|
| |12,245 |12,743 |14,992 |15,045 |14,583 |12,772 | | |
| |12,502 |13,123 |15,173 |13,344 |12,592 |14,666 | | |
| |12,976 |13,812 |15,706 |15,414 |15,655 |14,494 | | |
|14 |14,162 |15,519 |16,403 |17,273 |15,211 |18,008 |12 |0,5|
| | | | | | | | |96 |
| |12,522 |12,853 |15,488 |15,031 |14,035 |14,447 | | |
| |13,123 |13,967 |13,330 |14,221 |13,849 |16,304 | | |
| |12,043 |13,658 |13,493 |13,774 |14,343 |13,151 | | |
| |11,472 |12,136 |14,103 |12,386 |12,564 |13,363 | | |
| |12,441 |13,616 |12,717 |14,347 |15,090 |15,575 | | |
|15 |11,265 |12,052 |14,016 |14,047 |12,064 |11,667 |13 |0,7|
| |12,131 |12,983 |12,296 |15,291 |14,095 |13,940 | | |
| |14,480 |16,275 |16,717 |16,194 |15,413 |15,427 | | |
| |12,572 |13,244 |14,897 |14,571 |15,340 |15,674 | | |
| |10,865 |11,659 |10,923 |11,533 |13,089 |11,709 | | |
| |11,962 |13,388 |12,492 |14,907 |13,977 |14,358 | | |
|16 |10,908 |11,114 |13,790 |11,873 |13,029 |11,012 |13,5 |2 |
| |9,766 |11,117 |12,354 |11,287 |12,546 |10,249 | | |
| |11,702 |12,455 |13,484 |12,153 |13,075 |12,310 | | |
| |11,472 |12,053 |11,617 |14,065 |11,503 |13,322 | | |
| |13,503 |14,469 |14,195 |16,018 |14,812 |15,556 | | |
| |15,456 |17,355 |16,685 |15,598 |16,603 |19,311 | | |
|17 |10,161 |10,431 |10,695 |13,393 |11,153 |11,751 |12 |0,6|
| | | | | | | | |8 |
| |11,492 |13,087 |11,889 |12,564 |13,613 |11,699 | | |
| |12,428 |14,259 |12,561 |13,100 |13,888 |14,348 | | |
| |12,416 |14,059 |12,522 |13,706 |14,389 |13,536 | | |
| |10,813 |10,818 |12,951 |12,192 |11,765 |14,450 | | |
| |13,388 |14,590 |14,628 |14,764 |14,307 |16,962 | | |
|18 |9,889 |11,198 |10,095 |12,783 |11,183 |10,835 |13,33 |1,5|
| |12,517 |13,735 |14,247 |13,208 |15,072 |15,429 | | |
| |12,786 |13,231 |15,070 |13,013 |14,133 |16,174 | | |
| |11,863 |12,183 |13,377 |13,203 |11,916 |12,421 | | |
| |11,444 |11,999 |13,243 |14,233 |13,024 |12,491 | | |
| |14,696 |14,906 |14,730 |17,126 |17,331 |15,297 | | |
|19 |11,999 |12,509 |12,361 |14,850 |14,026 |15,078 |10 |0,1|
| |12,241 |13,124 |15,153 |14,655 |15,038 |15,460 | | |
| |12,120 |12,240 |12,945 |12,701 |13,006 |13,616 | | |
| |11,506 |12,815 |13,497 |13,746 |13,218 |14,658 | | |
| |12,376 |12,808 |14,477 |15,690 |14,127 |12,427 | | |
| |12,148 |13,932 |13,771 |14,039 |14,440 |12,250 | | |
|20 |11,293 |11,563 |14,165 |14,763 |12,874 |14,426 |12 |0,2|
| | | | | | | | |8 |
| |12,112 |13,348 |13,988 |12,222 |14,409 |13,381 | | |
| |11,429 |11,680 |14,364 |11,472 |13,201 |11,925 | | |
| |10,526 |11,960 |11,740 |12,709 |12,061 |12,319 | | |
| |11,467 |11,774 |11,862 |12,466 |12,013 |12,865 | | |
| |11,467 |11,747 |12,326 |13,699 |13,968 |12,173 | | |
|21 |11,954 |13,543 |13,158 |14,299 |14,420 |12,797 |13,6 |0,0|
| | | | | | | | |6 |
| |11,913 |12,292 |13,565 |13,888 |13,886 |12,930 | | |
| |11,572 |11,745 |12,146 |12,162 |13,720 |15,055 | | |
| |12,591 |14,354 |12,829 |14,346 |13,412 |16,083 | | |
| |11,638 |13,317 |13,026 |11,899 |14,227 |13,862 | | |
| |12,536 |14,156 |14,004 |15,164 |14,165 |12,651 | | |
|22 |11,820 |12,499 |11,834 |15,220 |12,420 |12,394 |13,281|0,5|
| |11,806 |12,803 |14,115 |14,830 |12,295 |14,506 | | |
| |13,376 |13,724 |15,571 |14,055 |15,511 |14,009 | | |
| |12,175 |13,275 |14,218 |14,957 |13,936 |12,930 | | |
| |10,139 |10,635 |10,975 |12,273 |10,431 |13,031 | | |
| |11,786 |13,607 |14,470 |14,452 |13,871 |12,949 | | |
|23 |11,574 |12,615 |12,977 |14,600 |11,962 |12,629 |12,630|1 |
| | | | | | | |4 | |
| |12,602 |14,600 |13,219 |12,806 |14,657 |13,855 | | |
| |12,012 |12,482 |12,072 |13,876 |13,781 |12,645 | | |
| |12,245 |14,012 |13,432 |14,994 |14,489 |14,450 | | |
| |12,502 |12,511 |12,574 |12,581 |13,727 |13,138 | | |
| |12,976 |14,279 |15,732 |15,464 |15,332 |15,686 | | |
|24 |14,162 |15,097 |16,664 |15,119 |15,614 |16,602 |14 |0,9|
| | | | | | | | |9 |
| |12,522 |13,107 |13,259 |15,520 |14,122 |15,000 | | |
| |13,123 |13,462 |14,243 |15,733 |14,196 |13,900 | | |
| |12,043 |12,656 |14,471 |13,502 |13,883 |15,184 | | |
| |11,472 |12,402 |14,301 |11,937 |12,424 |13,662 | | |
| |12,441 |12,922 |12,501 |14,496 |14,711 |16,107 | | |
|25 |11,265 |12,585 |11,693 |11,892 |12,272 |11,771 |13,050|1,8|
| | | | | | | |3 | |
| |12,131 |13,804 |14,553 |12,888 |12,203 |13,570 | | |
| |14,480 |15,883 |16,938 |17,964 |15,827 |16,217 | | |
| |12,572 |13,682 |14,710 |13,215 |14,412 |12,883 | | |
| |10,865 |11,008 |12,093 |10,942 |11,787 |14,353 | | |
| |11,962 |12,771 |12,948 |12,553 |14,741 |14,898 | | |
|26 |10,908 |12,573 |13,457 |13,093 |13,315 |12,251 |13,476|2,5|
| | | | | | | |8 | |
| |9,766 |11,044 |11,508 |11,785 |10,927 |10,205 | | |
| |11,702 |13,345 |13,567 |14,966 |14,416 |13,449 | | |
| |11,472 |11,740 |12,569 |12,698 |13,065 |11,547 | | |
| |13,503 |14,632 |16,452 |14,309 |15,559 |16,024 | | |
| |15,456 |16,674 |17,416 |16,571 |17,512 |19,215 | | |
|27 |10,161 |12,013 |12,309 |13,480 |10,737 |10,362 |12,653|2 |
| | | | | | | |1 | |
| |11,492 |12,874 |12,130 |11,774 |12,208 |13,078 | | |
| |12,428 |14,133 |13,361 |15,555 |13,970 |12,772 | | |
| |12,416 |13,743 |12,485 |15,630 |14,477 |14,736 | | |
| |10,813 |10,866 |12,196 |10,991 |12,082 |11,145 | | |
| |13,388 |15,128 |13,703 |16,777 |13,895 |17,200 | | |
|28 |9,889 |11,361 |10,420 |10,167 |10,772 |11,689 |13,209|1,8|
| |12,517 |12,568 |13,011 |12,590 |13,770 |14,967 | | |
| |12,786 |14,656 |12,976 |13,292 |14,371 |13,211 | | |
| |11,863 |13,064 |14,263 |15,093 |13,658 |12,023 | | |
| |11,444 |12,354 |13,277 |12,915 |13,978 |15,040 | | |
| |14,696 |16,068 |17,289 |15,475 |15,921 |16,822 | | |
|29 |11,999 |13,785 |12,086 |13,075 |12,001 |14,557 |12,489|0,4|
| | | | | | | |1 |88 |
| |12,241 |13,972 |12,655 |15,409 |14,427 |15,364 | | |
| |12,120 |12,223 |13,483 |14,749 |13,943 |15,458 | | |
| |11,506 |12,741 |13,154 |14,019 |13,421 |14,352 | | |
| |12,376 |12,607 |15,165 |15,504 |12,505 |16,273 | | |
| |12,148 |13,647 |13,685 |13,575 |13,531 |13,580 | | |
|30 |11,293 |11,455 |11,496 |13,262 |12,301 |13,370 |12,126|0,5|
| | | | | | | |05 | |
| |12,112 |13,212 |14,231 |14,946 |12,130 |13,687 | | |
| |11,429 |12,990 |11,766 |14,277 |12,649 |12,901 | | |
| |10,526 |10,985 |11,664 |10,955 |12,575 |11,408 | | |
| |11,467 |13,087 |13,639 |12,660 |11,969 |14,170 | | |
| |11,467 |12,661 |13,769 |11,926 |13,023 |14,202 | | |
Задача 2. Формирование оптимального портфеля ценных бумаг по модели
Тобина.
Порядок выполнения задачи.
1. В соответствии с вариантом задания получить данные по эффективности
безрисковых бумаг [pic]и допустимому риску портфеля [pic].
2. Данные по эффективности рисковых бумаг [pic] и необходимые
результаты расчетов взять из предыдущей задачи.
3. Составить математическую модель портфеля Тобина минимального риска
(1) и решить ее.
4. Составить математическую модель портфеля Тобина максимальной
доходности и решить ее. При численном решении использовать метод
сопряженных градиентов или Ньютона. Для вычислений можно
использовать ЭВМ.
5. Сделать выводы по работе.
Краткие теоретические сведения.
Портфель Тобина минимального риска
[pic] (1)
где m0 – эффективность безрисковых бумаг;
x0 – доля капитала вложенная в безрисковые бумаги;
xi,xj - доля капитала вложенная в ценные бумаги i-го и j–го видов;
mi – математическое ожидание (среднее арифметическое) доходности i - й
ценной бумаги;
vij – корреляционный момент между эффективностью бумаг i-го и j –го
видов;
Портфель Тобина максимальной эффективности
[pic](2)
где rp – риск портфеля
Расчетные формулы аналогичны формулам задачи составления оптимального
портфеля ценных бумаг Марковица.
Варианты заданий
|№ варианта |m0 |rp |mp |№ варианта |m0 |rp |X0 |
|1 |10 |0,3 |13,5 |16 |9 |0,05 |12,2|
|2 |10 |0,3 |13,3 |17 |9 |0,05 |12,2|
|3 |10 |0,3 |12,55 |18 |9 |0,05 |12,2|
|4 |10 |0,3 |12,55 |19 |9 |0,05 |12,2|
|5 |10 |1 |12,55 |20 |9 |0,05 |12,2|
|6 |10 |0,5 |12,7 |21 |9 |0,05 | |
|7 |10 |0,04|12,7 |22 |9 |0,088 |12,8|
|8 |10 |0,04|12,7 |23 |9 |0,09 |12,8|
|9 |10 |0,04|12,7 |24 |9 |0,12 |12,8|
|10 |10 |0,04|12,7 |25 |9 |0,1 |12 |
|11 |8 |0,05|12,7 |26 |9 |0,05 |12 |
|12 |8 |0,05|12,7 |27 |9 |0,05 |12,3|
|13 |8 |0,09|12,5 |28 |9 |0,12 |12,2|
|14 |8 |0,05|12,5 |29 |8 |0,1 |12 |
|15 |9 |0,05|12,2 |30 |8 |0,1 |12 |
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