From: Stressed portfolio optimization with semiparametric method
Period | Markowitz model | ||||||||
---|---|---|---|---|---|---|---|---|---|
VOO | TLT | LQD | IAU | VNQ | Volatility | Return | SR | VaR | |
2015.10–2015.12 | 0.177457 | 0.236393 | 0.237593 | 0.251497 | 0.097060 | 0.004914 | 0.030581 | 0.306925 | 0.006247 |
2015.11–2016.01 | 0.191533 | 0.189183 | 0.330781 | 0.151453 | 0.137050 | 0.002987 | − 0.005483 | − 0.098757 | 0.007346 |
2015.12–2016.02 | 0.194609 | 0.355099 | 0.082842 | 0.298886 | 0.068564 | 0.004341 | 0.005303 | 0.056277 | 0.006773 |
2016.01–2016.03 | 0.260998 | 0.075808 | 0.533044 | 0.059611 | 0.070539 | 0.002181 | 0.008187 | 0.178133 | 0.003308 |
2016.02–2016.04 | 0.438323 | 0.064790 | 0.067393 | 0.369232 | 0.060262 | 0.002125 | 0.035512 | 0.825654 | 0.001020 |
2016.03–2016.05 | 0.390102 | 0.240234 | 0.210918 | 0.075207 | 0.083540 | 0.001978 | 0.012604 | 0.308068 | 0.002448 |
2016.04–2016.06 | 0.479150 | 0.070969 | 0.089529 | 0.298833 | 0.061519 | 0.002832 | 0.007287 | 0.121279 | 0.004774 |
2016.05–2016.07 | 0.738519 | 0.068578 | 0.061201 | 0.072736 | 0.058966 | 0.002899 | 0.016837 | 0.283215 | 0.003153 |
2016.06–2016.08 | 0.320867 | 0.055845 | 0.230660 | 0.336898 | 0.055729 | 0.005984 | 0.001661 | 0.010396 | 0.013003 |
2016.07–2016.09 | 0.050000 | 0.050000 | 0.050000 | 0.050000 | 0.800000 | 0.006583 | 0.027021 | 0.202071 | 0.011142 |
2016.08–2016.10 | 0.139885 | 0.050013 | 0.050025 | 0.710035 | 0.050042 | 0.006969 | − 0.048987 | − 0.354452 | 0.015765 |
2016.09–2016.11 | 0.050087 | 0.091749 | 0.050325 | 0.757647 | 0.050192 | 0.003759 | − 0.003168 | − 0.047676 | 0.006812 |
2016.10–2016.12 | 0.438323 | 0.064790 | 0.067393 | 0.369232 | 0.060262 | 0.002109 | 0.035072 | 0.821653 | 0.001010 |
2016.11–2017.01 | 0.390102 | 0.240234 | 0.210918 | 0.075207 | 0.083540 | 0.001967 | 0.012639 | 0.310623 | 0.002446 |
2016.12–2017.02 | 0.479150 | 0.070969 | 0.089529 | 0.298833 | 0.061519 | 0.002872 | 0.007412 | 0.121802 | 0.004850 |
2017.01–2017.03 | 0.738519 | 0.068578 | 0.061201 | 0.072736 | 0.058966 | 0.002898 | 0.016696 | 0.280854 | 0.003139 |
2017.02–2017.04 | 0.052075 | 0.081504 | 0.053957 | 0.750060 | 0.062405 | 0.005907 | 0.008514 | 0.068544 | 0.010037 |
2017.03–2017.05 | 0.050000 | 0.050000 | 0.050000 | 0.050000 | 0.800000 | 0.006613 | 0.027088 | 0.201664 | 0.011180 |
2017.04–2017.06 | 0.268480 | 0.506691 | 0.100368 | 0.066477 | 0.057984 | 0.003795 | 0.003241 | 0.037208 | 0.007439 |
2017.05–2017.07 | 0.050087 | 0.091749 | 0.050325 | 0.757647 | 0.050192 | 0.003773 | − 0.003187 | − 0.047763 | 0.006848 |
2017.06–2017.08 | 0.158318 | 0.147202 | 0.286875 | 0.077530 | 0.330075 | 0.003091 | 0.008758 | 0.134928 | 0.004218 |
2017.07–2017.09 | 0.068086 | 0.099889 | 0.581654 | 0.196896 | 0.053475 | 0.002464 | 0.011891 | 0.232854 | 0.003164 |
2017.08–2017.10 | 0.054063 | 0.324698 | 0.054747 | 0.226128 | 0.340363 | 0.004020 | 0.052083 | 0.642620 | 0.003341 |
2017.09–2017.11 | 0.694957 | 0.056122 | 0.065574 | 0.125798 | 0.057549 | 0.002685 | 0.013336 | 0.240615 | 0.004102 |
2017.10–2017.12 | 0.294399 | 0.078843 | 0.166064 | 0.401023 | 0.059670 | 0.003378 | 0.017698 | 0.255765 | 0.005440 |
2017.11–2018.01 | 0.050000 | 0.050000 | 0.050000 | 0.050000 | 0.800000 | 0.006603 | 0.026934 | 0.200794 | 0.011140 |
2017.12–2018.02 | 0.689011 | 0.050565 | 0.051537 | 0.156637 | 0.052250 | 0.008303 | − 0.012137 | − 0.075602 | 0.015948 |
2018.01–2018.03 | 0.050087 | 0.091749 | 0.050325 | 0.757647 | 0.050192 | 0.003766 | − 0.003195 | − 0.047956 | 0.006847 |
2018.02–2018.04 | 0.158318 | 0.147202 | 0.286875 | 0.077530 | 0.330075 | 0.003057 | 0.008730 | 0.135977 | 0.004188 |
2018.03–2018.05 | 0.068086 | 0.099889 | 0.581654 | 0.196896 | 0.053475 | 0.002495 | 0.011707 | 0.226234 | 0.003159 |
2018.04–2018.06 | 0.054063 | 0.324698 | 0.054747 | 0.226128 | 0.340363 | 0.004048 | 0.052520 | 0.643533 | 0.003367 |
2018.05–2018.07 | 0.694957 | 0.056122 | 0.065574 | 0.125798 | 0.057549 | 0.002736 | 0.013147 | 0.232666 | 0.004110 |
2018.06–2018.08 | 0.325014 | 0.342751 | 0.141088 | 0.076066 | 0.115081 | 0.003133 | − 0.015913 | − 0.260602 | 0.005865 |
2018.07–2018.09 | 0.227873 | 0.050683 | 0.242898 | 0.428362 | 0.050185 | 0.005906 | 0.032595 | 0.272428 | 0.009340 |
2018.08–2018.10 | 0.050000 | 0.050000 | 0.050000 | 0.800000 | 0.050000 | 0.015891 | − 0.004267 | − 0.014737 | 0.036630 |
2018.09–2018.11 | 0.583894 | 0.054994 | 0.249566 | 0.055026 | 0.056520 | 0.006741 | 0.064711 | 0.476899 | 0.006162 |
2018.10–2018.12 | 0.158318 | 0.147202 | 0.286875 | 0.077530 | 0.330075 | 0.003061 | 0.008743 | 0.136008 | 0.004196 |
2018.11–2019.01 | 0.068086 | 0.099889 | 0.581654 | 0.196896 | 0.053475 | 0.002444 | 0.011862 | 0.234118 | 0.003148 |
2018.12–2019.02 | 0.054063 | 0.324698 | 0.054747 | 0.226128 | 0.340363 | 0.004022 | 0.052921 | 0.652735 | 0.003368 |
2019.01–2019.03 | 0.694957 | 0.056122 | 0.065574 | 0.125798 | 0.057549 | 0.002692 | 0.013332 | 0.239855 | 0.004107 |
2019.02–2019.04 | 0.178815 | 0.345249 | 0.250347 | 0.082559 | 0.143030 | 0.003362 | 0.005718 | 0.078847 | 0.005336 |
2019.03–2019.05 | 0.227873 | 0.050683 | 0.242898 | 0.428362 | 0.050185 | 0.005817 | 0.032549 | 0.276187 | 0.009269 |
2019.04–2019.06 | 0.050000 | 0.050000 | 0.050000 | 0.800000 | 0.050000 | 0.016006 | − 0.004323 | − 0.014807 | 0.037009 |
2019.05–2019.07 | 0.583894 | 0.054994 | 0.249566 | 0.055026 | 0.056520 | 0.006845 | 0.065511 | 0.475499 | 0.006247 |
2019.06–2019.08 | 0.059228 | 0.520589 | 0.060882 | 0.063095 | 0.296206 | 0.007853 | − 0.017620 | − 0.114845 | 0.014456 |
2019.07–2019.09 | 0.185526 | 0.312187 | 0.109350 | 0.328851 | 0.064085 | 0.003799 | − 0.005244 | − 0.074500 | 0.006928 |
2019.08–2019.10 | 0.069817 | 0.050163 | 0.050104 | 0.050025 | 0.779891 | 0.005226 | 0.016017 | 0.149260 | 0.007558 |
2019.09–2019.11 | 0.354102 | 0.143553 | 0.259630 | 0.157578 | 0.085137 | 0.002090 | 0.019192 | 0.449085 | 0.001906 |
2019.10–2019.12 | 0.450722 | 0.062094 | 0.089300 | 0.325553 | 0.072330 | 0.002482 | 0.026369 | 0.522830 | 0.003108 |
2019.11–2020.01 | 0.227873 | 0.050683 | 0.242898 | 0.428362 | 0.050185 | 0.005841 | 0.032588 | 0.275389 | 0.009291 |
2019.12–2020.02 | 0.050000 | 0.050000 | 0.050000 | 0.800000 | 0.050000 | 0.015897 | − 0.004250 | − 0.014678 | 0.036575 |
2020.01–2020.03 | 0.583894 | 0.054994 | 0.249566 | 0.055026 | 0.056520 | 0.006741 | 0.065250 | 0.480855 | 0.006186 |
2020.02–2020.04 | 0.256336 | 0.353002 | 0.113060 | 0.160268 | 0.117334 | 0.007432 | 0.009408 | 0.060487 | 0.011529 |
2020.03–2020.05 | 0.400734 | 0.051429 | 0.066797 | 0.429053 | 0.051987 | 0.008963 | 0.001657 | 0.006922 | 0.021945 |
2020.04–2020.06 | 0.069817 | 0.050163 | 0.050104 | 0.050025 | 0.779891 | 0.005254 | 0.016093 | 0.149191 | 0.007597 |
2020.05–2020.07 | 0.050059 | 0.409585 | 0.243612 | 0.246698 | 0.050045 | 0.007639 | − 0.027503 | − 0.182747 | 0.016412 |
2020.06–2020.08 | 0.050112 | 0.050673 | 0.796835 | 0.052323 | 0.050057 | 0.002337 | 0.027782 | 0.585563 | 0.002510 |
2020.07–2020.09 | 0.129021 | 0.324443 | 0.074690 | 0.414853 | 0.056993 | 0.009845 | − 0.014013 | − 0.073286 | 0.022706 |
2020.08–2020.10 | 0.074008 | 0.425982 | 0.067759 | 0.050285 | 0.381966 | 0.004700 | 0.017964 | 0.186668 | 0.004731 |
2020.09–2020.11 | 0.327937 | 0.110332 | 0.315693 | 0.055792 | 0.190245 | 0.003739 | 0.009645 | 0.123414 | 0.006185 |
Period | Semiparametric method | ||||||||
---|---|---|---|---|---|---|---|---|---|
VOO | TLT | LQD | IAU | VNQ | Volatility | Return | SR | VaR | |
2015.10–2015.12 | 0.160183 | 0.201954 | 0.389901 | 0.155095 | 0.092867 | 0.003968 | 0.023492 | 0.290764 | 0.004389 |
2015.11–2016.01 | 0.216752 | 0.131119 | 0.448274 | 0.112298 | 0.091557 | 0.002686 | − 0.004560 | − 0.092644 | 0.006486 |
2015.12–2016.02 | 0.172940 | 0.343354 | 0.067331 | 0.351387 | 0.064988 | 0.004277 | 0.002737 | 0.027125 | 0.006675 |
2016.01–2016.03 | 0.287010 | 0.051091 | 0.560270 | 0.050384 | 0.051246 | 0.002134 | 0.008876 | 0.198229 | 0.002867 |
2016.02–2016.04 | 0.530729 | 0.080792 | 0.096155 | 0.230098 | 0.062226 | 0.001641 | 0.035218 | 1.060395 | 0.000373 |
2016.03–2016.05 | 0.399718 | 0.218111 | 0.252014 | 0.062924 | 0.067233 | 0.001865 | 0.012726 | 0.329927 | 0.002181 |
2016.04–2016.06 | 0.407809 | 0.055219 | 0.058044 | 0.425151 | 0.053778 | 0.002812 | 0.010829 | 0.185165 | 0.003766 |
2016.05–2016.07 | 0.687917 | 0.086119 | 0.068683 | 0.096677 | 0.060604 | 0.002701 | 0.016116 | 0.290572 | 0.002939 |
2016.06–2016.08 | 0.295074 | 0.058944 | 0.345485 | 0.241187 | 0.059309 | 0.005659 | 0.000088 | − 0.002902 | 0.012696 |
2016.07–2016.09 | 0.169464 | 0.063972 | 0.058819 | 0.053705 | 0.654040 | 0.005967 | 0.026090 | 0.215117 | 0.009871 |
2016.08–2016.10 | 0.490535 | 0.078949 | 0.127607 | 0.210662 | 0.092247 | 0.003839 | − 0.007447 | − 0.102409 | 0.005604 |
2016.09–2016.11 | 0.053734 | 0.255260 | 0.067222 | 0.565168 | 0.058617 | 0.002900 | 0.000532 | 0.001990 | 0.004256 |
2016.10–2016.12 | 0.530729 | 0.080792 | 0.096155 | 0.230098 | 0.062226 | 0.001617 | 0.034387 | 1.050693 | 0.000369 |
2016.11–2017.01 | 0.399718 | 0.218111 | 0.252014 | 0.062924 | 0.067233 | 0.001847 | 0.012803 | 0.335297 | 0.002178 |
2016.12–2017.02 | 0.407809 | 0.055219 | 0.058044 | 0.425151 | 0.053778 | 0.002863 | 0.011203 | 0.188381 | 0.003825 |
2017.01–2017.03 | 0.687917 | 0.086119 | 0.068683 | 0.096677 | 0.060604 | 0.002702 | 0.015835 | 0.285352 | 0.002926 |
2017.02–2017.04 | 0.059820 | 0.299233 | 0.074893 | 0.404997 | 0.161057 | 0.004510 | 0.009389 | 0.099466 | 0.007155 |
2017.03–2017.05 | 0.169464 | 0.063972 | 0.058819 | 0.053705 | 0.654040 | 0.006025 | 0.026201 | 0.213990 | 0.009905 |
2017.04–2017.06 | 0.349012 | 0.250337 | 0.257934 | 0.077485 | 0.065231 | 0.003048 | 0.008530 | 0.133072 | 0.005830 |
2017.05–2017.07 | 0.053734 | 0.255260 | 0.067222 | 0.565168 | 0.058617 | 0.002923 | 0.000539 | 0.002094 | 0.004277 |
2017.06–2017.08 | 0.121561 | 0.082417 | 0.495424 | 0.060742 | 0.239856 | 0.002705 | 0.007115 | 0.123810 | 0.003664 |
2017.07–2017.09 | 0.073791 | 0.114737 | 0.509979 | 0.248497 | 0.052996 | 0.002456 | 0.011837 | 0.232526 | 0.003139 |
2017.08–2017.10 | 0.074851 | 0.306618 | 0.072666 | 0.167985 | 0.377880 | 0.003839 | 0.048566 | 0.627128 | 0.002693 |
2017.09–2017.11 | 0.775866 | 0.052707 | 0.055846 | 0.061907 | 0.053674 | 0.002652 | 0.017581 | 0.323599 | 0.003499 |
2017.10–2017.12 | 0.334962 | 0.071289 | 0.272083 | 0.263743 | 0.057923 | 0.002980 | 0.017407 | 0.285051 | 0.005007 |
2017.11–2018.01 | 0.169464 | 0.063972 | 0.058819 | 0.053705 | 0.654040 | 0.006003 | 0.025920 | 0.212413 | 0.009870 |
2017.12–2018.02 | 0.275426 | 0.065573 | 0.140699 | 0.386802 | 0.131500 | 0.004183 | 0.002988 | 0.030737 | 0.006914 |
2018.01–2018.03 | 0.053734 | 0.255260 | 0.067222 | 0.565168 | 0.058617 | 0.002910 | 0.000541 | 0.002142 | 0.004278 |
2018.02–2018.04 | 0.121561 | 0.082417 | 0.495424 | 0.060742 | 0.239856 | 0.002646 | 0.007070 | 0.125743 | 0.003638 |
2018.03–2018.05 | 0.073791 | 0.114737 | 0.509979 | 0.248497 | 0.052996 | 0.002485 | 0.011472 | 0.222401 | 0.003134 |
2018.04–2018.06 | 0.074851 | 0.306618 | 0.072666 | 0.167985 | 0.377880 | 0.003891 | 0.049404 | 0.629415 | 0.002714 |
2018.05–2018.07 | 0.775866 | 0.052707 | 0.055846 | 0.061907 | 0.053674 | 0.002735 | 0.017075 | 0.304586 | 0.003507 |
2018.06–2018.08 | 0.527862 | 0.270079 | 0.069391 | 0.057903 | 0.074765 | 0.002891 | − 0.011236 | − 0.201531 | 0.004917 |
2018.07–2018.09 | 0.163395 | 0.117267 | 0.299596 | 0.369493 | 0.050250 | 0.005635 | 0.026281 | 0.229476 | 0.009048 |
2018.08–2018.10 | 0.469976 | 0.153788 | 0.057899 | 0.266291 | 0.052046 | 0.007470 | 0.019957 | 0.130787 | 0.017045 |
2018.09–2018.11 | 0.485838 | 0.061267 | 0.326615 | 0.062098 | 0.064182 | 0.005929 | 0.057045 | 0.477570 | 0.005171 |
2018.10–2018.12 | 0.121561 | 0.082417 | 0.495424 | 0.060742 | 0.239856 | 0.002656 | 0.007093 | 0.125695 | 0.003643 |
2018.11–2019.01 | 0.073791 | 0.114737 | 0.509979 | 0.248497 | 0.052996 | 0.002434 | 0.011858 | 0.234983 | 0.003122 |
2018.12–2019.02 | 0.074851 | 0.306618 | 0.072666 | 0.167985 | 0.377880 | 0.003844 | 0.050094 | 0.646250 | 0.002715 |
2019.01–2019.03 | 0.775866 | 0.052707 | 0.055846 | 0.061907 | 0.053674 | 0.002669 | 0.017557 | 0.321148 | 0.003503 |
2019.02–2019.04 | 0.185337 | 0.143157 | 0.531074 | 0.067048 | 0.073384 | 0.002593 | 0.009933 | 0.183488 | 0.003530 |
2019.03–2019.05 | 0.163395 | 0.117267 | 0.299596 | 0.369493 | 0.050250 | 0.005476 | 0.026232 | 0.235693 | 0.008973 |
2019.04–2019.06 | 0.469976 | 0.153788 | 0.057899 | 0.266291 | 0.052046 | 0.007581 | 0.020493 | 0.132420 | 0.017219 |
2019.05–2019.07 | 0.485838 | 0.061267 | 0.326615 | 0.062098 | 0.064182 | 0.006122 | 0.058396 | 0.473563 | 0.005243 |
2019.06–2019.08 | 0.092558 | 0.397549 | 0.119787 | 0.104515 | 0.285590 | 0.006938 | − 0.014984 | − 0.110994 | 0.012743 |
2019.07–2019.09 | 0.174315 | 0.320654 | 0.315521 | 0.106787 | 0.082724 | 0.003515 | − 0.009353 | − 0.138969 | 0.006173 |
2019.08–2019.10 | 0.402554 | 0.081189 | 0.056218 | 0.051299 | 0.408739 | 0.004420 | 0.019300 | 0.213619 | 0.005823 |
2019.09–2019.11 | 0.462187 | 0.133589 | 0.120307 | 0.221211 | 0.062705 | 0.001887 | 0.023460 | 0.610738 | 0.001066 |
2019.10–2019.12 | 0.302124 | 0.051589 | 0.053442 | 0.540133 | 0.052713 | 0.002479 | 0.030260 | 0.601898 | 0.002362 |
2019.11–2020.01 | 0.163395 | 0.117267 | 0.299596 | 0.369493 | 0.050250 | 0.005517 | 0.026285 | 0.234431 | 0.008997 |
2019.12–2020.02 | 0.469976 | 0.153788 | 0.057899 | 0.266291 | 0.052046 | 0.007489 | 0.019791 | 0.129359 | 0.017014 |
2020.01–2020.03 | 0.485838 | 0.061267 | 0.326615 | 0.062098 | 0.064182 | 0.005933 | 0.057920 | 0.484621 | 0.005193 |
2020.02–2020.04 | 0.272085 | 0.162933 | 0.233367 | 0.201392 | 0.130223 | 0.007076 | 0.017931 | 0.123754 | 0.011220 |
2020.03–2020.05 | 0.211447 | 0.054567 | 0.294013 | 0.384679 | 0.055294 | 0.006421 | 0.006489 | 0.047289 | 0.015313 |
2020.04–2020.06 | 0.402554 | 0.081189 | 0.056218 | 0.051299 | 0.408739 | 0.004465 | 0.019502 | 0.213715 | 0.005853 |
2020.05–2020.07 | 0.062204 | 0.342805 | 0.350125 | 0.186273 | 0.058592 | 0.006584 | − 0.024562 | − 0.189698 | 0.013904 |
2020.06–2020.08 | 0.055680 | 0.294309 | 0.415059 | 0.181089 | 0.053865 | 0.002336 | 0.040450 | 0.856912 | 0.001602 |
2020.07–2020.09 | 0.201736 | 0.393465 | 0.188655 | 0.144974 | 0.071170 | 0.006108 | − 0.013680 | − 0.115384 | 0.012968 |
2020.08–2020.10 | 0.051031 | 0.603457 | 0.050679 | 0.050169 | 0.244664 | 0.004696 | 0.023206 | 0.242621 | 0.004484 |
2020.09–2020.11 | 0.225476 | 0.057092 | 0.474217 | 0.051103 | 0.192112 | 0.003403 | 0.006678 | 0.092000 | 0.005677 |