 0.003187 |
2016.09 | 0.320867 | 0.054747 | 0.230660 | 0.336898 | 0.054747 | 0.006014 | 0.001688 | 0.010570 | 0.013133 |
2016.10 | 0.054747 | 0.054747 | 0.054747 | 0.054747 | 0.800000 | 0.006678 | 0.027345 | 0.201620 | 0.011283 |
2016.11 | 0.139885 | 0.054747 | 0.054747 | 0.710035 | 0.054747 | 0.006985 | − 0.049834 | − 0.359704 | 0.015914 |
2016.12 | 0.054747 | 0.091749 | 0.054747 | 0.757647 | 0.054747 | 0.003830 | − 0.003225 | − 0.047541 | 0.006936 |
2017.01 | 0.438323 | 0.064790 | 0.067393 | 0.369232 | 0.060262 | 0.002141 | 0.035697 | 0.823922 | 0.001026 |
2017.02 | 0.390102 | 0.240234 | 0.210918 | 0.075207 | 0.083540 | 0.002005 | 0.012844 | 0.309909 | 0.002488 |
2017.03 | 0.479150 | 0.070969 | 0.089529 | 0.298833 | 0.061519 | 0.002885 | 0.007432 | 0.121583 | 0.004865 |
2017.04 | 0.738519 | 0.068578 | 0.061201 | 0.072736 | 0.054747 | 0.002956 | 0.016902 | 0.278845 | 0.003187 |
2017.05 | 0.054747 | 0.081504 | 0.054747 | 0.750060 | 0.062405 | 0.005917 | 0.008666 | 0.069709 | 0.010132 |
2017.06 | 0.054747 | 0.054747 | 0.054747 | 0.054747 | 0.800000 | 0.006678 | 0.027345 | 0.201620 | 0.011283 |
2017.07 | 0.268480 | 0.506691 | 0.100368 | 0.066477 | 0.054747 | 0.003863 | 0.003252 | 0.036699 | 0.007514 |
2017.08 | 0.054747 | 0.091749 | 0.054747 | 0.757647 | 0.054747 | 0.003830 | − 0.003225 | − 0.047541 | 0.006936 |
2017.09 | 0.158318 | 0.147202 | 0.286875 | 0.077530 | 0.330075 | 0.003094 | 0.008857 | 0.136398 | 0.004243 |
2017.10 | 0.068086 | 0.099889 | 0.581654 | 0.196896 | 0.054747 | 0.002497 | 0.011911 | 0.230163 | 0.003186 |
2017.11 | 0.054747 | 0.324698 | 0.054747 | 0.226128 | 0.340363 | 0.004058 | 0.054747 | 0.669423 | 0.003384 |
2017.12 | 0.694957 | 0.054747 | 0.065574 | 0.125798 | 0.054747 | 0.002740 | 0.013373 | 0.236429 | 0.004147 |
2018.01 | 0.294399 | 0.078843 | 0.166064 | 0.401023 | 0.054747 | 0.003388 | 0.017857 | 0.257384 | 0.005469 |
2018.02 | 0.054747 | 0.054747 | 0.054747 | 0.054747 | 0.800000 | 0.006678 | 0.027345 | 0.201620 | 0.011283 |
2018.03 | 0.689011 | 0.054747 | 0.054747 | 0.156637 | 0.054747 | 0.008469 | − 0.012166 | − 0.074287 | 0.016114 |
2018.04 | 0.054747 | 0.091749 | 0.054747 | 0.757647 | 0.054747 | 0.003830 | − 0.003225 | − 0.047541 | 0.006936 |
2018.05 | 0.158318 | 0.147202 | 0.286875 | 0.077530 | 0.330075 | 0.003094 | 0.008857 | 0.136398 | 0.004243 |
2018.06 | 0.068086 | 0.099889 | 0.581654 | 0.196896 | 0.054747 | 0.002497 | 0.011911 | 0.230163 | 0.003186 |
2018.07 | 0.054747 | 0.324698 | 0.054747 | 0.226128 | 0.340363 | 0.004058 | 0.054747 | 0.669423 | 0.003384 |
2018.08 | 0.694957 | 0.054747 | 0.065574 | 0.125798 | 0.054747 | 0.002740 | 0.013373 | 0.236429 | 0.004147 |
2018.09 | 0.325014 | 0.342751 | 0.141088 | 0.076066 | 0.115081 | 0.003169 | − 0.016129 | − 0.261055 | 0.005934 |
2018.10 | 0.227873 | 0.054747 | 0.242898 | 0.428362 | 0.054747 | 0.005928 | 0.033072 | 0.275433 | 0.009425 |
2018.11 | 0.054747 | 0.054747 | 0.054747 | 0.800000 | 0.054747 | 0.016173 | − 0.004332 | − 0.014681 | 0.037222 |
2018.12 | 0.583894 | 0.054747 | 0.249566 | 0.054747 | 0.054747 | 0.006862 | 0.065737 | 0.475957 | 0.006263 |
2019.01 | 0.158318 | 0.147202 | 0.286875 | 0.077530 | 0.330075 | 0.003094 | 0.008857 | 0.136398 | 0.004243 |
2019.02 | 0.068086 | 0.099889 | 0.581654 | 0.196896 | 0.054747 | 0.002497 | 0.011911 | 0.230163 | 0.003186 |
2019.03 | 0.054747 | 0.324698 | 0.054747 | 0.226128 | 0.340363 | 0.004058 | 0.054747 | 0.669423 | 0.003384 |
2019.04 | 0.694957 | 0.054747 | 0.065574 | 0.125798 | 0.054747 | 0.002740 | 0.013373 | 0.236429 | 0.004147 |
2019.05 | 0.178815 | 0.345249 | 0.250347 | 0.082559 | 0.143030 | 0.003428 | 0.005799 | 0.078505 | 0.005423 |
2019.06 | 0.227873 | 0.054747 | 0.242898 | 0.428362 | 0.054747 | 0.005928 | 0.033072 | 0.275433 | 0.009425 |
2019.07 | 0.054747 | 0.054747 | 0.054747 | 0.800000 | 0.054747 | 0.016173 | − 0.004332 | − 0.014681 | 0.037222 |
2019.08 | 0.583894 | 0.054747 | 0.249566 | 0.054747 | 0.054747 | 0.006862 | 0.065737 | 0.475957 | 0.006263 |
2019.09 | 0.054747 | 0.520589 | 0.060882 | 0.063095 | 0.296206 | 0.007866 | − 0.017978 | − 0.116925 | 0.014608 |
2019.10 | 0.185526 | 0.312187 | 0.109350 | 0.328851 | 0.064085 | 0.003843 | − 0.005305 | − 0.074443 | 0.007008 |
2019.11 | 0.069817 | 0.054747 | 0.054747 | 0.054747 | 0.779891 | 0.005293 | 0.016356 | 0.150570 | 0.007682 |
2019.12 | 0.354102 | 0.143553 | 0.259630 | 0.157578 | 0.085137 | 0.002122 | 0.019442 | 0.448288 | 0.001931 |
2020.01 | 0.450722 | 0.062094 | 0.089300 | 0.325553 | 0.072330 | 0.002505 | 0.026534 | 0.521304 | 0.003131 |
2020.02 | 0.227873 | 0.054747 | 0.242898 | 0.428362 | 0.054747 | 0.005928 | 0.033072 | 0.275433 | 0.009425 |
2020.03 | 0.054747 | 0.054747 | 0.054747 | 0.800000 | 0.054747 | 0.016173 | − 0.004332 | − 0.014681 | 0.037222 |
2020.04 | 0.583894 | 0.054747 | 0.249566 | 0.054747 | 0.054747 | 0.006862 | 0.065737 | 0.475957 | 0.006263 |
2020.05 | 0.256336 | 0.353002 | 0.113060 | 0.160268 | 0.117334 | 0.006493 | 0.009454 | 0.069593 | 0.010594 |
2020.06 | 0.400734 | 0.054747 | 0.066797 | 0.429053 | 0.054747 | 0.009111 | 0.001678 | 0.006922 | 0.022245 |
2020.07 | 0.069817 | 0.054747 | 0.054747 | 0.054747 | 0.779891 | 0.005293 | 0.016356 | 0.150570 | 0.007682 |
2020.08 | 0.054747 | 0.409585 | 0.243612 | 0.246698 | 0.054747 | 0.007719 | − 0.027772 | − 0.182593 | 0.016567 |
2020.09 | 0.054747 | 0.054747 | 0.796835 | 0.054747 | 0.054747 | 0.002363 | 0.028087 | 0.585492 | 0.002537 |
2020.10 | 0.129021 | 0.324443 | 0.074690 | 0.414853 | 0.054747 | 0.009991 | − 0.014027 | − 0.072283 | 0.022879 |
2020.11 | 0.074008 | 0.425982 | 0.067759 | 0.054747 | 0.381966 | 0.004043 | 0.017995 | 0.217392 | 0.004757 |
2020.12 | 0.327937 | 0.110332 | 0.315693 | 0.054747 | 0.190245 | 0.003744 | 0.009747 | 0.124604 | 0.006219 |
Period | Semiparametric method | ||||||||
---|---|---|---|---|---|---|---|---|---|
VOO | TLT | LQD | IAU | VNQ | Volatility | Return | SR | VaR | |
2016.01 | 0.160183 | 0.201954 | 0.389901 | 0.155095 | 0.092867 | 0.004933 | 0.031204 | 0.312025 | 0.006300 |
2016.02 | 0.216752 | 0.131119 | 0.448274 | 0.112298 | 0.091557 | 0.003016 | − 0.005562 | − 0.099114 | 0.007419 |
2016.03 | 0.172940 | 0.343354 | 0.067331 | 0.351387 | 0.064988 | 0.004394 | 0.005335 | 0.055969 | 0.006118 |
2016.04 | 0.287010 | 0.054747 | 0.560270 | 0.054747 | 0.054747 | 0.002226 | 0.008351 | 0.178215 | 0.003367 |
2016.05 | 0.530729 | 0.080792 | 0.096155 | 0.230098 | 0.062226 | 0.002136 | 0.035733 | 0.826709 | 0.001019 |
2016.06 | 0.399718 | 0.218111 | 0.252014 | 0.062924 | 0.067233 | 0.002004 | 0.012855 | 0.310363 | 0.002485 |
2016.07 | 0.407809 | 0.054747 | 0.054747 | 0.425151 | 0.054747 | 0.002885 | 0.007420 | 0.121381 | 0.004855 |
2016.08 | 0.687917 | 0.086119 | 0.068683 | 0.096677 | 0.060604 | 0.002954 | 0.016922 | 0.279345 | 0.003185 |
2016.09 | 0.295074 | 0.054747 | 0.345485 | 0.241187 | 0.054747 | 0.006011 | 0.001698 | 0.010658 | 0.013130 |
2016.10 | 0.169464 | 0.063972 | 0.054747 | 0.054747 | 0.654040 | 0.006672 | 0.027376 | 0.202028 | 0.011270 |
2016.11 | 0.490535 | 0.078949 | 0.127607 | 0.210662 | 0.092247 | 0.006954 | − 0.050094 | − 0.363171 | 0.015812 |
2016.12 | 0.054747 | 0.255260 | 0.067222 | 0.565168 | 0.054747 | 0.003822 | − 0.003247 | − 0.047937 | 0.006910 |
2017.01 | 0.530729 | 0.080792 | 0.096155 | 0.230098 | 0.062226 | 0.002136 | 0.035697 | 0.825874 | 0.001019 |
2017.02 | 0.399718 | 0.218111 | 0.252014 | 0.062924 | 0.067233 | 0.002004 | 0.012843 | 0.310043 | 0.002485 |
2017.03 | 0.407809 | 0.054747 | 0.054747 | 0.425151 | 0.054747 | 0.002885 | 0.007413 | 0.121253 | 0.004855 |
2017.04 | 0.687917 | 0.086119 | 0.068683 | 0.096677 | 0.060604 | 0.002954 | 0.016906 | 0.279059 | 0.003185 |
2017.05 | 0.054747 | 0.299233 | 0.074893 | 0.404997 | 0.161057 | 0.005903 | 0.008661 | 0.069835 | 0.010103 |
2017.06 | 0.169464 | 0.063972 | 0.054747 | 0.054747 | 0.654040 | 0.006672 | 0.027349 | 0.201823 | 0.011270 |
2017.07 | 0.349012 | 0.250337 | 0.257934 | 0.077485 | 0.065231 | 0.003856 | 0.003225 | 0.036419 | 0.007498 |
2017.08 | 0.054747 | 0.255260 | 0.067222 | 0.565168 | 0.054747 | 0.003822 | − 0.003244 | − 0.047895 | 0.006910 |
2017.09 | 0.121561 | 0.082417 | 0.495424 | 0.060742 | 0.239856 | 0.003091 | 0.008865 | 0.136680 | 0.004237 |
2017.10 | 0.073791 | 0.114737 | 0.509979 | 0.248497 | 0.054747 | 0.002497 | 0.011912 | 0.230163 | 0.003186 |
2017.11 | 0.074851 | 0.306618 | 0.072666 | 0.167985 | 0.377880 | 0.004056 | 0.054747 | 0.669677 | 0.003378 |
2017.12 | 0.775866 | 0.054747 | 0.054747 | 0.061907 | 0.054747 | 0.002740 | 0.013351 | 0.236031 | 0.004141 |
2018.01 | 0.334962 | 0.071289 | 0.272083 | 0.263743 | 0.054747 | 0.003384 | 0.017858 | 0.257689 | 0.005464 |
2018.02 | 0.169464 | 0.063972 | 0.054747 | 0.054747 | 0.654040 | 0.006672 | 0.027349 | 0.201823 | 0.011270 |
2018.03 | 0.275426 | 0.065573 | 0.140699 | 0.386802 | 0.131500 | 0.008428 | − 0.012242 | − 0.075094 | 0.016023 |
2018.04 | 0.054747 | 0.255260 | 0.067222 | 0.565168 | 0.054747 | 0.003822 | − 0.003244 | − 0.047895 | 0.006910 |
2018.05 | 0.121561 | 0.082417 | 0.495424 | 0.060742 | 0.239856 | 0.003091 | 0.008865 | 0.136680 | 0.004237 |
2018.06 | 0.073791 | 0.114737 | 0.509979 | 0.248497 | 0.054747 | 0.002497 | 0.011912 | 0.230163 | 0.003186 |
2018.07 | 0.074851 | 0.306618 | 0.072666 | 0.167985 | 0.377880 | 0.004056 | 0.054747 | 0.669677 | 0.003378 |
2018.08 | 0.775866 | 0.054747 | 0.054747 | 0.061907 | 0.054747 | 0.002740 | 0.013351 | 0.236031 | 0.004141 |
2018.09 | 0.527862 | 0.270079 | 0.069391 | 0.054747 | 0.074765 | 0.003167 | − 0.016152 | − 0.261580 | 0.005924 |
2018.10 | 0.163395 | 0.117267 | 0.299596 | 0.369493 | 0.054747 | 0.005925 | 0.033102 | 0.275813 | 0.009422 |
2018.11 | 0.469976 | 0.153788 | 0.054747 | 0.266291 | 0.054747 | 0.016089 | − 0.004456 | − 0.015144 | 0.037023 |
2018.12 | 0.485838 | 0.061267 | 0.326615 | 0.062098 | 0.064182 | 0.006855 | 0.065792 | 0.476833 | 0.006253 |
2019.01 | 0.121561 | 0.082417 | 0.495424 | 0.060742 | 0.239856 | 0.003091 | 0.008865 | 0.136680 | 0.004237 |
2019.02 | 0.073791 | 0.114737 | 0.509979 | 0.248497 | 0.054747 | 0.002497 | 0.011912 | 0.230163 | 0.003186 |
2019.03 | 0.074851 | 0.306618 | 0.072666 | 0.167985 | 0.377880 | 0.004056 | 0.054747 | 0.669677 | 0.003378 |
2019.04 | 0.775866 | 0.054747 | 0.054747 | 0.061907 | 0.054747 | 0.002740 | 0.013351 | 0.236031 | 0.004141 |
2019.05 | 0.185337 | 0.143157 | 0.531074 | 0.067048 | 0.073384 | 0.003420 | 0.005777 | 0.078357 | 0.005404 |
2019.06 | 0.163395 | 0.117267 | 0.299596 | 0.369493 | 0.054747 | 0.005925 | 0.033102 | 0.275813 | 0.009422 |
2019.07 | 0.469976 | 0.153788 | 0.054747 | 0.266291 | 0.054747 | 0.016089 | − 0.004456 | − 0.015144 | 0.037023 |
2019.08 | 0.485838 | 0.061267 | 0.326615 | 0.062098 | 0.064182 | 0.006855 | 0.065792 | 0.476833 | 0.006253 |
2019.09 | 0.092558 | 0.397549 | 0.119787 | 0.104515 | 0.285590 | 0.007857 | − 0.017990 | − 0.117138 | 0.014591 |
2019.10 | 0.174315 | 0.320654 | 0.315521 | 0.106787 | 0.082724 | 0.003840 | − 0.005284 | − 0.074225 | 0.007000 |
2019.11 | 0.402554 | 0.081189 | 0.054747 | 0.054747 | 0.408739 | 0.005285 | 0.016337 | 0.150626 | 0.007665 |
2019.12 | 0.462187 | 0.133589 | 0.120307 | 0.221211 | 0.062705 | 0.002120 | 0.019419 | 0.448147 | 0.001923 |
2020.01 | 0.302124 | 0.054747 | 0.054747 | 0.540133 | 0.054747 | 0.002509 | 0.026513 | 0.519973 | 0.003123 |
2020.02 | 0.163395 | 0.117267 | 0.299596 | 0.369493 | 0.054747 | 0.005925 | 0.033102 | 0.275813 | 0.009422 |
2020.03 | 0.469976 | 0.153788 | 0.054747 | 0.266291 | 0.054747 | 0.016089 | − 0.004456 | − 0.015144 | 0.037023 |
2020.04 | 0.485838 | 0.061267 | 0.326615 | 0.062098 | 0.064182 | 0.006855 | 0.065792 | 0.476833 | 0.006253 |
2020.05 | 0.272085 | 0.162933 | 0.233367 | 0.201392 | 0.130223 | 0.006500 | 0.009411 | 0.069192 | 0.010601 |
2020.06 | 0.211447 | 0.054747 | 0.294013 | 0.384679 | 0.054747 | 0.009086 | 0.001653 | 0.006804 | 0.022178 |
2020.07 | 0.402554 | 0.081189 | 0.054747 | 0.054747 | 0.408739 | 0.005285 | 0.016337 | 0.150626 | 0.007665 |
2020.08 | 0.062204 | 0.342805 | 0.350125 | 0.186273 | 0.054747 | 0.007709 | − 0.027786 | − 0.182916 | 0.016542 |
2020.09 | 0.054747 | 0.294309 | 0.415059 | 0.181089 | 0.054747 | 0.002363 | 0.028021 | 0.584064 | 0.002527 |
2020.10 | 0.201736 | 0.393465 | 0.188655 | 0.144974 | 0.071170 | 0.009954 | − 0.014029 | − 0.072564 | 0.022781 |
2020.11 | 0.054747 | 0.603457 | 0.054747 | 0.054747 | 0.244664 | 0.004051 | 0.017969 | 0.216659 | 0.004755 |
2020.12 | 0.225476 | 0.054747 | 0.474217 | 0.054747 | 0.192112 | 0.003741 | 0.009762 | 0.124904 | 0.006214 |