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Выбор оптимального портфеля ценных бумаг инвестиционным отделом ‘ПриватБанка’

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Введение

Коммерческие банки – это учреждения, которые стали создавать в Украине в
1989 г. для привлечения денежных средств от юридических и физических лиц
и размещения их от своего имени на условиях срочности, платности и
возвратности, а также осуществления иных банковских операций на началах
коммерческого расчета. В своей деятельности банки используют не только
свой собственный, но и привлеченный капитал в виде вкладов, депозитов,
межбанковских кредитов и других источников. И, как правило, привлеченные
денежные средства намного превосходят объем собственного капитала
коммерческих банков.

Коммерческие банки – важнейшее звено банковской системы, концентрируют
основную часть кредитных ресурсов и осуществляют широкий диапазон
банковских операций и финансовых услуг для юридических и физических лиц.
Они представляют второй уровень банковской системы страны после
национальных (государственных, центральных) банков.

С одной стороны, банк, как и любое предприятие, создается для
оперативного получения их учредителями и клиентами широкого спектра
банковских услуг, включая получение кредитов. С другой стороны, банк –
это предприятие особого вида, которое организует и осуществляет движение
ссудного капитала, обеспечивая получение прибыли собственникам банка.

Инвестициями в банковской практике являются средства банков, вложенные в
ценные бумаги предприятий, организаций, учреждений различных форм
собственности на продолжительный период времени.

Вся сумма ценных бумаг, купленных банком в ходе активных операций,
составляет его инвестиционный портфель. В эту сумму входят все
обязательства, которые обращаются на рынке в виде акций, облигаций и
векселей.

Ценные бумаги, как правило, являются объектом банковских инвестиций,
если они:

– обращаются на рынке ценных бумаг;

– служат долговыми обязательствами.

Главными целями банков как инвесторов являются, прежде всего,
обеспечение сбережения средств, т.е. безопасность вложений, а также
доходность банковских инвестиций, их ликвидность и рост.

Неуязвимость банковских вложений от потрясений на фондовом рынке и
гарантированную стабильность в получении дохода обеспечивает
безопасность. Она обычно достигается в ущерб доходности и росту
вложений. Наиболее безопасными считаются вложения в облигации
государственных займов, так как они обеспечиваются экономическим весом и
платежеспособностью государства.

Если же банк, прежде всего, заинтересован в доходности акций или
облигаций, т.е. в получении максимально возможных дивидендов, то ему
придется пожертвовать безопасностью, поскольку считается, что наиболее
доходными являются ценные бумаги акционерных обществ с низким
инвестиционным рейтингом. Вместе с тем, это не означает, что чем менее
надежны ценные бумаги, тем они доходнее, так как доходность зависит от
различных факторов. Оптимальное сочетание безопасности и доходности
осуществляется путем тщательной и периодической проверки и подбора
ценных бумаг.

Ликвидность ценных бумаг означает достаточно быстрое и, как правило, без
потерь для их держателей обращение этих ценных бумаг в деньги. Она не
всегда связана с другими инвестиционными целями. Ликвидность, прежде
всего, означает, что при определенной цене всегда найдутся покупатели,
которые приобретут данные ценные бумаги.

Увеличивать свои вложения могут только владельцы акций. Рост капитала
гарантируется в основном за счет увеличения числа обыкновенных акций
акционерных обществ, работающих в передовых отраслях народного
хозяйства. Такие акции, хотя и приносят низкий уровень дивидендов, но,
как правило, обеспечивают быстрое удорожание капитала.

В связи с этим, необходимо подчеркнуть, что, так как ни одна бумага не
отвечает одновременно всем инвестиционным целям, то необходим компромисс
между целями инвестора. Например, если ценные бумаги надежны, то
доходность их будет низкой, потому что инвесторы, предпочитающие
надежность, будут покупать их по более высокой, по сравнению с
номинальной ценой, что соответственно снизит доходность.

Конечно, коммерческие банки уделяют серьезное внимание качеству ценных
бумаг сразу при их покупке, однако надежного, с гарантией метода
определения защиты вложенных средств на долгий период нет, так как
нередко возникают ситуации, которые нельзя заранее спрогнозировать.

Поэтому очень важно, когда определены цели инвестирования, выбрать
именно те ценные бумаги, которые соответствуют этим целям.

1. Общая характеристика «ПриватБанка»

1.1 Общая информация о «ПриватБанке»

«ПриватБанк» – признанный лидер украинской банковской системы и одна из
наиболее динамично развивающихся отечественных финансовых структур. Банк
постоянно предлагает принципиально новые высококачественные технологии
обслуживания клиентов, продукты и услуги.

«ПриватБанк» обладает обширной филиальной сетью по всей Украине, куда
входят 443 филиала и отделения. Основан в марте 1992 года.

Банк первым в Украине:

– вступил в Ассоциацию клиринговых банков Центральной и Восточной Европы
(1996 г.);

– стал действительным членом международной платежной системы VISA
International и приступил к массовой эмиссии пластиковых карт;

– получил рейтинговое заключение от международного рейтингового
агентства Thomson BankWatch (1997 г.);

– установил банкоматы, сертифицированные системой VISA, по работе с
международными картами (1997 г.).

С 1993 г. банк инициирует проведение ежегодных Ялтинских межбанковских
конференций.

Банк успешно работает по обслуживанию кредитной линии ЕБРР: В 2004 году
им выдан 100 000-й кредит в рамках программы микрокредитования за счет
средств международных финансовых организаций KfW и ЕБРР, в июле 2000 г.

«ПриватБанк» был включен в число банков-агентов по обслуживанию второй
кредитной линии Европейского Банка Реконструкции и Развития,
направленной на развитие мелкого и среднего бизнеса.

В течение 12 лет надёжность банка подтверждается аудиторскими
заключениями фирм «Coopers & Librand» и «PricewaterhouseCoopers».

Сегодня приоритетными задачами банка являются:

– повышение качества обслуживания и расширение клиентской базы;

– активное продвижение инновационных банковских продуктов на всех
сегментах финансового рынка;

– повышение профессионально-квалификационного уровня и благосостояния
персонала банка;

– эффективное управление финансовыми и трудовыми ресурсами проведение
сбалансированной политики управления рисками;

– дальнейшее укрепление надежности банка создание гибкой системы
управления, отвечающей передовым мировым достижениям.

1.2 Операции, выполняемые банком

Современный коммерческий банк – это универсальное предприятие,
стремящееся развивать как можно больше видов операций и услуг. При
разнообразии проводимых ПриватБанком операций их можно разделить на
отдельные группы: кредитные, расчетные, кассовые, межбанковские
расчетные операции, вексельные, операции с ценными бумагами, операции в
иностранной валюте, посреднические, финансовые, учредительские.

– кредитные операции – это операции кредитора по размещению свободных
ресурсов заемщику, причем банк может выступать в этих операциях, как в
роли кредитора, так и в роли заемщика, получая кредиты в национальном
банке и других коммерческих банках.

– расчетные операции – хранение средств клиентов, движение, перемещение
их с помощью обращения платежных инструментов (по распоряжению
держателей денежных средств). Для осуществления этих операций клиент
открывает в банке счет (расчетный, депозитный, ссудный, контокоррентный
и т.д.).

– кассовые операции – операции банка по приему и выдаче денег и
ценностей клиентам банка через операционную кассу банка.

– межбанковские операции в соответствии с действующим законодательством
предполагают расчеты между банками и другими кредитными учреждениями.
Расчеты между банками могут производиться через расчетно-кассовые
центры, клиринговые учреждения и корреспондентские счета банков.

– вексельные операции банк совершает как с собственными векселями, так и
с векселями других предприятий: производит учет векселей, выдачу ссуд до
востребования по специальному ссудному счету под обеспечение векселей,
принятие векселей на инкассо для получения платежей и для оплаты их в
срок.

– операции банка с ценными бумагами различны. Банк может выпускать
собственные ценные бумаги (акции, облигации), финансовые инструменты
(сертификаты, векселя) для увеличения уставного фонда акционерного
банка, для привлечения заемных средств и совершать акты купли-продажи с
ценными бумагами других предприятий и банков. Такой тип операций
называют курсовыми операциями. Другими словами, банки могут выпускать,
покупать, продавать, хранить платежные документы и ценные бумаги: чеки,
аккредитивы, векселя, акции, облигации и др.

– операции с иностранной валютой заключаются в покупке у украинских и
иностранных юридических и физических лиц и продаже им наличной валюты,
находящейся на счетах и вкладах.

– комиссионные (посреднические) операции весьма разнообразны и относятся
к различного рода операциям по купле и продаже, производству и принятию
платежей. Банк выступает в роли посредника и консультанта по различным
сделкам (перевод денег, оформление ценных бумаг, управление имуществом и
т.д.).

– финансовые операции банк осуществляет при реализации государственных,
коммунальных, акционерных облигационных займов, т.е. банк берет на себя
обязательство выплачивать капитал держателям облигаций.

– банк может осуществлять учредительские операции по основанию новых
предприятий.

1.3 Функции коммерческого банка

В современных условиях возрастает влияние банков на экономику.
Деятельность кредитных учреждений не ограничивается аккумуляцией и
размещением растущей массы денежных средств компаний, предприятий и
части населения. Они способствуют накоплению капитала, не только активно
вмешиваясь во все стороны хозяйственной жизни, но и непосредственно
участвуя в деятельности функционирующего капитала или осуществляя
контроль над ним. Благодаря банкам действует механизм распределения и
перераспределения капитала по сферам и отраслям производства, который в
значительной степени обеспечивает развитие народного хозяйства в
зависимости от объективных потребностей производства.

Финансируя дополнительные потребности предприятий промышленности,
транспорта, сельского хозяйства в инвестициях, расширении производства,
банки имеют возможность воздействовать на создание прогрессивной
воспроизводственной структуры народного хозяйства. Важная экономическая
роль коммерческих банков существенно расширила сферу их деятельности.
Так, выполняя функцию мобилизации свободных денежных средств и
превращения их в капитал, банки аккумулируют денежные доходы и
сбережения в виде вкладов. Вкладчик получает вознаграждение в виде
процента или оказываемых банком услуг. Сконцентрированные на вкладах
сбережения превращаются в ссудный капитал, используемый банками для
предоставления кредита предприятиям, предпринимателям. Использование
кредита обеспечивает развитие производительных сил страны в целом.
Заемщики вкладывают средства в расширение производства, покупку
недвижимости, потребительских товаров. В результате с помощью банков
сбережения, в конечном счете, превращаются в капитал.

Кредитные возможности банков зависят от накопления денежных средств
населения и увеличения собственных денежных средств предприятий.
Постоянный рост этих средств в промышленно развитых странах и
потребность в кредитных ресурсах со стороны предприятий создают условия
для расширения кредитования.

Важное экономическое значение имеет функция кредитования предприятий,
государства и населения. Прямое предоставление в ссуду свободных
денежных капиталов их владельцами заемщикам в практической хозяйственной
жизни затруднено. Банк выступает в качестве финансового посредника,
получая денежные средства у конечных кредиторов и давая их конечным
заемщикам.

За счет кредитов банка осуществляется финансирование промышленности,
сельского хозяйства, торговли, обеспечивается расширение производства.
Коммерческие банки предоставляют кредиты потребителям на приобретение
товаров длительного пользования, способствуя росту уровня жизни. Так как
государственные расходы не всегда покрываются доходами, банки кредитуют
финансовую деятельность правительства, но, как правило, не путем прямого
кредитования.

В последние годы повышается спрос на кредит. Предприятиям не обходимы
дополнительные денежные средства для обновления капитала и расширения
производственных мощностей. Для удовлетворения спроса со стороны
предприятий коммерческие банки разрабатывают новые формы кредитования,
совершенствуют его механизм. Выпуск кредитных денег является
специфической функцией, отличающей коммерческие банки от других
финансовых инструментов.

Современный механизм денежной эмиссии связан с двумя понятиями:
банкнотная и депозитная эмиссия. Соответственно денежная масса выступает
в наличной (банковские билеты и разменная монета) и безналичной
(денежные средства на счетах и депозитах в коммерческих банках и других
кредитных учреждениях) формах.

Доля наличных денег составляет в промышленно развитых странах до 10%,
причем наблюдается ее дальнейшее уменьшение.

В структуре денежного оборота преобладает безналичный оборот, а
основными эмитентами денег являются не центральные, а коммерческие
банки.

Коммерческие банки осуществляют депозитную эмиссию – выпуск кредитных
инструментов обращения на основе создания банком вкладов (депозитов),
которые образуются в результате выдачи ссуды клиенту. Денежная масса
увеличивается, когда банки выдают ссуды своим клиентам, и уменьшается,
когда возвращаются ссуды, полученные от банков.

Предоставляемая клиенту ссуда зачисляется на его счет в банке, т.е. банк
создает депозит (вклад до востребования). При этом увеличиваются
долговые обязательства банка. Владелец депозита может получить в банке
наличные деньги в размере вклада; таким образом, банки создают деньги
против требований клиента, и происходит увеличение количества денег в
обращении. При наличии спроса на банковские кредиты современный
эмиссионный механизм позволяет расширять денежную эмиссию, что
подтверждается ростом денежной массы в промышленно развитых странах.
Банковский кредит стал одной из главных причин этого роста. Вместе с
тем, экономика нуждается в необходимом, но не чрезмерном количестве
денег, поэтому коммерческие банки функционируют в рамках ограничений,
предусматриваемых государством в лице национального банка. Эти
ограничения должны регулировать процесс кредитования и, следовательно,
процесс создания денег и осуществлять контроль над этим процессом.

В период преобразования украинской экономики регулирование депозитной
эмиссии стало острой проблемой. Нестабильность денежного обращения,
инфляция в значительных размерах потребовали от Национального банка
Украины проведения политики ограничения предложения кредитных ресурсов
коммерческим байкам. Ограничителями возможностей коммерческих банков
увеличивать денежную массу являются, прежде всего, резервные требования
и уровень процентной ставки НБУ при кредитовании коммерческих банков.
Норма хранения средств на резервном счете коммерческих банков в НБУ
довольно высока и составила в 1997 г. 20% от вкладов до востребования и
5% – от срочных вкладов. Ставка НБУ в 1997 г. ориентировалась на
рыночную ставку по межбанковским кредитам и оставалась высокой.

Одной из основных функций коммерческих банков является обеспечение
расчетно-платежного механизма. Большая часть расчетов между
предприятиями осуществляется безналичным путем. Выступая в качестве
посредников в платежах, банки выполняют для своих клиентов операции,
связанные с проведением расчетов и платежей. Необходимость проведения в
установленные сроки каждого платежного документа, бесперебойность
расчетов и их ускорение требуют от банков разработки методологии
организации расчетов с целью их совершенствования и соответствующего
контроля.

Эффективное функционирование системы расчетов в странах с развитой
банковской инфраструктурой базируется на постоянном улучшении технологии
расчетных операций, стремлении предприятий и частных лип выгоднее
использовать спои средства. В этих странах сосуществует несколько
расчетных систем, например, расчетные системы крупных коммерческих
банков так называемых клиринговых с их филиалами и отделениями, в
которые могут входить и другие кредитно-финансовые учреждения. Эти
банки, как правило, производят клиринговый зачет значительной части
платежных документов в стране. Жиросистемы – это акционерные общества,
образованные банками-участниками расчетов, включая центральные банки
государств. В системе расчетов Украины главную роль выполняют
расчетно-кассовые центры (РКЦ) НБУ.

Расчеты осуществляются также через сеть банков-корреспондентов, когда
банки устанавливают взаимные корреспондентские отношения.

Для ускорения расчетов, снижения издержек и повышения надежности
операций внедряются электронные системы расчетов.
Эмиссионно-учредительская функция осуществляется коммерческими байками
путем выпуска и размещения ценных бумаг (акций, облигации). Выполняя эту
функцию, банки становятся каналом, обеспечивающим направление сбережений
для производственных целей. Рынок ценных бумаг дополняет систему
банковского кредита и взаимодействует с ней. Например, коммерческие
банки предоставляют посредникам рынка ценных бумаг
(компаниям-учредителям) ссуды для подписки на ценные бумаги новых
выпусков, а те продают банкам ценные бумаги для перепродажи в розницу.
Если компания-учредитель, на имя которой зарегистрированы ценные бумаги,
сама продает их, то банк может обеспечивать подписчиков на выпущенные
ценные бумаги. Как правило, при этом банк организует консорциум по
размещению ценных бумаг. Обязательства на значительные суммы, выпущенные
крупными компаниями, могут быть размещены банком путем продажи своим
клиентам (в основном институциональным инвесторам), а не посредством
свободной продажи на фондовой бирже.

Располагая возможностями постоянно контролировать экономическую
ситуацию, коммерческие банки дают консультации по широкому кругу проблем
(по слияниям и поглощениям, новым инвестициям и регистрации предприятий,
составлению годовых отчетов). В настоящее время возросла роль банков в
предоставлении клиентам экономической информации.

На современном этапе в сфере деятельности коммерческих банков
наблюдается тенденция к универсализации, что объясняется влиянием
конкуренции. Для повышения эффективности банковской деятельности
банковское законодательство промышленно развитых стран стимулирует
конкуренцию» создавая равные условия для деятельности различных
кредитных учреждений. В рамках данной тенденции (при параллельном
сохранении и развитии специализации) изменяется концепция
взаимоотношений банков с клиентами, создаются принципиально новые
направления развития банковского дела. Это выражается не только в
увеличении числа предлагаемых клиентам услуг, но и в качественном
изменении структуры операций, снижении удельного веса
ссудо-сберегательных операций и увеличении объемов операций с ценными
бумагами.

В последние годы в банковской практике появились операции, связанные со
страхованием: предоставление клиентам гарантии погашения задолженности,
увеличение суммы вклада при болезни или несчастном случае, мобилизация
денежных средой путем продажи страховых полисов населению. Банки
приобретает уже функционирующие страховые компании, что оказывается
выгодным как для банков, получающих стабильно прибыльные страховые
компании, так и для страховых компаний, которым предоставляется
возможность использовать широкую сеть банковских филиалов и отделений на
территории своей страны и за рубежом.

Таким образом, в современных условиях продолжается развитие тенденции
расширения функций коммерческих банков, которые для улучшения банковской
ликвидности, получения доходов, занятия позиций на рынке развивают
нехарактерные раннее для банков операции и услуги.

2 Экономический анализ «ПриватБанка»

2.1 Понятие ликвидности банка, методы ее оценки и регулирования

В своей повседневной деятельности коммерческий банк должен решать
следующие три экономически взаимосвязанные задачи, обеспечивающие
дееспособность коммерческого банка вообще и успех банковского дела в
целом:

– достижение доходности банковского дела для покрытия своих затрат,
обеспечение перспектив развития, выплаты дивидендов акционерам банка и
процентов клиентам-вкладчикам денежных средств, создания необходимых
страховых резервов, оплаты государственных отчислений. (приложение А);

– обеспечение платежеспособности банка, т.е. способности в должные сроки
и в полной сумме отвечать по своим обязательствам перед кредиторами –
государством, банками, вкладчиками и др.;

– обеспечение ликвидности, т.е. возможности быстрого (желательно без
потерь доходности или дополнительных затрат) превращения активов банка в
платежные средства для своевременного выполнения обязательств по пассиву
(погашения своих долговых обязательств).

Термин «ликвидность» (от лат. Liquidus – жидкий, текущий) в буквальном
смысле слова означает легкость реализации, продажи, превращения
материальных ценностей в денежные средства. Как вода по признаку
текучести относится к жидкости, так и активы банка в зависимости от
легкости превращения в денежную форму (в наличные деньги или в средства
на счетах банка) определяются как ликвидные или неликвидные средства.

В нашей экономической литературе подчас смешиваются два понятия –
ликвидность и платежеспособность коммерческого банка, что в последующем
на практике приводит к отождествлению методов и способов их поддержания.
А это в свою очередь может привести к нарушению нормального
функционирования коммерческого банка.

В международной же практике банкиры считают, что в основе
платежеспособности коммерческого банка лежит, прежде всего, его
ликвидность. Так как банк вряд ли может быть платежеспособным при
отсутствии ликвидности. И как показывает банковский опыт, если банк
теряет ликвидность, то он теряет и платежеспособность. И в результате
наступает его банкротство.

Исходя их этого, в обеспечении деятельности коммерческого банка высокого
уровня стабильности, устойчивости и надежности ликвидность – первична, а
платежеспособность – вторична.

Вместе с тем, учитывая фактор риска активных операций в оценке
ликвидности баланса коммерческого банка, можно вывести следующую
зависимость между основными свойствами его активов, формирующих его
политику и стратегическую цель деятельности: Чем выше доходность активов
банка, тем больше риск операций по ним, но тем ниже уровень ликвидности
баланса, а, следовательно, и платежеспособность банка в целом, и
наоборот.

Таким образом, обеспечение ликвидности банка – это сложная и.
многофакторная задача, успех решения которой определяет суть и
содержание политики и деятельности любого коммерческого банка как
предпринимательской структуры в системе банковского дела.

Применительно к практике банковского дела в Украине для оценки состояния
и последующего расчета показателей ликвидности активы коммерческого
банка подразделяют на пять групп по степени риска банковских вложений и
возможности потери ими части своей стоимости при невозвратности. При
этом отдельным категориям и группам присваиваются соответствующие
поправочные коэффициенты риска (см. табл. 2.1)

Таблица 2.1. Активы банка, сгруппированные по степени риска

Группы и виды активовКоэффициент риска1 группа1. банкноты, монеты,
дорожные чеки02. банковские металлы03. средства до востребования в
НБУ04. срочные депозиты в НБУ05. долговые обязательства, которые
рефинансируются НБУ06. долговые ценные бумаги центрального
правительства02 группа7. кредиты, предоставленные центральным органам
государственного управления103 группа8. кредиты, предоставленные местным
органам власти209. долговые ценные бумаги

центральных органов государственного управления и местных органов
власти204 группа10. средства до востребования в других банках5011.
срочные депозиты, размещенные в других банках505 группа12. операции с
ценными бумагами10013. другие кредиты и финансовый лизинг,
предоставленные банком (кроме100пролонгированных, просроченных и
сомнительных)

14. пролонгированная задолженность10015. просроченная
задолженность10016. сомнительная задолженность10017. дебиторы10018.
основные средства и товарно-материальные ценности10019. начисленные и
просроченные начисленные доходы100Внебалансовые счета20. предоставленные
кредитные обязательства10021. гарантии, поручительства, аккредитивы и
акцепты10022. обязательства по операциям с валютой, банковскими
металлами и ценными бумагами100

Данные приведенной таблицы свидетельствуют, что, прежде всего в первую
группу включены активы, свободные от риска. Действительно, денежная
наличность и остатки на корреспондентском счете и других счетах в
Национальном Банке Украины по первому требованию могут быть направлены
на выплату вкладов, покрытие долгов и расходов банка.

А во вторую и третью группы входят активы с минимальным риском. К ним
относятся, как кредиты, предоставленные центральным и местным органам
власти, так и долговые ценные бумаги центральных и местных органов
власти. Потеря таких средств для банка является маловероятной.

К четвертой группе, как показывает опыт, относятся наименее ликвидные
активы.

А в пятую группу уже включены активы с повышенным риском.

И чтобы добиться высокой платежеспособности, коммерческий банк должен
постоянно следить за качеством своих активов. Прежде всего, ему следует
добиваться ликвидности или уменьшения статей с высоким коэффициентом
риска.

Правда, приведенные коэффициенты риска не совсем объективны. Вряд ли во
всех случаях дебиторская задолженность является объектом повышенного
риска. Очевидно, завышена степень риска и в четвертой группе. Ведь
зарубежный опыт показывает, что такие активы являются гарантированными и
высоко ликвидными.

В условиях рыночной экономики, где главная цель деятельности
коммерческих банков – это получение максимально большой прибыли,
обеспечение ликвидности как главного фактора устойчивости и надежности
функционирования коммерческих банков – задача сложная как для самих
банков, так и для всей государственной банковской системы.

Причины этих проблем, в частности для коммерческих банков Украины,
заключаются в следующем:

1) ликвидность банка и его доходность связаны обратно пропорциональной
зависимостью – чем выше ликвидность баланса банка, тем ниже его
доходность и, наоборот, – что явно противоречит основному
предпринимательскому интересу банка – получению прибыли от своей
деятельности;

2) достижение и тем более поддержание необходимого уровня ликвидности
баланса банка представляет собой весьма сложную задачу, решение которой
требует от работников банка профессиональных знаний, умений, наличия в
сфере банковского дела соответствующих денежно-финансовых инструментов и
нормативно-законодательных актов. Все это сегодня в Украинской
банковской системе находятся в становлении и развитии.

Для государственной банковской системы в целом важность и необходимость
управления ликвидностью коммерческих банков заключается в том, чтобы
через регулирующие функции Национального банка Украины обеспечить:

– поддержание стабильности функционирования банковской системы в целом;

– исключение нарушений функциональных обязанностей в деятельности
коммерческих банков как структурных звеньев всей государственной системы
без вмешательства в их оперативную предпринимательскую деятельность;

– защиту интересов государства, вкладчиков и кредиторов;

– реализацию государственной денежно-кредитной и финансовой политики.

В плане решения проблем управления и регулирования ликвидностью
коммерческих банков позиция и роль государства имеют первостепенное
значение. Срывы в их работе из-за потери ликвидности, из-за
неплатежеспособности, банкротства, необоснованности проведения
рискованных операций нередко связаны с отсутствием четких и
профессионально грамотных нормативно-правовых инструментов и институтов.
А это снижает практическую значимость банков в скорейшем становлении и
развитии рыночных отношений в финансово кредитной системе, а также
наносит непоправимый вред всей государственной банковской системе и
экономике народного хозяйства в целом.

Проблема ликвидности коммерческих банков, регулирования со стороны
государства и управления со стороны самих банков возникла с момента
зарождения банков и существует до настоящего времени во всех странах
мира, где есть свои национальные банковские системы.

В условиях складывающихся рыночных отношений, когда главным
экономическим интересом, которому подчинена вся активная деятельность
коммерческих банков – «добывание денег на любых банковских операциях», –
соблюдение требований ликвидности баланса и способы ее поддержания в
целях обеспечения надежности и устойчивости их работы приобретают особое
значение.

2.2 Экономические нормативы регулирования деятельности коммерческого
банка

Необходимость управления ликвидностью самих банков дополняется
государственным регулированием в интересах макроэкономики. Посредством
установления центральными банками государств показателей и норм
ликвидности, контроля за соблюдением этих требований и общего надзора за
деятельностью банков государства управляют операциями коммерческих
банков, обеспечивая этим поддержание стабильности банковской системы,
защиту интересов вкладчиков и кредиторов и по существу реализуя
государственную денежно-кредитную политику.

С целью обеспечения стабильности финансового состояния коммерческих
банков, поддержания ликвидной структуры их баланса, а также защиты
интересов вкладчиков в 1997 г. Национальным банком Украины разработан
ряд экономических показателей и нормативов, регулирующих деятельность
коммерческих банков. В соответствии с Инструкцией №10 «О порядке
регулирования и анализа деятельности коммерческих банков» НБУ установил
следующие обязательные экономические нормативы регулирования
деятельности коммерческих банков:

2.2.1 Нормативы капитала коммерческого банка

2.2.1.1 Норматив минимального размера капитала банка (H1)

Капитал банка определяется уравнением:

Капитал = Активы – Обязательства

Капитал банка состоит из суммы основного капитала (капитал 1 уровня) и
дополнительного капитала (капитал 2 уровня) минус общие отчисления: при
расчете сумма дополнительного капитала не должна превышать сумму
основного капитана. Норматив минимального размера капитала
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) устанавливается для действующих банков, которые
были зарегистрированы Национальным банком Украины до 1.01.96 г.:

– в сумме, эквивалентной 2 млн. евро на 1 января 1998 года;

– в сумме, эквивалентной 3 млн. евро, на 1 января. 1999 года.

Для банков, которые были зарегистрированы Национальным банком Украины
после 1.01.96 г., а также для вновь созданных банков норматив
минимального размера капитала банка устанавливается в соответствии с
указанными размерами, начиная после первого календарного года с начала
деятельности.

Капитал «Приватбанка» составляет 7 000 000.грн. (приложение Б).

2.2.1.2 Минимальный размер уставного капитала (Н2)

Для регистрации коммерческого банка устанавливается минимальный размер
уставного капитала в сумме, эквивалентной 1 млн ЕВРО.

Действующие коммерческие банки должны были увеличить свой уставной
капитал до 1 млн ЕВРО и осуществить перерегистрацию до 1 января 1998 г.

Минимальный размер уставного капитала вновь созданного банка с участием
иностранного капитала в случае, если доля иностранного капитала в
уставном капитале банка составляет менее 50%, должна быть не меньше
суммы, эквивалентной 5 млн. евро в день подписания учредительного
договора по официальному курсу Национального банка Украины.

Если доля иностранного капитала в уставном капитале банка составляет 50%
и больше, то минимальный размер уставного капитала с участием
иностранного капитала должна быть не меньше суммы, эквивалентной 10 млн.
евро в день подписания учредительного договора по официальному курсу
Национального банка Украины.

Начиная с 1 января 1998 года в случае, если размер внесенного уставного
капитала коммерческого банка по состоянию на 31 марта каждого года будет
составлять сумму, эквивалентную менее чем 1 млн. евро по официальному
курсу национальной денежной единицы Украины, Национальный банк Украины
аннулирует разрешение на создание коммерческого банка и отзывает все
лицензии на выполнение банковских операций.

По состоянию на 31 января 2005 года сумма утвержденного,
зарегистрированного и полностью внесенного уставного фонда составляла
917 917 тысяч гривен (табл. 2.2, рис. 2.1)

Таблица 2.2. Уставной капитал

Участник2005 г.2004 г.Зарегистрированный уставный фонд%
собственностиЗарегистрированный уставный фонд% собственностиАОЗТ
Приватинтертрейдинг182 00029229 47925ООО Сентоза175 00025238 65829ООО
Вист175 00025220 30021ООО Солм168 00021229 48025Всего уставного фонда700
000100917 917100

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2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
60000000460000005c00000050000000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c00000000000000044000000c00000000000000180000000c00000000000000
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1302c3008601050000001402d9004600050000001302ae006c00050000001302ae008601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Рис. 2.1 – Динамика увеличения уставного капитала

2.2.1.3 Норматив платежеспособности (Н3)

Норматив платежеспособности банка
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) – соотношение капитала банка и суммарных активов,
взвешенных с учетом риска (по табл. 2.1).

Соотношение капитала банка и активов определяет достаточность капитала
банка для проведения активных операций с учетом рисков, характерных для
разнообразных видов банковской деятельности.

(picscalex100010009000003b6000000020017000000000005000000090200000000040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) рассчитывается по формуле:
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(2.1)

где К – капитал банка;

Ар – активы, взвешенные с учетом риска.

Платежеспособность «ПриватБанка» на 2001 г. составила:
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Минимально допустимое значение норматива платежеспособности установлено
в размере не ниже 8%, что соответствует мировым стандартам уровня
достаточности капитала.

2.2.2 Нормативы ликвидности

2.2.2.1 Норматив мгновенной ликвидности (Н4)

Рассчитывается как отношение суммы средств на корреспондентском счете и
в кассе к расчетным и текущим обязательствам по формуле:
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(2.2)

где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- средства на корреспондентском
счете;
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- средства в кассе;
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 – расчетные обязательства;
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- текущие обязательства.

Норматив мгновенной ликвидности «ПриватБанка» равен:
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Нормативное значение норматива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 должно быть не менее, чем 20%. По экономическому
содержанию данный норматив означает способность банка, выполнить свои
обязательства перед вкладчиками на текущий момент.

2.2.2.2 Норматив общей ликвидности (Н5)

Рассчитывается как отношение общих активов к общим обязательствам банка
по такой формуле:
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 (А/О)* 100%(2.3)

где А – активы банка;

О – обязательства.

Норматив общей ликвидности «ПриватБанка» составляет:

picscalex100010009000003350100000300170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02e00340131200000026060f001a00ffffffff00001000
0000c0ffffffbfffffff001300009f0300000b00000026060f000c004d61746854797065
0000c00009000000fa02000008000000000000002200040000002d010000050000001402
000208040500000013020002700917000000fb0280fe0000000000009001000000cc0402
001054696d6573204e657720526f6d616e2043797200cce7040000002d01010008000000
320a6002b51101000000250009000000320a6002750f030000003130350008000000320a
6002e20c01000000250009000000320a6002a20a030000003130300008000000320a6002
c409010000002a000b000000320a8e0316040700000036303934343732000b000000320a
6d01160407000000363338353035320008000000320a3d03870101000000350010000000
fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d010200
04000000f001010008000000320a6002800e010000003d0008000000320a6002d7020100
00003d0017000000fb0280fe0000000000009001010000cc0402001054696d6573204e65
7720526f6d616e2043797200cce7040000002d01010004000000f001020008000000320a
60023a000100000048000a00000026060f000a00ffffffff01000000000010000000fb02
1000070000000000bc02000000cc0102022253797374656d00cc040000002d0102000400
0000f0010100030000000000

Нормативное значение норматива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 должно быть не менее 100%

2.2.2.3 Норматив соотношения высоколиквидных активов к рабочим активам
банка (Н6)

Он характеризует удельный вес высоко ликвидных активов в рабочих активах
и рассчитывается по формуле:
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(2.4)

где
picscalex100010009000003970000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00280021200000026060f001a00ffffffff00001000
0000c0ffffffacffffff400200004c0200000b00000026060f000c004d61746854797065
0000900017000000fb0280fe0000000000009001010000cc0402001054696d6573204e65
7720526f6d616e2043797200cc61040000002d01000008000000320a5d02500101000000
c00008000000320a80013a0001000000c2000a00000026060f000a00ffffffff01000000
000010000000fb021000070000000000bc02000000cc0102022253797374656d00cc0400
00002d01010004000000f0010000030000000000- высоколиквидные активы;
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- рабочие активы.
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Нормативное значение норматива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 должно быть не менее 20%. По экономическому
содержанию данный норматив означает, в каких предельных пропорциях
необходимо и экономически целесообразно поддерживать соотношение высоко
ликвидных активов к рабочим активам, чтобы были одновременно обеспечены
и должный уровень ликвидности баланса, и высокий уровень доходности
банка по активным операциям.

В случае снижения минимально допустимого значения норматива H8 банк
теряет свою ликвидность, а следовательно и способность вовремя
рассчитаться по своим долговым обязательствам. При завышении минимально
допустимого значения норматива H8 банк будет нести реальные потери по
доходам от активных операций, что свидетельствует о его неспособности
управлять ликвидностью и эффективно осуществлять свою деятельность в
целом.
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Рис. 2.1 Активы, распределенные по группам риска

Наряду с группой нормативов, связанных непосредственно с оценкой
ликвидности банка
(picscalex100010009000003e6000000020017000000000005000000090200000000040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),
Национальный банк Украины в целях повышения общей финансовой
устойчивости украинской банковской системы и ее интеграции в мировое
банковское сообщество установил Инструкцией №10 целый ряд других важных
экономических нормативов, максимально приближенных к стандартам мировой
практики. Эти нормативы также сопряжены с ликвидностью, хотя и имеют
свое собственное функциональное назначение.

2.2.3 Нормативы риска

2.2.3.1 Норматив максимального размера риска на одного заемщика (Н7)

Этот показатель рассчитывается по формуле:
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(2.5)

где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 – совокупная задолженность по
ссудам, межбанковским кредитам и учтенным векселям одного заемщика и
100% суммы внебалансовых обязательств, выданных, предоставленных банком
одному заемщику.

К – собственные средства (капитал) банка.

Нормативное значение норматива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 не должно превышать 25%.

Общая сумма обязательств любого заемщика (физического или юридического
лица, в том числе банка) перед банком в результате предоставления
последним одного или нескольких кредитов не должна превышать 25%
капитала банка, т.е. 72645 тыс. грн.

Из практики известно, что выдача банком кредитов одна из наиболее
доходных операций, в то же время сопряженная с возможной
некредитоспособностью заемщика, риском невозвратности банковских ссуд в
срок, что в конечном итоге приводит к потере ликвидности
банка-кредитора, невыполнению им собственных долговых обязательств,
возможному банкротству.
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Рис. 2.3 – Структура кредитов «ПриватБанка»

2.2.3.2 Норматив «крупных» кредитных рисков (Н8)

НБУ, с целью обеспечения банками ликвидности и платежеспособности
установил Инструкцией №10 норматив «крупных» кредитных рисков
(picscalex100010009000003b6000000020017000000000005000000090200000000040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).

Максимальный размер «крупных» кредитных рисков
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) определяется как отношение совокупной величины
крупных кредитных рисков к величине капитала коммерческого банка.

Этот норматив рассчитывается по формуле:
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(2.6)

где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 – совокупный размер «крупных»
кредитов предоставляемых коммерческим банком с учетом 100% в не
балансовых обязательств банка;

К – капитал коммерческого банка.

Решение о предоставлении «крупного» кредита должно быть оформлено
соответствующим выводом кредитного комитета коммерческого банка,
утвержденного его Правлением.

Норматив «крупных» кредитов для «ПриватБанка» равен:
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Максимальное значение норматива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 не должно превышать 8-кратного размера капитала
банка. Если же сумма всех крупных «кредитов» превышает 8-кратный размер
капитала не более, чем на 50%, то требования к платежеспособности
удваиваются (16%), если же превышает более чем на 50%, то требования
утраиваются, т.е. значение показателя платежеспособности банка
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) должно быть не меньше 24%.

2.2.3.3 Норматив рефинансирования (Н9)

Важную роль в управлении ликвидностью коммерческого банка играет также
норматив рефинансирования
(picscalex100010009000003b6000000020017000000000005000000090200000000040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), направленный на защиту вкладов (депозитов)
населения. Он рассчитывается по формуле:
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(2.7)

где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 – (общая сумма полученных
коммерческим банком межбанковских ссуд);

ЦС – (общая сумма привлеченных централизованных средств);

К – капитал банка.

Максимальное значение норматива рефинансирования
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) не должно превышать 30%.
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Конечно, данный показатель до определенной степени будет сдерживать
экономическое развитие банков. Однако привлечение банками
незастрахованных депозитов в неограниченных суммах, значительно
превышающих величину собственных средств (капитала), может на практике
привести к тому, что при снижении допустимого уровня ликвидности банк
потеряет свою платежеспособность, а с ней и реальную возможность
возвратить денежные средства по вкладам своим клиентам.

С развитием украинской банковской системы, созданием
финансово-промышленных групп, банковских холдингов и других
банковско-финансовых объединений, союзов и структур актуальным в
сегодняшней банковской практике становится активное использование
собственных средств банков для приобретения долей (акций, ценных бумаг)
других юридических лиц.

2.2.3.4 Норматив инвестирования(Н10)

Согласно Инструкции №10 этот показатель банковского участия называется
нормативом инвестирования
(picscalex100010009000003b6000000020017000000000005000000090200000000040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).

Норматив инвестирования характеризует использование капитала банка для
приобретения долей (акций, ценных бумаг) акционерных товариществ,
предприятий и негосударственных долговых обязательств.

Норматив
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) устанавливается в форме процентного отношения
между размером средств, которые инвестируются и общей суммой капитала
коммерческого банка, и рассчитывается по формуле:
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(2.8)

где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 – средства коммерческого банка,
которые инвестируются на приобретение долей (акций, ценных бумаг)
акционерных товариществ, предприятий, негосударственных долговых
обязательств;

К – капитал банка;

ЦБ – ценные бумаги в портфеле банка на инвестиции;
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– вложения в ассоциированные
компании.
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Максимально допустимое значение норматива
(picscalex100010009000003b6000000020017000000000005000000090200000000040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) не должно превышать 50% размера капитала банка.

Итак, экономические нормативы являются важнейшими относительными
показателями, которые способствуют повышению надежности и эффективности
коммерческого банка.

В реальной же практике мирового банковского дела пока не решен вопрос о
всеобъемлющей формуле или наборе нормативов, которые достаточно точно и
стабильно определяли бы потребность коммерческих банков в ликвидных
средствах.

Необходимая сумма ликвидных средств отдельно взятого коммерческого
банка, как правило, зависит от колебаний общей суммы вкладов и спроса на
кредитные ресурсы. В свою очередь, эти колебания зависят от состояния
экономики той или иной страны, в которой постоянно происходят различного
рода изменения: программно-целевые, случайные, сезонные, циклические,
долговременные и др.

Примерами программно-целевых событий могут служить сегодняшняя
экономическая политика, проводимая на этапе перехода к рыночным
отношениям во всех сферах и отраслях народного хозяйства, включая
банковскую, финансовую и денежно-кредитную системы.

Случайные события – это забастовки, последствия катастроф
(землетрясения, наводнения и т.п.), военные конфликты, неординарные
экономические и политические действия.

Сезонные изменения, как правило, связаны с сельскохозяйственными
работами. Коммерческие банки, расположенные в сельской местности,
сталкиваются с ростом вкладов осенью после урожая и с большим спросом на
кредитные ресурсы весной.

Циклические изменения в большей степени обусловлены подъемом либо спадом
деловой активности товаропроизводителей и предпринимателей в
экономических процессах страны. Эта изменения наиболее характерны для
периодов экономических кризисов или фаз подъема и экономического
процветания.

Долговременные колебания могут охватывать несколько экономических циклов
и являются результатами таких факторов, как сдвиги в потреблении,
сбережениях, инвестиционных процессах, численности населения и его
трудовой занятости, научно-техническом уровне производства и т.п.

Очевидно, что на уровень банковской ликвидности влияют многие
экономические и другие факторы, в связи с чем вопросы расчетов,
планирования и управления становятся важнейшими направлениями в
деятельности коммерческих банков.

Завершая рассмотрение данного вопроса можно сделать вывод, что на
динамику изменений ликвидности коммерческих банков влияют три основных
фактора:

– приобретение или утрата средств в связи с увеличением или уменьшением
вкладов;

– то же, но в связи с ростом или сокращением кредитов и (или)
инвестиций;

– увеличение или уменьшение величины обязательных резервов вследствие
роста или сокращения вкладов.

2.3 Управление ликвидностью коммерческого банка

Исходя из этих трех основополагающих факторов, формирующих политику,
стратегию и повседневную деятельность коммерческих банков, исторически
зарождались, развивались и совершенствовались теория и практика
управления банковской ликвидностью.

Теория управления ликвидностью появилась и развивалась практически
одновременно с организацией и развитием коммерческих банков.
Первоначально вопрос о банковской ликвидности имел два теоретических
подхода. Первый подход был основан на том, что структура активов банка
по срокам должна точно соответствовать структуре его пассивов, а это
практически исключало возможность проведения коммерческими банками
активной политики управления своей ликвидностью. На данной теоретической
основе было выработано, так называемое, золотое банковское правило,
состоящее в том, что величина и сроки финансовых требований банка должны
соответствовать размерам и срокам его обязательств.

Второй подход базировался на реальном несоответствии структур активов и
пассивов баланса, поскольку ни один даже самый мощный коммерческий банк
не застрахован от последствий финансово-кредитных явлений, постоянно
происходящих в социально-экономических системах: экономических кризисов,
банкротств, неплатежей по ссудам, конъюнктуры спроса и предложения на
рынках ссудных капиталов денежных средств, ценных бумаг и других
проявлений несбалансированности рыночных отношений. Такие явления
наиболее характерны для стран, осуществляющих переход от
планово-централизованной к рыночной экономике.

Все вышеуказанные и другие сложности, реально возникавшие на различных
этапах развития или преобразования социально-экономических систем,
требовали постоянной заботы банковского руководства о поддержании
определенного уровня ликвидности. Обеспечение этого базисного условия
устойчивой деятельности коммерческих банков вызвало объективную
необходимость решить проблему ликвидности через возможность управления
структурой баланса, т.е. возможность управления активами и пассивами
коммерческих банков.

В процессе усложнения и совершенствования мировой практики банковского
дела второй подход к вопросу ликвидности коммерческих банков получил
дальнейшее развитие по двум основным направлениям: теории управления
активами и теории управления пассивами коммерческих банков.

В настоящее время теория управления активами основывается на трех
методологических утверждениях.

Первое – коммерческий банк может сохранить ликвидность, если его активы
размещены в краткосрочных ссудах и своевременно погашаются. Хотя данное
утверждение и находит отражение в банковских законодательствах некоторых
западных стран, оно обеспечивает ликвидность лишь при нормальном
экономическом развитии, но не в условиях экономического спада, когда
ликвидные средства особенно необходимы. К тому же это утверждение не
учитывает потребностей кредитных ресурсов в условиях развивающейся
экономики, а также стабильности или нестабильности банковских вкладов.

Второе – коммерческий банк может быть ликвидным, если его активы можно
переместить или продать другим кредиторам или инвесторам за наличные
деньги. На практике источниками ликвидных ресурсов выступают отдельные
виды ценных бумаг, которые можно Легко превратить в наличные деньги.
Такие ценные бумаги получили в мировой практике банковского дела
название «резервы второй очереди».

Третье – ликвидность коммерческого банка можно планировать, если в
основу графика платежей в погашение кредитов положить будущие доходы
заемщика. Следовательно, на банковскую ликвидность можно воздействовать,
изменяя структуру сроков погашения кредитов и инвестиций. На практике
данное утверждение вошло в основу формирования и управления портфелем
инвестиций с помощью эффекта ступенчатости. Метод проведения
коммерческими банками инвестиционной политики, использующей эффект
ступенчатости доходов и расходов получил название диверсификация.

А теория управления пассивами, развивающая и дополняющая политику
управления ликвидностью коммерческих банков, основывается на следующих
двух утверждениях.

Первое – коммерческий банк может решать проблемы ликвидности путем
привлечения дополнительных денежных средств, покупая их на рынке
капитала. Реально данное утверждение нашло практическое воплощение в
западных странах,

Второе – коммерческий банк может обеспечить свою ликвидность, прибегая к
обширным займам денежных средств в федеральной резервной системе либо у
банков – корреспондентов, а также к займам, получаемым на рынке
евровалют.

Реализуя на практике теоретические положения, касающиеся ликвидности
коммерческих банков, управляя активами и пассивами, банки вынуждены
постоянно балансировать между прибыльностью, ликвидностью и
платежеспособностью.

Банки, оказавшиеся не в состоянии обеспечить ликвидность в некоторых
непредвиденных ситуациях, могут оказаться неплатежеспособными, а в
итоге, возможно, и банкротами. Вот почему вопрос управления ликвидностью
коммерческих банков имеет принципиальное значение и занимает в практике
мирового банковского дела одно из первостепенных мест.

Потребность в ликвидности определяется характером банковских ссуд и
депозитов /вкладов/, выбор ссуд зависит в такой же мере от величины
денежных средств. В свою очередь, привлечение депозитов зависит от
доступных банку инвестиционных возможностей. Все эти факторы
взаимосвязаны и объединены единой стратегией управления ликвидностью
коммерческих банков, получившей название управление портфелем
коммерческого банка (управление портфелем – это управление активами и
пассивами банка, преследующее достижение целей прибыльности,
платежеспособности и ликвидности).

Если же коммерческий банк систематически не придерживается экономических
нормативов и других правил банковского законодательства, в частности
вследствие своей убыточной деятельности, что угрожает интересам его
вкладчиков и кредиторов, такой банк может быть ликвидирован.
Деятельность коммерческого банка прекращается на основании:

– решения высшего органа управления банком;

– отзыва Национальным (регистрационным) банком лицензии на проведение
банковских операций.

На этот период создается ликвидационная комиссия, к которой полностью
переходят полномочия по управлению банковскими делами.

Комиссия осуществляет такие мероприятия по ликвидации банка:

– опубликовывает объявление о ликвидации банка в прессе;

– оценивает активы и пассивы банка по балансу, а также материальные
ценности, которые были переданы банку под кредитное обеспечение;

– выявляет должников банка и устанавливает порядок досрочного
возвращения банковских кредитов;

– выявляет кредиторов банка и рассчитывается с ними.

Ликвидационной комиссии открывается специальный счет, на который идет
зачисление средств, поступивших в банк, а также перечисляются остатки
средств с корреспондентского счета и счетов филиалов. С этого счета
удовлетворяются претензии кредиторов.

После расчетов с бюджетом, по оплате труда банковских работников и
погашения обязательств перед кредиторами, остаток, включая выручку от
распродажи банковского имущества, ликвидационная комиссия распределяет
между участниками пропорционально их паевому взносу.

При осуществлении активных и пассивных операций банк стремился к
достижению их сбалансированности по срокам. Поддержание необходимого
объема ликвидных средств (корреспондентский счет в НБУ, касса,
корреспондентские счета в других банках) было сдерживающим фактором
роста прибыли, однако позволило банку создать значительный запас
ликвидности для обеспечения стабильного режима проведения платежей
клиентов, возврата средств по обязательствам Банка, а также строго
соблюдения установленных Национальным банком нормативных требований.

Объем высоколиквидных средств в течение года вырос на 14 миллионов
гривен и составил на конец года 681 миллиона гривен, в том числе
значительно увеличились средства банка на корреспондентском счете в НБУ:
с 209 до 244 миллионов гривен. Увеличение объема высоколиквидных средств
в течение прошедшего года обусловлено последовательной политикой Банка
по укреплению ликвидности, а также возросшими требованиями Национального
банка Украины и внесенными им изменениями в методику расчета нормы
обязательного резервирования. Таким образом, норма обязательного резерва
с начала года возросла в 1,8 раза. В течение года Банком приобретались
депозитные сертификаты НБУ: их объем колебался в пределах 40–60
миллионов гривен.

Одним из факторов, обеспечившим удержание ликвидности на высоком уровне
в 2004 г. было сохранение объема привлеченных срочных вкладов физических
лиц в пределах 775 – 794 миллионов гривен, что составило 13–14% от всех
обязательств, а так же рост срочных депозитов юридических лиц со 825 до
1 485 миллионов гривен, являющихся диверсифицированными источниками
ресурсов.

Собственные средства банка в течение 2004 года выросли значительно по
сравнению с концом 2003 года (с 454 812 до 744 649 тысяч гривен).

Составляющими этого роста явились увеличение оплаченного уставного фонда
на 28 000 тысяч гривен и полученная в течение года прибыль.

Коэффициент адекватности капитала продолжал расти, так в 1997 году он
составлял 8,1%, в 1998 – 8,3%, в 1999 – 9,22%, а по итогам 2004 года
составил 10,22%. Такой последовательный рост отражает, несмотря на
нестабильную экономическую ситуацию, повышение надёжности банка.

Кроме обеспечения надежности, банк, как и любое другое предприятие,
должен стремится к достижению доходности банковского дела. Так чистая
прибыль увеличилась на 20 733 419,55 гривен и составила на начало
2005 г. 25 033 364,16 гривен. Увеличение произошло, в основном из-за
повышения доходов от валютных, кредитных операций и операций с ценными
бумагами.

В настоящее время рынок ценных бумаг в Украине начинает, развивается, в
то время как в современной кредитной системе ряда развитых стран
вложение в ценные бумаги получили широкое распространение.

Главными целями банка как инвестора являются доходность и безопасность
вложений. Поэтому эксперты банка должны определится с этими
показателями.

Безопасность обычно достигается в ущерб доходности и росту вложений.
Наиболее безопасными считаются вложения в облигации государственных
займов, так как они обеспечиваются экономическим весом и
платежеспособностью государства

3. Выбор оптимального портфеля ценных бумаг

3.1 Банковские инвестиции, их сущность и цели

В современной кредитной системе ряда развитых стран мира широкое
распространение получили инвестиционные банки. К их выделению привело
разделение труда и специализация в кредитной сфере в большинстве стран
Запада прежде всего в США, Японии, Англии, Франции. Главная задача
инвестиционных банков – это мобилизация долгосрочного ссудного капитала
и предоставление его заемщикам посредством выпуска и размещения акций,
облигаций и других видов заемных обязательств.

Учитывая, что у нас в Украине сегодня еще не получили широкого
распространения специализированные инвестиционные банки, активную
инвестиционную деятельность проводят все коммерческие банки.

Правовые, экономические и социальные условия инвестиционной
деятельности; равную защиту прав, интересов и имущества субъектов
инвестиционной деятельности Украины независимо от форм собственности
определяет и обеспечивает закон Украины «Об инвестиционной
деятельности». Он определяет инвестиции как все виды имущественных и
интеллектуальных ценностей, вкладываемых в объекты предпринимательской и
других видов деятельности, в результате которой образуется прибыль
(доход) или достигается социальный эффект.

Инвестициями в банковской практике являются средства банков, вложенные в
ценные бумаги предприятий, организаций, учреждений различных форм
собственности на продолжительный период времени.

Вся сумма ценных бумаг, купленных банком в ходе активных операций,
составляет его инвестиционный портфель. В эту сумму входят все
обязательства, которые обращаются на рынке в виде акций, облигаций и
векселей.

Ценные бумаги, как правило, являются объектом банковских инвестиций,
если они:

– обращаются на рынке ценных бумаг;

– служат долговыми обязательствами.

Главными целями банков как инвесторов являются, прежде всего,
обеспечение сбережения средств, т.е. безопасность вложений, а также
доходность банковских инвестиций, их ликвидность и рост.

Ряд западных ученых относит к инвестиционным целям диверсификацию
портфеля (расширение его состава или номенклатуры), хотя она выступает,
скорее всего, методом регулирования инвестиционной деятельности банка
для достижения поставленных целей.

Неуязвимость банковских вложений от потрясений на фондовом рынке и
гарантированную стабильность в получении дохода обеспечивает
безопасность. Она обычно достигается в ущерб доходности и росту
вложений. Наиболее безопасными считаются вложения в облигации
государственных займов, так как они обеспечиваются экономическим весом и
платежеспособностью государства.

Если же банк, прежде всего, заинтересован в доходности акций или
облигаций, т.е. в получении максимально возможных дивидендов, то ему
придется пожертвовать безопасностью, поскольку считается, что наиболее
доходными являются ценные бумаги акционерных обществ с низким
инвестиционным рейтингом. Вместе с тем, это не означает, что чем менее
надежны ценные бумаги, тем они доходнее, так как доходность зависит от
различных факторов. Оптимальное сочетание безопасности и доходности
осуществляется путем тщательной и периодической проверки и подбора
ценных бумаг.

Ликвидность ценных бумаг означает достаточно быстрое и, как правило, без
потерь для их держателей обращение этих ценных бумаг в деньги. Она не
всегда связана с другими инвестиционными целями.

Ликвидность, прежде всего, означает, что при определенной цене всегда
найдутся покупатели, которые приобретут данные ценные бумаги.

Увеличивать свои вложения могут только владельцы акций. Рост капитала
гарантируется в основном за счет увеличения числа обыкновенных акций
акционерных обществ, работающих в передовых отраслях народного
хозяйства. Такие акции, хотя и приносят низкий уровень дивидендов, но,
как правило, обеспечивают быстрое удорожание капитала.

В связи с этим, необходимо подчеркнуть, что, так как ни одна бумага не
отвечает одновременно всем инвестиционным целям, то необходим компромисс
между целями инвестора. Например, если ценные бумаги надежны, то
доходность их будет низкой, потому что инвесторы, предпочитающие
надежность, будут покупать их по более высокой, по сравнению с
номинальной, цене, что соответственно снизит доходность.

Такое же положение сохраняется и при выборе других целей. Например, если
прогнозы указывают на рост капитала, то, как правило, на такие ценные
бумаги возникает повышенный спрос, что приводит к росту их цены и
снижению доходности.

Конечно, коммерческие банки уделяют серьезное внимание качеству ценных
бумаг сразу при их покупке, однако надежного, с гарантией метода
определения защиты вложенных средств на долгий период нет, так как
нередко возникают ситуации, которые нельзя заранее спрогнозировать.

Поэтому очень важно, когда определены цели инвестирования, выбрать
именно те ценные бумаги, которые соответствуют этим целям.

В соответствии с законом Украины «О ценных бумагах и фондовой бирже»
основными ценными бумагами являются акции и облигации, остальные
производные от них.

Акция – это ценная бумага без установленного срока обращения,
свидетельствующая о внесении известного пая в капитал акционерного
общества, подтверждающая членство в этом обществе и право ее владельца
на получение части прибыли в виде дивиденда, а также на участие в
распределении имущества при ликвидации акционерного общества.

Таким образом, если банк участвует в капитале акционерного общества, то
это позволяет ему изыскать дивиденды на вложенный капитал, а также быть
полноправным совладельцем данного общества.

Вложения в облигации (свидетельства о внесении их собственником денежных
средств и подтверждающие обязательство отчисления ему номинальной
стоимости этой ценной бумаги в предвиденный в ней срок с выплатой
фиксированного процента) являются менее рискованными по сравнению с
вложениями в акции.

Государственные долговые обязательства считаются самыми надежными и
безопасными на мировом фондовом рынке. В Украине и сегодня еще трудно
гарантировать ликвидность правительственных займов из-за экономической
нестабильности и хронического дефицита государственного бюджета.

В связи с принятием инструкции №10 «О порядке регулирования и анализе
деятельности коммерческих банков» общая сумма вложений не должна
превышать 50% размера капитала банка, что способствовало активизации
инвестиционной деятельности банков. Она осуществляется работниками
банковского отдела инвестиций. Функция инвестирования требует
систематического анализа риска приобретаемых ценных бумаг, оценку
качества этих бумаг, определение способности банка осуществлять
инвестиции. Для этого необходимо тщательное, непрерывное и
квалифицированное наблюдение и изучение рынка ценных бумаг.

После проведения тщательного исследования рынка ценных бумаг отделом
инвестиций были выбраны пять предприятий энергетического комплекса
(Центрэнерго, Днепрэнерго, Киевэнерго, Укрнафта и Турбоатом).

Были выбраны наиболее приемлемые для банка показатели доходности и риска
ценных бумаг (риск – 0,71%, доходность – 8%). Специалисты столкнулись с
проблемой выбора оптимального портфеля ценных бумаг из акций
вышеуказанных предприятий.

3.2 Постановка задачи об оптимальном портфеле

Рассмотрим общую задачу распределения капитала, который участник рынка
хочет потратить на покупку ценных бумаг. Цель инвестора – вложить деньги
так, чтобы сохранить свой капитал, а по возможности и увеличить его.

Набор ценных бумаг, находящийся у участника рынка, называется портфелем.
Стоимость портфеля – это суммарная стоимость всех составляющих бумаг.

Пустьpicscalex1000100090000039500000002001500000000000500000009020000000
00400000002010100050000000102ffffff00040000002e0118000500000031020100000
0050000000b0200000000050000000c026002a0011200000026060f001a00ffffffff000
010000000c0ffffffa6ffffff60010000060200000b00000026060f000c004d617468547
970650000700015000000fb0280fe0000000000009001010000000402001054696d65732
04e657720526f6d616e0000a3040000002d01000008000000320a1102f60001000000690
008000000320a80014c000100000078000a00000026060f000a00ffffffff01000000000
010000000fb021000070000000000bc02000000cc0102022253797374656d00cc0400000
02d01010004000000f0010000030000000000 – доля капитала, потраченная на
покупку ценных бумаг i – ого вида. Весь выделенный капитал принимается
за единицу. Пусть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- доходность в процентах i – ого вида в
расчете на одну денежную единицу.

Найдем доходность всего портфеля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. С одной стороны, через год капитал
портфеля будет равен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, с другой – стоимость бумаг i – ого вида увеличится
с х до
picscalex100010009000003d50000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600280051200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffff40050000060200000b00000026060f000c004d61746854797065
0000700015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000086040000002d01000008000000320a1102cc040100000069000800
0000320a8001220401000000780008000000320a1102800301000000690008000000320a
8001ac0201000000640008000000320a1102f60001000000690008000000320a80014c00
01000000780010000000fb0280fe0000000000009001000000020002001053796d626f6c
0002040000002d01010004000000f001000008000000320a8001b601010000002b000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01000004000000f0010100030000000000
, так что суммарная стоимость портфеля будет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. Приравнивая оба выражения для стоимости
портфеля, получаем:
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(3.1)

Итак, задача увеличения капитала портфеля эквивалентна аналогичной
задаче о доходности портфеля, выраженной через доходности бумаг и их
доли формулой (3.1).

Как правило, доходность колеблется во времени, так что будем считать ее
случайной величиной. Пусть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,picscalex100010009000003ad0000000200150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- средняя ожидаемая доходность и среднеквадратическое
отклонение (СКО) этой случайной доходности,
т.е.picscalex1000100090000030d010000020015000000000005000000090200000000
0400000002010100050000000102ffffff00040000002e01180005000000310201000000
050000000b0200000000050000000c026002e0061200000026060f001a00ffffffff0000
10000000c0ffffffa6ffffffa0060000060200000b00000026060f000c004d6174685479
70650000700010000000fb0283fde300000000009001000000020002001053796d626f6c
0002040000002d01000008000000320a7c017a04010000005b0010000000fb0283fde300
000000009001000000020002001053796d626f6c0002040000002d01010004000000f001
000008000000320a7c015706010000005d0015000000fb0280fe00000000000090010100
00000402001054696d6573204e657720526f6d616e000086040000002d01000004000000
f001010008000000320a1102aa0501000000690008000000320a8001d604010000006400
08000000320a80010003010000004d0008000000320a11024a0101000000690008000000
320a80013a00010000006d0010000000fb0280fe00000000000090010000000200020010
53796d626f6c0002040000002d01010004000000f001000008000000320a80010a020100
00003d000a00000026060f000a00ffffffff01000000000010000000fb02100007000000
0000bc02000000cc0102022253797374656d00cc040000002d01000004000000f0010100
030000000000- математическое ожидание доходности и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, где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- дисперсия i – ой доходности. Будем
называть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 соответственно эффективностью и риском i –
ой ценной бумаги. Обозначим через
picscalex100010009000003950000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00220021200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffe0010000660200000b00000026060f000c004d61746854797065
0000a00015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000086040000002d01000008000000320a1102f70002000000696a0800
0000320a800116000100000056000a00000026060f000a00ffffffff0100000000001000
0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
010004000000f0010000030000000000ковариацию доходностей ценных бумаг i –
ого и j – ого видов.

Так как доходность составляющих портфель ценных бумаг случайна, то и
доходность портфеля
естьpicscalex10001000900000333020000020015000000000005000000090200000000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, обозначим его через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. Дисперсия доходности портфеля есть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. Так же, как и для
ценных бумаг назовем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 соответственно эффективностью и риском портфеля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.

Каждый владелец портфеля ценных бумаг сталкивается с дилеммой: хочется
иметь эффективность больше, а риск меньше. Однако необходимо сделать
определенный выбор между эффективностью и риском.

Пусть имеется данные о доходности акций 5 предприятий за определенный
период (табл. 3.1)

Таблица 3.1. Данные о доходности акций 5 предприятий за период с 3.01.01
по 21.02.01.

ПериодЦентрэнергоДнепрэнергоКиевэнергоУкрнафтаТурбоатом03.01–10.01765681
1.01–17.018675918.01–24.0110767725.01–01.0210455601.02–07.028446608.02–1
4.027657714.02–21.02977793.3 Оптимальный портфель ценных бумаг Марковица

3.3.1 Портфель Марковица минимального риска

Рассмотрим сначала математическую формализацию задачи формирования
оптимального портфеля, которую предложил американский экономист
Г. Марковиц в 1952 г., за что позднее получил Нобелевскую премию:

Найдем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, минимизирующие вариации портфеля
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(3.2)

при условии, что обеспечивается заданное значение эффективности портфеля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, т.е.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.

Поскольку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- доли, то в сумме они должны составлять
единицу:picscalex100010009000003ea00000002001500000000000500000009020000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.

В такой постановке минимизация вариации равносильна минимизации риска
портфеля, поэтому задача Марковица может быть сформулирована следующим
образом.

Найти
picscalex100010009000003950000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c026002a0011200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffff60010000060200000b00000026060f000c004d61746854797065
0000700015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e0000a3040000002d01000008000000320a1102f6000100000069000800
0000320a80014c000100000078000a00000026060f000a00ffffffff0100000000001000
0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
010004000000f0010000030000000000, минимизирующие риск портфеля:
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(3.3)

где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- матрица ковариацию.
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при условии, что учитываются следующие ограничения:
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;
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(3.4)picscalex1000100090000032101000003001500000000000500000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.

Решая задачу с помощью табличного процессора Excel и его надстройки
Поиск решения, получим (рис. 3.1):
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0,739

х1 =0,58; х2=0; х3=0; х4=0,01; х5=0,41.

picscalex100010009000003b016000007009e0d000000009e0d000026060f00321b574d
4643010000000000010019480000000001000000101b000000000000101b000001000000
6c000000050000000500000045010000a4000000000000000000000068280000a1140000
20454d4600000100101b0000580100000500000000000000000000000000000000040000
0003000040010000f000000000000000000000000000000000e2040080a9030046000000
2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
60000000460000005c00000050000000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c00000000000000044000000c00000000000000180000000c00000000000000
190000000c000000ffffff00140000000c0000000d000000120000000c00000002000000
2100000008000000220000000c000000ffffffff2100000008000000220000000c000000
ffffffff0a0000001000000000000000000000002100000008000000190000000c000000
ffffff00180000000c00000000000000220000000c000000ffffffff2100000008000000
190000000c000000ffffff00180000000c000000000000001e0000001800000000000000
000000004b010000a9000000260000001c00000001000000000000000000000000000000
00000000250000000c0000000100000027000000180000000200000000000000ffffff00
00000000250000000c00000002000000180000000c000000ffffff00190000000c000000
00000000140000000c0000000d000000120000000c000000020000002b00000018000000
050000000500000045010000a4000000250000000c00000007000080250000000c000000
00000080220000000c000000ffffffff2100000008000000250000000c00000002000000
250000000c00000001000000190000000c00000000000000180000000c000000ffffff00
1e0000001800000000000000000000004b010000a9000000250000000c00000007000080
250000000c00000000000080220000000c000000ffffffff210000000800000025000000
0c00000002000000250000000c00000001000000190000000c0000000000000018000000
0c000000ffffff001e00000018000000050000000500000046010000a400000027000000
1800000003000000000000003300330000000000250000000c0000000300000028000000
0c00000002000000260000001c0000000200000000000000010000000000000000000000
250000000c00000002000000280000000c00000001000000180000000c00000033003300
190000000c00000033003300140000000c0000000d000000120000000c00000002000000
56000000e8000000470000004700000073000000760000003300000073005c0070005c00
6c005b0069005a006600590063005900600058005e0057005c0057005900560057005500
5400540052005300510052004f0051004e0050004c004f004b004e004a004d0049004c00
48004c0047004a0047004900470048004700470047006100470062004700630047006400
48006600490066004a0067004b0068004c0069004e006a004f006b0051006c0052006d00
54006e0057006f00590070005c0071005e00710060007200630073006600730069007400
6c007500700076007300760073005c002700000018000000010000000000000066006600
00000000250000000c00000001000000280000000c00000003000000180000000c000000
66006600190000000c000000ffffff00560000000c010000470000002f000000a4000000
5c0000003c00000073005c006f005b006c005b0068005a0066005900620059005f005800
5d0057005a005600580055005500540052005300510052004f0051004e0050004c004f00
4a004e004a004d0048004c0048004b0047004a0047004900470048004700460047004600
4700440048004300490042004a0041004b0040004c003f004e003e0050003d0052003c00
53003b0056003a00580039005b0038005e00370060003700630036006600350069003400
6d0033007000330074003200770032007b0031008000310083003000870030008a003000
8f002f0094002f0097002f009c002f009f002f00a4002f00a400470073005c0026000000
1c0000000300000000000000000000000000000000000000250000000c00000003000000
280000000c00000002000000270000001800000002000000000000006680800000000000
250000000c00000002000000280000000c00000001000000260000001c00000001000000
00000000010000000000000000000000250000000c00000001000000280000000c000000
03000000180000000c00000066808000190000000c000000668080005600000040000000
730000005c00000077000000770000000900000077005d0075005c0074005c0073005c00
7300760074007600750076007700770077005d0027000000180000000300000000000000
ccffff0000000000250000000c00000003000000280000000c0000000200000018000000
0c000000ccffff00190000000c000000ffffff0056000000340000007300000047000000
a40000005d0000000600000077005d0075005c0074005c0073005c00a400470077005d00
260000001c0000000200000000000000000000000000000000000000250000000c000000
02000000280000000c00000001000000260000001c000000010000000000000001000000
0000000000000000250000000c00000001000000280000000c0000000200000027000000
180000000200000000000000ffffcc0000000000250000000c0000000200000028000000
0c00000003000000260000001c0000000300000000000000000000000000000000000000
250000000c00000003000000280000000c000000010000001b000000100000006b000000
78000000120000000c000000010000003600000010000000710000007800000036000000
100000007600000076000000260000001c00000001000000000000000100000000000000
00000000250000000c00000001000000280000000c000000030000002700000018000000
03000000000000009933660000000000250000000c00000003000000280000000c000000
02000000260000001c000000020000000000000000000000000000000000000025000000
0c00000002000000280000000c000000010000001b000000100000006b0000008f000000
3600000010000000710000008f0000003600000010000000760000007600000027000000
1800000001000000000000004d4d800000000000250000000c0000000100000028000000
0c00000003000000260000001c0000000300000000000000010000000000000000000000
250000000c00000003000000280000000c00000002000000180000000c0000004d4d8000
190000000c0000004d4d8000120000000c00000002000000560000009001000077000000
47000000020100007a0000005d00000002014700020149000101490001014b0000014c00
ff004d00fe004e00fd004f00fc005000fa005100f8005200f6005300f4005400f2005500
ef005600ec005700ea005800e6005900e3005900e0005a00dd005b00d9005c00d6005c00
d2005d00cf005d00ca005e00c6005e00c3005e00be005f00b9005f00b6005f00b1006000
ac006000a9006000a40060009f0060009c0060009700600094005f008f005f008a005f00
87005f0083005e007e005e007b005d0077005d00770077007b0077007e00780083007800
870079008a0079008f0079009400790097007a009c007a009f007a00a4007a00a9007a00
ac007a00b1007a00b6007900b9007900be007900c3007800c6007800ca007800cf007700
d2007700d6007600d9007600dd007500e0007400e3007300e6007300ea007200ec007100
ef007000f2006f00f4006e00f6006d00f8006c00fa006b00fc006a00fd006900fe006800
ff0067000001660001016500010163000201630002016100020147002700000018000000
02000000000000009999ff0000000000250000000c00000002000000280000000c000000
01000000180000000c0000009999ff00190000000c000000ffffff00560000006c010000
770000002f000000020100006000000054000000a4002f00a9002f00ac002f00b1002f00
b4002f00b9002f00bc003000c1003000c6003000c9003100cd003100d0003200d4003200
d9003300db003300df003400e2003500e5003600e8003600eb003700ee003800f0003900
f3003a00f4003b00f7003c00f9003d00fa003e00fc003f00fd004000ff004100ff004200
0001430001014400010145000201460002014700020149000101490001014b0000014c00
ff004d00fe004e00fd004f00fc005000fa005100f8005200f6005300f4005400f2005500
f0005600ed005700ea005800e8005800e4005900e2005a00de005b00db005b00d7005c00
d3005c00d0005d00cc005d00c9005e00c4005e00c0005f00bc005f00b8005f00b4005f00
b0006000ac006000a8006000a30060009f0060009a0060009700600092005f008e005f00
8a005f0086005e0083005e007e005e007b005d0077005d00a4004700a4002f0026000000
1c0000000100000000000000000000000000000000000000250000000c00000001000000
280000000c00000003000000250000000c00000007000080250000000c00000000000080
220000000c000000ffffffff2100000008000000250000000c0000000200000025000000
0c00000001000000190000000c000000ffffff00180000000c0000009999ff001e000000
1800000000000000000000004b010000a9000000250000000c0000000700008025000000
0c00000000000080220000000c000000ffffffff2100000008000000250000000c000000
02000000250000000c00000001000000190000000c000000ffffff00180000000c000000
9999ff001e0000001800000000000000000000004b010000a90000005200000070010000
03000000f5ffffff00000000000000000000000090010000000000cc0000000041007200
690061006c00200043007900720000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000f0000000000000
00000000000000001e000000b3000000000000004b00000002000000a8eb1300bcb71f02
78e4f9024492883028ec1300f1a5093050b71f02200000007f0000008020000001000000
000000006ced1300782cfa02f89edea728ec1300782cfa02000000006ced130090eb1300
05a50930000000000000000058d8f90200000000c8000000000000002e0000000c000000
4d0000004a0000001e000000b30000000000000050b71f0278ec13000b0000006ced1300
0000023026ec13006eed1300090000000900000050b71f02be8102300900410072006900
61006c002000430079007200000000000000000000000000000000006476000800000000
250000000c00000003000000250000000c0000000d000080250000000c00000003000000
250000000c0000000d000080250000000c00000003000000250000000c00000007000080
250000000c00000000000080250000000c0000000d000080220000000c000000ffffffff
2100000008000000250000000c00000003000000250000000c0000000200000025000000
0c00000001000000190000000c000000ffffff00180000000c0000009999ff001e000000
1800000002010000600000001c01000075000000180000000c0000000000000014000000
0c0000000d000000120000000c0000000100000054000000600000000401000063000000
1901000070000000010000000000fa410000fa410401000063000000030000004c000000
000000000000000000000000ffffffffffffffff54000000350038002500000006000000
060000000a000000250000000c0000000d000080250000000c0000000300000025000000
0c00000007000080250000000c00000000000080250000000c0000000d00008022000000
0c000000ffffffff2100000008000000250000000c00000003000000250000000c000000
02000000250000000c00000001000000190000000c000000ffffff00180000000c000000
000000001e0000001800000000000000000000004b010000a9000000250000000c000000
0d000080250000000c00000003000000250000000c0000000d000080250000000c000000
03000000250000000c00000007000080250000000c00000000000080250000000c000000
0d000080220000000c000000ffffffff2100000008000000250000000c00000003000000
250000000c00000002000000250000000c00000001000000190000000c000000ffffff00
180000000c000000000000001e0000001800000058000000850000006c0000009a000000
140000000c0000000d000000120000000c0000000100000054000000580000005a000000
880000006900000095000000010000000000fa410000fa415a0000008800000002000000
4c000000000000000000000000000000ffffffffffffffff500000003000250006000000
0a000000250000000c0000000d000080250000000c00000003000000250000000c000000
07000080250000000c00000000000080250000000c0000000d000080220000000c000000
ffffffff2100000008000000250000000c00000003000000250000000c00000002000000
250000000c00000001000000190000000c000000ffffff00180000000c00000000000000
1e0000001800000000000000000000004b010000a9000000250000000c0000000d000080
250000000c00000003000000250000000c0000000d000080250000000c00000003000000
250000000c00000007000080250000000c00000000000080250000000c0000000d000080
220000000c000000ffffffff2100000008000000250000000c0000000300000025000000
0c00000002000000250000000c00000001000000190000000c000000ffffff0018000000
0c000000000000001e00000018000000580000006e0000006c0000008300000014000000
0c0000000d000000120000000c0000000100000054000000580000005a00000071000000
690000007e000000010000000000fa410000fa415a00000071000000020000004c000000
000000000000000000000000ffffffffffffffff5000000030002500060000000a000000
250000000c0000000d000080250000000c00000003000000250000000c00000007000080
250000000c00000000000080250000000c0000000d000080220000000c000000ffffffff
2100000008000000250000000c00000003000000250000000c0000000200000025000000
0c00000001000000190000000c000000ffffff00180000000c000000000000001e000000
1800000000000000000000004b010000a9000000250000000c0000000d00008025000000
0c00000003000000250000000c0000000d000080250000000c0000000300000025000000
0c00000007000080250000000c00000000000080250000000c0000000d00008022000000
0c000000ffffffff2100000008000000250000000c00000003000000250000000c000000
02000000250000000c00000001000000190000000c000000ffffff00180000000c000000
000000001e000000180000002d000000330000004700000048000000140000000c000000
0d000000120000000c0000000100000054000000600000002f0000003600000044000000
43000000010000000000fa410000fa412f00000036000000030000004c00000000000000
0000000000000000ffffffffffffffff5400000034003100250000000600000006000000
0a000000250000000c0000000d000080250000000c00000003000000250000000c000000
07000080250000000c00000000000080250000000c0000000d000080220000000c000000
ffffffff2100000008000000250000000c00000003000000250000000c00000002000000
250000000c00000001000000190000000c000000ffffff00180000000c00000000000000
1e0000001800000000000000000000004b010000a9000000250000000c0000000d000080
250000000c00000003000000250000000c0000000d000080250000000c00000003000000
250000000c00000007000080250000000c00000000000080250000000c0000000d000080
220000000c000000ffffffff2100000008000000250000000c0000000300000025000000
0c00000002000000250000000c00000001000000190000000c000000ffffff0018000000
0c000000000000001e0000001800000068000000780000007c0000008d00000014000000
0c0000000d000000120000000c0000000100000054000000580000006a0000007b000000
7900000088000000010000000000fa410000fa416a0000007b000000020000004c000000
000000000000000000000000ffffffffffffffff5000000031002500060000000a000000
250000000c0000000d000080250000000c00000003000000250000000c00000007000080
250000000c00000000000080250000000c0000000d000080220000000c000000ffffffff
2100000008000000250000000c00000003000000250000000c0000000200000025000000
0c00000001000000190000000c000000ffffff00180000000c000000000000001e000000
1800000000000000000000004b010000a9000000250000000c0000000700008025000000
0c00000000000080250000000c0000000d000080220000000c000000ffffffff21000000
08000000250000000c00000003000000250000000c00000002000000250000000c000000
01000000190000000c000000ffffff00180000000c000000000000001e00000018000000
00000000000000004b010000a9000000260000001c000000040000000000000000000000
0000000000000000250000000c00000004000000280000000c0000000100000025000000
0c00000005000080280000000c00000002000000180000000c000000ffffff0019000000
0c00000000000000140000000c0000000d000000120000000c000000020000002b000000
18000000050000000500000045010000a4000000250000000c0000000400008025000000
0c00000007000080280000000c00000004000000250000000c0000000d00008022000000
0c000000ffffffff09000000100000004b010000a9000000210000000800000019000000
0c00000000000000180000000c000000ffffff00220000000c000000ffffffff0a000000
1000000000000000000000002100000008000000190000000c0000000000000018000000
0c000000ffffff00220000000c000000ffffffff460000003400000028000000454d462b
2a40000024000000180000000000803f00000080000000800000803f0000008000000080
460000001c00000010000000454d462b024000000c000000000000000e00000014000000
0000000010000000140000000400000003010800050000000b0200000000050000000c02
a9004b0105000000090200000000050000000102ffffff000400000004010d0004000000
02010200030000001e00040000002701ffff030000001e00040000002701ffff03000000
1e00050000000102ffffff0005000000090200000000040000002701ffff030000001e00
050000000102ffffff0005000000090200000000040000002c010000070000001604a900
4b010000000008000000fa0200000000000000000000040000002d01000007000000fc02
0000ffffff000000040000002d010100050000000902ffffff0005000000010200000000
0400000004010d000400000002010200070000001b04a50046010500050008000000fa02
00000000000000000000040000002d01020007000000fc020000ffffff00000004000000
2d010300040000002701ffff030000001e00040000002d010100040000002d0100000500
0000010200000000050000000902ffffff00040000002c010000070000001604a9004b01
00000000040000002d010200040000002d010300040000002701ffff030000001e000400
00002d010100040000002d01000005000000010200000000050000000902ffffff000400
00002c010000070000001604a40046010500050007000000fc0200003300330000000400
00002d01040004000000f001010008000000fa0200000100000000000000040000002d01
010004000000f00100000500000009023300330005000000010233003300040000000401
0d0004000000020102006a0000002403330073005c0070005c006c005b0069005a006600
590063005900600058005e0057005c005700590056005700550054005400520053005100
52004f0051004e0050004c004f004b004e004a004d0049004c0048004c0047004a004700
490047004800470047004700610047006200470063004700640048006600490066004a00
67004b0068004c0069004e006a004f006b0051006c0052006d0054006e0057006f005900
70005c0071005e007100600072006300730066007300690074006c007500700076007300
760073005c0007000000fc020000660066000000040000002d01000004000000f0010400
05000000090266006600050000000102ffffff007c00000024033c0073005c006f005b00
6c005b0068005a0066005900620059005f0058005d0057005a0056005800550055005400
52005300510052004f0051004e0050004c004f004a004e004a004d0048004c0048004b00
47004a00470049004700480047004600470046004700440048004300490042004a004100
4b0040004c003f004e003e0050003d0052003c0053003b0056003a00580039005b003800
5e003700600037006300360066003500690034006d003300700033007400320077003200
7b0031008000310083003000870030008a0030008f002f0094002f0097002f009c002f00
9f002f00a4002f00a400470073005c0008000000fa020000000000000000000004000000
2d01040004000000f001010007000000fc020000668080000000040000002d0101000400
0000f001000008000000fa0200000100000000000000040000002d01000004000000f001
04000500000009026680800005000000010266808000160000002403090077005d007500
5c0074005c0073005c007300760074007600750076007700770077005d0007000000fc02
0000ccffff000000040000002d01040004000000f0010100050000000902ccffff000500
00000102ffffff00100000002403060077005d0075005c0074005c0073005c00a4004700
77005d0008000000fa0200000000000000000000040000002d01010004000000f0010000
08000000fa0200000100000000000000040000002d01000004000000f001010007000000
fc020000ffffcc000000040000002d01010004000000f001040008000000fa0200000000
000000000000040000002d01040004000000f001000005000000140278006b0004000000
02010100050000001302780071000500000013027600760008000000fa02000001000000
00000000040000002d01000004000000f001040007000000fc0200009933660000000400
00002d01040004000000f001010008000000fa0200000000000000000000040000002d01
010004000000f00100000500000014028f006b000500000013028f007100050000001302
7600760007000000fc0200004d4d80000000040000002d01000004000000f00104000800
0000fa0200000100000000000000040000002d01040004000000f0010100050000000902
4d4d80000500000001024d4d80000400000002010200be00000024035d00020147000201
49000101490001014b0000014c00ff004d00fe004e00fd004f00fc005000fa005100f800
5200f6005300f4005400f2005500ef005600ec005700ea005800e6005900e3005900e000
5a00dd005b00d9005c00d6005c00d2005d00cf005d00ca005e00c6005e00c3005e00be00
5f00b9005f00b6005f00b1006000ac006000a9006000a40060009f0060009c0060009700
600094005f008f005f008a005f0087005f0083005e007e005e007b005d0077005d007700
77007b0077007e00780083007800870079008a0079008f0079009400790097007a009c00
7a009f007a00a4007a00a9007a00ac007a00b1007a00b6007900b9007900be007900c300
7800c6007800ca007800cf007700d2007700d6007600d9007600dd007500e0007400e300
7300e6007300ea007200ec007100ef007000f2006f00f4006e00f6006d00f8006c00fa00
6b00fc006a00fd006900fe006800ff006700000166000101650001016300020163000201
61000201470007000000fc0200009999ff000000040000002d01010004000000f0010000
0500000009029999ff00050000000102ffffff00ac00000024035400a4002f00a9002f00
ac002f00b1002f00b4002f00b9002f00bc003000c1003000c6003000c9003100cd003100
d0003200d4003200d9003300db003300df003400e2003500e5003600e8003600eb003700
ee003800f0003900f3003a00f4003b00f7003c00f9003d00fa003e00fc003f00fd004000
ff004100ff00420000014300010144000101450002014600020147000201490001014900
01014b0000014c00ff004d00fe004e00fd004f00fc005000fa005100f8005200f6005300
f4005400f2005500f0005600ed005700ea005800e8005800e4005900e2005a00de005b00
db005b00d7005c00d3005c00d0005d00cc005d00c9005e00c4005e00c0005f00bc005f00
b8005f00b4005f00b0006000ac006000a8006000a30060009f0060009a00600097006000
92005f008e005f008a005f0086005e0083005e007e005e007b005d0077005d00a4004700
a4002f0008000000fa0200000000000000000000040000002d01000004000000f0010400
040000002d010200040000002d010300040000002701ffff030000001e00040000002d01
0100040000002d010000050000000102ffffff000500000009029999ff00040000002c01
0000070000001604a9004b0100000000040000002d010200040000002d01030004000000
2701ffff030000001e00040000002d010100040000002d010000050000000102ffffff00
0500000009029999ff00040000002c010000070000001604a9004b01000000001c000000
fb02f5ff0000000000009001000000cc00000000417269616c2043797200000000000000
00000000000000000000000000000000040000002d0104001c000000fb02100007000000
0000bc02000000cc0102022253797374656d000000000000000000000000000000000000
0000000000000000040000002d010500040000002d010400040000002d01050004000000
2d010400040000002d010200040000002d010300040000002d010500040000002701ffff
030000001e00040000002d010400040000002d010100040000002d010000050000000102
ffffff000500000009029999ff00040000002c01000007000000160475001c0160000201
050000000902000000000400000004010d0004000000020101000c000000320a63000401
0300000035382500060006000a00040000002d010500040000002d010400040000002d01
0200040000002d010300040000002d010500040000002701ffff030000001e0004000000
2d010400040000002d010100040000002d010000050000000102ffffff00050000000902
00000000040000002c010000070000001604a9004b0100000000040000002d0105000400
00002d010400040000002d010500040000002d010400040000002d010200040000002d01
0300040000002d010500040000002701ffff030000001e00040000002d01040004000000
2d010100040000002d010000050000000102ffffff000500000009020000000004000000
2c0100000700000016049a006c00850058000400000004010d0004000000020101000a00
0000320a88005a0002000000302506000a00040000002d010500040000002d0104000400
00002d010200040000002d010300040000002d010500040000002701ffff030000001e00
040000002d010400040000002d010100040000002d010000050000000102ffffff000500
0000090200000000040000002c010000070000001604a9004b0100000000040000002d01
0500040000002d010400040000002d010500040000002d010400040000002d0102000400
00002d010300040000002d010500040000002701ffff030000001e00040000002d010400
040000002d010100040000002d010000050000000102ffffff0005000000090200000000
040000002c01000007000000160483006c006e0058000400000004010d00040000000201
01000a000000320a71005a0002000000302506000a00040000002d010500040000002d01
0400040000002d010200040000002d010300040000002d010500040000002701ffff0300
00001e00040000002d010400040000002d010100040000002d010000050000000102ffff
ff0005000000090200000000040000002c010000070000001604a9004b01000000000400
00002d010500040000002d010400040000002d010500040000002d010400040000002d01
0200040000002d010300040000002d010500040000002701ffff030000001e0004000000
2d010400040000002d010100040000002d010000050000000102ffffff00050000000902
00000000040000002c0100000700000016044800470033002d000400000004010d000400
0000020101000c000000320a36002f000300000034312500060006000a00040000002d01
0500040000002d010400040000002d010200040000002d010300040000002d0105000400
00002701ffff030000001e00040000002d010400040000002d010100040000002d010000
050000000102ffffff0005000000090200000000040000002c010000070000001604a900
4b0100000000040000002d010500040000002d010400040000002d010500040000002d01
0400040000002d010200040000002d010300040000002d010500040000002701ffff0300
00001e00040000002d010400040000002d010100040000002d010000050000000102ffff
ff0005000000090200000000040000002c0100000700000016048d007c00780068000400
000004010d0004000000020101000a000000320a7b006a0002000000312506000a000400
00002d010500040000002d010400040000002d010200040000002d010300040000002d01
0500040000002701ffff030000001e00040000002d010400040000002d01010004000000
2d010000050000000102ffffff0005000000090200000000040000002c01000007000000
1604a9004b0100000000040000002d010200040000002d010300040000002d0105000400
00002701ffff030000001e00040000002d010400040000002d010100040000002d010000
050000000102ffffff0005000000090200000000040000002c010000070000001604a900
4b010000000008000000fa0200000000000000000000040000002d01060004000000f001
000007000000fc020100000000000000040000002d01000004000000f001010005000000
0902ffffff00050000000102000000000400000004010d00040000000201020007000000
1b04a50046010500050007000000fc020000000000000000040000002d01010004000000
2d01020004000000f0010600040000002d010500040000002701ffff030000001e000500
0000010200000000050000000902ffffff00040000002701ffff030000001e0005000000
010200000000050000000902ffffff00040000002701ffff030000000000

Рис. 3.1 – Оптимальный портфель ценных бумаг Марковица минимального
риска

3.3.2 Портфель Марковица максимальной эффективности

picscalex100010009000003540000000000120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02200220011200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffe0000000c60100000b00000026060f000c004d61746854797065
000050000a00000026060f000a00ffffffff010000000000030000000000Модель
оптимального портфеля Марковица, которая обеспечивает максимальную
доходность при заданном
риске(picscalex100010009000003950000000200150000000000050000000902000000
000400000002010100050000000102ffffff00040000002e011800050000003102010000
00050000000b0200000000050000000c02c00200021200000026060f001a00ffffffff00
0010000000c0ffffffa6ffffffc0010000660200000b00000026060f000c004d61746854
7970650000a00015000000fb0280fe0000000000009001010000000402001054696d6573
204e657720526f6d616e000086040000002d01000008000000320a1102ea000100000070
0008000000320a80013a000100000072000a00000026060f000a00ffffffff0100000000
0010000000fb021000070000000000bc02000000cc0102022253797374656d00cc040000
002d01010004000000f0010000030000000000=0.88) имеет вид:
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picscalex100010009000003420100000200150000000000050000000902000000000400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picscalex100010009000003ea0000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a003a0041200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffff60040000460300000b00000026060f000c004d61746854797065
0000100115000000fb0280fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e00006d040000002d01000008000000320a8001c6030100000031001000
0000fb0280fe0000000000009001000000020002001053796d626f6c0002040000002d01
010004000000f001000008000000320a80010003010000003d0008000000320a9b013a00
01000000e50015000000fb0280fe0000000000009001010000000402001054696d657320
4e657720526f6d616e00006d040000002d01000004000000f001010008000000320a3f03
850001000000690008000000320a1102400201000000690008000000320a800196010100
000078000a00000026060f000a00ffffffff01000000000010000000fb02100007000000
0000bc02000000cc0102022253797374656d00cc040000002d01010004000000f0010000
030000000000(3.5)picscalex1000100090000032101000003001500000000000500000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Решая задачу с помощью табличного процессора Excel и его надстройки
Поиск решения, получим (рис. 3.2):
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7,9%

х1 =0,56; х2=0; х3=0; х4=0,05; х5=0,39.
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Рис. 3.2 – Оптимальный портфель ценных бумаг Марковица максимальной
эффективности

3.4 Оптимальный портфель ценных бумаг Тобина

3.4.1 Портфель Тобина минимального риска

Через несколько лет после исследования Марковица другой крупнейший
американский экономист Д. Тобин заметил, что если на рынке есть
безрисковые бумаги (к таким можно отнести с некоторой натяжкой
государственные ценные бумаги), то решение задачи об оптимальном
портфеле сильно упрощается и приобретает новое качество.

Пусть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- эффективность безрисковых бумаг (12%), а х0 – доля капитала,
вложенного в них, тогда в рисковую часть портфеля вложена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 часть всего капитала. Пусть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- эффективность и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 – вариация (дисперсия) рисковой части
портфеля и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– риск этой рисковой части. Тогда эффективность всего портфеля равна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, вариация портфеля равна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 и риск
портфеля равен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(считается, что
безрисковые бумаги некоррелированны с остальными). Исключая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, получим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, т.е. эффективность портфеля
линейно зависит от его риска. Задача Марковица об оптимальном портфеле в
этом случае такова:
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(3.6)

Изложим теперь окончательное решение этой задачи, полученное Тобиным.
Пусть V – матрица ковариаций рисковых ценных бумаг,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-
вектор-столбцы долей х капитала, вкладываемых в i – ый вид рисковых
ценных бумаг и ожидаемых эффективностей этого вида,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. Пусть также I n – мерный вектор-столбец, компоненты которого равны 1.
тогда оптимальное значение долей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есть
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(3.7)

Здесь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- матрица,
обратная к V. В числителе дроби стоит число, в знаменателе, если
выполнить все действия (операция транспонирования первого сомножителя в
знаменателе не указана, но подразумевается), тоже получится число,
причем константа, определяемая рынком и не зависящая от инвестора,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-
вектор-столбец размерности n. Как видим, этот вектор не зависит от
эффективности портфеля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. Таким образом, вектор долей рисковых
видов ценных бумаг, пропорциональный этому вектору также не зависит от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. Следовательно, структура рисковой
части портфеля не зависит от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. Однако сумма компонент вектора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 зависит от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, а именно, компоненты вектора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 пропорционально увеличиваются с ростом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, поэтому доля
picscalex100010009000003b20000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c002e0011200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffa0010000660200000b00000026060f000c004d61746854797065
0000a00015000000fb0280fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e000086040000002d01000008000000320a5b02ec000100000030001500
0000fb0280fe0000000000009001010000000402001054696d6573204e657720526f6d61
6e000086040000002d01010004000000f001000008000000320a80014c00010000007800
0a00000026060f000a00ffffffff01000000000010000000fb021000070000000000bc02
000000cc0102022253797374656d00cc040000002d01000004000000f001010003000000
0000 безрисковые вложений будет при этом сокращаться. Выразим риск
оптимального портфеля в зависимости от его доходности. Для этого в
формулу вариации портфеля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подставим оптимальный вектор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 из формулы (15.3) через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. Получим
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Окончательно:
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 или
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(3.8)

Можно также написать выражение эффективности оптимального портфеля от
его риска: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 или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. Видно, что эти зависимости линейные.

Полученный оптимальный портфель называется портфелем Тобина минимального
риска, т.е. портфель Тобина – это портфель Марковица при наличии на
рынке безрисковых бумаг.

Решая задачу с помощью табличного процессора Excel и его надстройки
Поиск решения, получим:

picscalex100010009000003950000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02c00200021200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffc0010000660200000b00000026060f000c004d61746854797065
0000a00015000000fb0280fe0000000000009001010000000402001054696d6573204e65
7720526f6d616e000086040000002d01000008000000320a1102ea000100000070000800
0000320a80013a000100000072000a00000026060f000a00ffffffff0100000000001000
0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
010004000000f0010000030000000000=0,51

х0=0,08; х1 =0,25; х2=0; х3=0; х4=0,44; х5=0,23.
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Рис. 3.3 – Оптимальный портфель ценных бумаг Тобина минимального риска.

3.4.2 Портфель Тобина максимальной эффективности и заданного риска

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0000fb021000070000000000bc02000000cc0102022253797374656d00cc040000002d01
010004000000f0010000030000000000(3.9)

Получим следующее решение (рис. 3.4):
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12,31% х0=0,4; х1 =0,6; х2=0; х3=0;
х4=0; х5=0.

picscalex100010009000003fe27000008001610000000001610000026060f002220574d
464301000000000001006132000000000200000000200000bc100000bc30000001000000
6c000000050000000500000063010000ed0000000000000000000000112c00008b1d0000
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0003000040010000f000000000000000000000000000000000e2040080a9030046000000
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60000000460000005c00000050000000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c00000000000000044000000c00000000000000180000000c00000000000000
190000000c000000ffffff00140000000c0000000d000000120000000c00000002000000
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00000000bc02000000cc00000000417269616c2043797200000000000000000000000000
00000000000000000000040000002d0100001c000000fb021000070000000000bc020000
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2d010100050000000102ffffff0005000000090299336600040000002c01000007000000
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1c0089000d000000fdf4f4e5eaf2e8e2edeef1f2e8520600090009000700060005000700
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2701ffff030000001e00040000002d010600040000002d010400040000002d0101000500
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2500060006000a00040000002d010500040000002d010600040000002d01020004000000
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00002c010000070000001604f200690100000000040000002d010500040000002d010600
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2d010500040000002701ffff030000001e00040000002d010600040000002d0104000400
00002d010100050000000102ffffff0005000000090200000000040000002c0100000700
00001604b40043009f0029000400000004010d0004000000020101000c000000320aa200
2b000300000036302500060006000a00040000002d010500040000002d01060004000000
2d010200040000002d010300040000002d010500040000002701ffff030000001e000400
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090200000000040000002c010000070000001604f200690100000000040000002d010500
040000002d010600040000002d010500040000002d010600040000002d01020004000000
2d010300040000002d010500040000002701ffff030000001e00040000002d0106000400
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00002c0100000700000016042500bc001000a8000400000004010d000400000002010100
0a000000320a1300aa0002000000302506000a00040000002d010500040000002d010600
040000002d010200040000002d010300040000002d010500040000002701ffff03000000
1e00040000002d010600040000002d010400040000002d010100050000000102ffffff00
05000000090200000000040000002c010000070000001604f20069010000000004000000
2d010500040000002d010600040000002d010500040000002d010600040000002d010200
040000002d010300040000002d010500040000002701ffff030000001e00040000002d01
0600040000002d010400040000002d010100050000000102ffffff000500000009020000
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020101000a000000320a2a00aa0002000000302506000a00040000002d01050004000000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00000902ffffff00050000000102000000000400000004010d0004000000020102000700
00001b04c900600156004201040000002d010200040000002d010300040000002d010500
040000002701ffff030000001e00040000002d010600040000002d010100040000002d01
070005000000010200000000050000000902ffffff00040000002c010000070000001604
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2701ffff030000001e00040000002d010600040000002d010100040000002d0107000500
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9999ff00050000000102ffffff000400000004010d000400000002010200070000001b04
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040000002d01020004000000f0010400040000002d010500040000002701ffff03000000
1e0005000000010200000000050000000902ffffff00040000002701ffff030000001e00
05000000010200000000050000000902ffffff00040000002701ffff030000000000

Рис. 3.4 – Оптимальный портфель Тобина максимальной эффективности

3.5 Формирование оптимального портфеля с помощью ведущего фактора
финансового рынка

В реальности доходности ценных бумаг зависят от факторов финансового
рынка. В роли ведущего фактора финансового рынка удобнее всего брать
среднюю доходность рисковых бумаг самого финансового рынка.

Обозначим этот фактор как f и будем считать, что доходности всех ценных
бумаг зависят от него. Пусть d – доходность какой-либо фиксированной
ценной бумаги. Простейшая форма зависимости – линейная, так что примем
гипотезу, что d линейно зависит от f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. Так как обе величины d, f – случайны, то равенство врядли
может быть точным. Найдем a и b.

Попробуем подобрать такую зависимость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, чтобы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 было минимальным. Имеем
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(3.10)

Дифференцируя
picscalex100010009000003d20000000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c020002a0041200000026060f001a00ffffffff00001000
0000c0ffffffc6ffffff60040000c60100000b00000026060f000c004d61746854797065
0000500015000000fb0280fe0000000000009001000000000402001054696d6573204e65
7720526f6d616e0000c8040000002d01000008000000320a6001ec030100000029000800
0000320a6001aa02010000002c0008000000320a60015a0101000000280015000000fb02
80fe0000000000009001010000000402001054696d6573204e657720526f6d616e0000c8
040000002d01010004000000f001000008000000320a6001260301000000620008000000
320a6001e40101000000610008000000320a600146000100000046000a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01000004000000f0010100030000000000частным
образом по а и b приравниваем частные производные 0, получим систему
уравненийpicscalex100010009000003920200000200150000000000050000000902000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.

Решая эту систему, получим:

picscalex100010009000003e20100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02800560121200000026060f001a00ffffffff00001000
0000c0ffffffa1ffffff20120000210500000b00000026060f000c004d61746854797065
0000300110000000fb02f1fde300000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a45042804010000005b0010000000fb02f1fde3000000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320a4504c305010000005d0010000000fb02f1fde30000000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a4504
fe08010000005b0010000000fb02f1fde300000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a45048c0a010000005d00
15000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f
6d616e0000a5040000002d01000004000000f001010008000000320a2105011101000000
460008000000320a4604ed0f01000000440008000000320a2105e40c0200000046440800
0000320a4604c40b010000004b0008000000320a4604750901000000460008000000320a
46048907010000004d0008000000320a46049f0401000000440008000000320a4604b302
010000004d0008000000320a46043a0001000000610008000000320a6002e50701000000
460008000000320a8501d10601000000440008000000320a6002c8030200000046440800
0000320a8501a802010000004b0008000000320a85012e0001000000620015000000fb02
80fe0000000000009001000000000402001054696d6573204e657720526f6d616e0000a5
040000002d01010004000000f001000008000000320a46043b0f010000002f0008000000
320a4604120b010000002f0008000000320a85011209010000002c0008000000320a8501
1f06010000002f0010000000fb0280fe0000000000009001000000020002001053796d62
6f6c0002040000002d01000004000000f001010008000000320a46046306010000002d00
08000000320a46046d01010000003d0008000000320a85015c01010000003d000a000000
26060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc
0102022253797374656d00cc040000002d01010004000000f0010000030000000000(3.1
1)

Найдем математическое ожидание случайной величины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, являющейся функцией от случайной величины D. Имеем
picscalex100010009000003450100000200150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c022002e0081200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffa0080000c60100000b00000026060f000c004d61746854797065
0000500010000000fb02f3fde300000000009001000000020002001053796d626f6c0002
040000002d01000008000000320a7f01b601010000005b0010000000fb02f3fde3000000
00009001000000020002001053796d626f6c0002040000002d01010004000000f0010000
08000000320a7f012d03010000005d0010000000fb02f3fde30000000000900100000002
0002001053796d626f6c0002040000002d01000004000000f001010008000000320a7f01
a906010000005b0010000000fb02f3fde300000000009001000000020002001053796d62
6f6c0002040000002d01010004000000f001000008000000320a7f014408010000005d00
15000000fb0280fe0000000000009001010000000402001054696d6573204e657720526f
6d616e000086040000002d01000004000000f001010008000000320a8001200701000000
440008000000320a80013305010000004d0008000000320a80012702010000005a000800
0000320a80014000010000004d0010000000fb0280fe0000000000009001000000020002
001053796d626f6c0002040000002d01010004000000f001000008000000320a8001ed03
010000003d000a00000026060f000a00ffffffff01000000000010000000fb0210000700
00000000bc02000000cc0102022253797374656d00cc040000002d01000004000000f001
0100030000000000. Значит, в частности, при найденных a, b для
математических ожиданий случайных величин D, F верно не приближенное
равенство, а точное.
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.

На практике совместное распределение случайных величин (F, D) не
известно, известны только результаты наблюдений, т.е. выборка пар (f, d)
значений (F, D). все рассмотренные величины заменяются их выборочными
аналогами. Так, для определения a, b получим систему уравнений:
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(3.12)

Решая эту систему, получим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, значит, прямая линия регрессии имеет
уравнение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. Через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 обозначим выборочные аналоги
корреляционного момента случайной величины F, D и дисперсии F
соответственно.

Также можно убедиться, что для средних арифметических значений верно
точное равенство, т.е.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Обычно вместо буквы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используют букву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. Этот
коэффициент так и называют «бета ценных бумаг i – ого вида относительно
рынка. Эта величина определяет влияние рынка на данные ценные бумаги:
если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, то доходность бумаг i –
ого вида колеблется в такт с рынком, а если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, то поведение бумаги прямо
противоположно колебаниям доходности рынка в целом.

Вариация доходности каждой ценной бумаги равна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, т.е. состоит из
двух слагаемых: «собственной» вариации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, не зависящей
от рынка, и «рыночной» части вариации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, определяемой
случайным поведением рынка в целом. Их
отношениеpicscalex130010009000003fa0000000200150000000000050000000902000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обозначается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и называется R-squared. Это
отношение характеризует долю риска данных ценных бумаг, вносимую рынком.
те бумаги, для которых R-squared велико, в каком-то смысле
предпочтительнее, так как их поведение более предсказуемо.

Найдем параметры линейной регрессии по выборке, представленной в таблице
3.1. Изобразим данные и регрессионную зависимость между ними на графиках
(рис. 3.5).

Таблица 3.2. Данные по доходности финансового рынка и ценных бумаг
Центрэнерго за определенный период

Период03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.02
14.02–21.02F4565567x1781010879

picscalex1000100090000038420000009001610000000001610000026060f002220574d
464301000000000001002527000000000200000000200000200900002029000001000000
6c000000050000000500000040010000bd0000000000000000000000cc270000af170000
20454d460000010020290000430200000500000000000000000000000000000000040000
0003000040010000f000000000000000000000000000000000e2040080a9030046000000
2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
60000000460000005c00000050000000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c00000000000000044000000c00000000000000180000000c00000000000000
190000000c000000ffffff00140000000c0000000d000000120000000c00000002000000
2100000008000000220000000c000000ffffffff2100000008000000220000000c000000
ffffffff0a0000001000000000000000000000002100000008000000190000000c000000
ffffff00180000000c00000000000000220000000c000000ffffffff2100000008000000
190000000c000000ffffff00180000000c000000000000001e0000001800000000000000
0000000046010000c2000000260000001c00000001000000000000000000000000000000
00000000250000000c0000000100000027000000180000000200000000000000ffffff00
00000000250000000c00000002000000180000000c000000ffffff00190000000c000000
00000000140000000c0000000d000000120000000c000000020000002b00000018000000
050000000500000040010000bd000000250000000c00000007000080250000000c000000
00000080220000000c000000ffffffff2100000008000000250000000c00000002000000
250000000c00000001000000190000000c00000000000000180000000c000000ffffff00
1e00000018000000000000000000000046010000c2000000250000000c00000005000080
280000000c00000002000000250000000c00000008000080280000000c00000001000000
140000000c0000000d000000120000000c0000000200000056000000300000003b000000
41000000db0000007b000000050000003b004100db004100db007b003b007b003b004100
260000001c0000000100000000000000000000000000000000000000250000000c000000
01000000250000000c00000007000080250000000c00000000000080220000000c000000
ffffffff2100000008000000250000000c00000005000080250000000c00000001000000
190000000c00000000000000180000000c000000ffffff001e000000180000003b000000
3d000000db0000007f0000001b000000100000003b00000071000000190000000c000000
ffffff00140000000c0000000d000000120000000c000000010000003600000010000000
db000000710000001b000000100000003b000000680000003600000010000000db000000
680000001b000000100000003b0000005e0000003600000010000000db0000005e000000
1b000000100000003b000000540000003600000010000000db000000540000001b000000
100000003b0000004b0000003600000010000000db0000004b0000001b00000010000000
3b000000410000003600000010000000db00000041000000250000000c00000007000080
250000000c00000000000080220000000c000000ffffffff210000000800000025000000
0c00000005000080250000000c00000001000000190000000c000000ffffff0018000000
0c000000ffffff001e00000018000000000000000000000046010000c200000026000000
1c0000000200000000000000010000000000000080808000250000000c00000002000000
280000000c000000010000001b000000100000003b00000041000000140000000c000000
0d000000120000000c000000010000003600000010000000db0000004100000036000000
10000000db0000007b00000036000000100000003b0000007b0000003600000010000000
3b00000041000000260000001c0000000100000000000000000000000000000000000000
250000000c00000001000000280000000c000000020000001b000000100000003b000000
4100000036000000100000003b0000007b000000520000007001000002000000f5ffffff
00000000000000000000000090010000000000cc0000000041007200690061006c002000
430079007200000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000f00000000000000000000000000000
1e000000b3000000000000004b00000002000000a8eb1300604f8a00f0f79b0244928830
28ec1300f1a50930f44e8a00200000007f0000008020000001000000000000006ced1300
14308a004489af2d28ec130014308a00000000006ced130090eb130005a5093000000000
0000000040a8f90200000000c800000000000000ead4907cc29a807cffffffff34ec1300
1e000000b3000000000000004b0000003c0000000f000000080000000000000035000000
010000000c000000b30000000100000001000000000000000000000078f79b0200000000
a000000000000000250000000a0000003e0000006476000800000000250000000c000000
020000001b00000010000000380000007b00000036000000100000003b0000007b000000
1b00000010000000380000007100000036000000100000003b000000710000001b000000
10000000380000006800000036000000100000003b000000680000001b00000010000000
380000005e00000036000000100000003b0000005e0000001b0000001000000038000000
5400000036000000100000003b000000540000001b00000010000000380000004b000000
36000000100000003b0000004b0000001b00000010000000380000004100000036000000
100000003b000000410000001b000000100000003b0000007b0000003600000010000000
db0000007b0000001b000000100000003b0000007e00000036000000100000003b000000
7b0000001b000000100000005b0000007e00000036000000100000005b0000007b000000
1b000000100000007b0000007e00000036000000100000007b0000007b0000001b000000
100000009b0000007e00000036000000100000009b0000007b0000001b00000010000000
bb0000007e0000003600000010000000bb0000007b0000001b00000010000000db000000
7e0000003600000010000000db0000007b000000250000000c0000000700008025000000
0c00000000000080250000000c0000000d000080220000000c000000ffffffff21000000
08000000250000000c00000002000000250000000c00000005000080250000000c000000
01000000190000000c000000ffffff00180000000c000000ffffff001e00000018000000
050000000500000041010000bd000000250000000c00000007000080250000000c000000
00000080250000000c0000000d000080220000000c000000ffffffff2100000008000000
250000000c00000002000000250000000c00000005000080250000000c00000001000000
190000000c000000ffffff00180000000c000000ffffff001e0000001800000038000000
3e000000e200000081000000250000000c00000007000080250000000c00000000000080
250000000c0000000d000080220000000c000000ffffffff210000000800000025000000
0c00000002000000250000000c00000005000080250000000c0000000100000019000000
0c000000ffffff00180000000c000000ffffff001e00000018000000380000003e000000
df0000007e000000250000000c000000050000801b000000100000005b00000068000000
270000001800000003000000000000000000800000000000250000000c00000003000000
260000001c0000000400000000000000010000000000000000008000250000000c000000
04000000280000000c00000001000000180000000c00000000008000190000000c000000
00000000140000000c0000000d000000120000000c000000020000005600000030000000
58000000650000005e0000006b000000050000005b0065005e0068005b006b0058006800
5b006500250000000c00000007000080250000000c00000000000080250000000c000000
0d000080220000000c000000ffffffff2100000008000000250000000c00000002000000
250000000c00000003000000250000000c00000004000000190000000c00000000000000
180000000c000000000080001e00000018000000380000003e000000df0000007e000000
1b000000100000007b0000005e000000140000000c0000000d000000120000000c000000
020000005600000030000000780000005b0000007e00000061000000050000007b005b00
7e005e007b00610078005e007b005b00250000000c00000007000080250000000c000000
00000080250000000c0000000d000080220000000c000000ffffffff2100000008000000
250000000c00000002000000250000000c00000003000000250000000c00000004000000
190000000c00000000000000180000000c000000000080001e0000001800000038000000
3e000000df0000007e0000001b00000010000000bb00000054000000140000000c000000
0d000000120000000c000000020000005600000030000000b800000051000000be000000
5700000005000000bb005100be005400bb005700b8005400bb005100250000000c000000
07000080250000000c00000000000080250000000c0000000d000080220000000c000000
ffffffff2100000008000000250000000c00000002000000250000000c00000003000000
250000000c00000004000000190000000c00000000000000180000000c00000000008000
1e00000018000000380000003e000000df0000007e0000001b00000010000000bb000000
5e000000140000000c0000000d000000120000000c000000020000005600000030000000
b80000005b000000be0000006100000005000000bb005b00be005e00bb006100b8005e00
bb005b00250000000c00000007000080250000000c00000000000080250000000c000000
0d000080220000000c000000ffffffff2100000008000000250000000c00000002000000
250000000c00000003000000250000000c00000004000000190000000c00000000000000
180000000c000000000080001e00000018000000380000003e000000df0000007e000000
1b000000100000007b0000005e000000140000000c0000000d000000120000000c000000
020000005600000030000000780000005b0000007e00000061000000050000007b005b00
7e005e007b00610078005e007b005b00250000000c00000007000080250000000c000000
00000080250000000c0000000d000080220000000c000000ffffffff2100000008000000
250000000c00000002000000250000000c00000003000000250000000c00000004000000
190000000c00000000000000180000000c000000000080001e0000001800000038000000
3e000000df0000007e0000001b000000100000005b00000054000000140000000c000000
0d000000120000000c00000002000000560000003000000058000000510000005e000000
57000000050000005b0051005e0054005b005700580054005b005100250000000c000000
07000080250000000c00000000000080250000000c0000000d000080220000000c000000
ffffffff2100000008000000250000000c00000002000000250000000c00000003000000
250000000c00000004000000190000000c00000000000000180000000c00000000008000
1e00000018000000380000003e000000df0000007e0000001b000000100000009b000000
4b000000140000000c0000000d000000120000000c000000020000005600000030000000
98000000480000009e0000004e000000050000009b0048009e004b009b004e0098004b00
9b004800250000000c00000007000080250000000c00000000000080250000000c000000
0d000080220000000c000000ffffffff2100000008000000250000000c00000002000000
250000000c00000003000000250000000c00000004000000190000000c00000000000000
180000000c000000000080001e00000018000000380000003e000000df0000007e000000
250000000c00000007000080250000000c00000000000080250000000c0000000d000080
220000000c000000ffffffff2100000008000000250000000c0000000200000025000000
0c00000003000000250000000c00000004000000190000000c0000000000000018000000
0c000000000080001e00000018000000380000003e000000e20000008100000025000000
0c00000007000080250000000c00000000000080250000000c0000000d00008022000000
0c000000ffffffff2100000008000000250000000c00000002000000250000000c000000
03000000250000000c00000004000000190000000c00000000000000180000000c000000
000080001e00000018000000000000000000000046010000c2000000250000000c000000
07000080250000000c00000000000080250000000c0000000d000080220000000c000000
ffffffff2100000008000000250000000c00000002000000250000000c00000003000000
250000000c00000004000000190000000c00000000000000180000000c00000000008000
1e00000018000000050000000500000041010000bd000000250000000c00000007000080
250000000c00000000000080250000000c0000000d000080220000000c000000ffffffff
2100000008000000250000000c00000002000000250000000c0000000300000025000000
0c00000004000000190000000c00000000000000180000000c000000000080001e000000
180000003b00000041000000df0000007e000000250000000c0000000700008025000000
0c00000000000080250000000c0000000d000080220000000c000000ffffffff21000000
08000000250000000c00000002000000250000000c00000003000000250000000c000000
04000000190000000c00000000000000180000000c000000000080001e00000018000000
3b00000041000000dc0000007b000000250000000c00000005000080280000000c000000
03000000260000001c000000030000000000000002000000000000000000000025000000
0c00000003000000280000000c000000040000001b000000100000005b0000005e000000
190000000c000000ffffff00140000000c0000000d000000120000000c00000001000000
3600000010000000bb00000056000000250000000c00000007000080250000000c000000
00000080250000000c0000000d000080220000000c000000ffffffff2100000008000000
250000000c00000002000000250000000c00000005000080250000000c00000003000000
190000000c000000ffffff00180000000c000000000080001e000000180000003b000000
41000000df0000007e000000250000000c00000007000080250000000c00000000000080
250000000c0000000d000080220000000c000000ffffffff210000000800000025000000
0c00000002000000250000000c00000005000080250000000c0000000300000019000000
0c000000ffffff00180000000c000000000080001e000000180000000000000000000000
46010000c2000000250000000c00000007000080250000000c0000000000008025000000
0c0000000d000080220000000c000000ffffffff2100000008000000250000000c000000
02000000250000000c00000005000080250000000c00000003000000190000000c000000
ffffff00180000000c000000000080001e00000018000000000000000000000046010000
c2000000250000000c00000007000080250000000c00000000000080250000000c000000
0d000080220000000c000000ffffffff2100000008000000250000000c00000002000000
250000000c00000005000080250000000c00000003000000190000000c000000ffffff00
180000000c000000000080001e00000018000000000000000000000046010000c2000000
250000000c0000000d000080250000000c00000002000000250000000c0000000d000080
250000000c00000002000000250000000c00000007000080250000000c00000000000080
250000000c0000000d000080220000000c000000ffffffff210000000800000025000000
0c00000002000000250000000c00000005000080250000000c0000000300000019000000
0c000000ffffff00180000000c000000000080001e00000018000000d700000091000000
41010000a6000000180000000c00000000000000140000000c0000000d00000012000000
0c0000000100000054000000c4000000d9000000940000003e010000a100000001000000
0000fa410000fa41d900000094000000140000004c000000000000000000000000000000
ffffffffffffffff74000000790020003d00200030002c00320037003900340078002000
2b002000310033002c003000370034000600000003000000060000000300000006000000
030000000600000006000000060000000600000006000000030000000600000003000000
060000000600000003000000060000000600000006000000250000000c0000000d000080
250000000c00000002000000250000000c00000007000080250000000c00000000000080
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0000000000009001000000cc00000000417269616c204379720000000000000000000000
000000000000000000000000040000002d0105000500000014027b003800050000001302
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380005000000130254003b000500000014024b0038000500000013024b003b0005000000
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db000500000013027b00db00040000002d010200040000002d0103001c000000fb021000
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000000000000000000000000040000002d010600040000002701ffff030000001e000400
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0902ffffff00040000002c010000070000001604bd00410105000500040000002d010200
040000002d010300040000002d010600040000002701ffff030000001e00040000002d01
0500040000002d010400040000002d010000050000000102ffffff00050000000902ffff
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5b0007000000fc020000000080000000040000002d01070008000000fa02000001000000
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5b006b00580068005b006500040000002d010200040000002d010300040000002d010600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5b00be005e00bb006100b8005e00bb005b00040000002d010200040000002d0103000400
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040000002d0108000500000001020000000005000000090200008000040000002c010000
0700000016047e00df003e0038000500000014025e007b000400000004010d0004000000
020102000e000000240305007b005b007e005e007b00610078005e007b005b0004000000
2d010200040000002d010300040000002d010600040000002701ffff030000001e000400
00002d010500040000002d010700040000002d0108000500000001020000000005000000
090200008000040000002c0100000700000016047e00df003e0038000500000014025400
5b000400000004010d0004000000020102000e000000240305005b0051005e0054005b00
5700580054005b005100040000002d010200040000002d010300040000002d0106000400
00002701ffff030000001e00040000002d010500040000002d010700040000002d010800
0500000001020000000005000000090200008000040000002c0100000700000016047e00
df003e0038000500000014024b009b000400000004010d0004000000020102000e000000
240305009b0048009e004b009b004e0098004b009b004800040000002d01020004000000
2d010300040000002d010600040000002701ffff030000001e00040000002d0105000400
00002d010700040000002d01080005000000010200000000050000000902000080000400
00002c0100000700000016047e00df003e003800040000002d010200040000002d010300
040000002d010600040000002701ffff030000001e00040000002d010500040000002d01
0700040000002d0108000500000001020000000005000000090200008000040000002c01
00000700000016048100e2003e003800040000002d010200040000002d01030004000000
2d010600040000002701ffff030000001e00040000002d010500040000002d0107000400
00002d0108000500000001020000000005000000090200008000040000002c0100000700
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040000002701ffff030000001e00040000002d010500040000002d010700040000002d01
08000500000001020000000005000000090200008000040000002c010000070000001604
bd00410105000500040000002d010200040000002d010300040000002d01060004000000
2701ffff030000001e00040000002d010500040000002d010700040000002d0108000500
000001020000000005000000090200008000040000002c0100000700000016047e00df00
41003b00040000002d010200040000002d010300040000002d010600040000002701ffff
030000001e00040000002d010500040000002d010700040000002d010800050000000102
0000000005000000090200008000040000002c0100000700000016047b00dc0041003b00
040000002d01040004000000f001070008000000fa020000020000000000000004000000
2d01000004000000f00108000500000014025e005b00050000000102ffffff0004000000
04010d0004000000020101000500000013025600bb00040000002d010200040000002d01
0300040000002d010600040000002701ffff030000001e00040000002d01050004000000
2d010400040000002d010000050000000102ffffff000500000009020000800004000000
2c0100000700000016047e00df0041003b00040000002d010200040000002d0103000400
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040000002d010000050000000102ffffff0005000000090200008000040000002c010000
070000001604c200460100000000040000002d010200040000002d010300040000002d01
0600040000002701ffff030000001e00040000002d010500040000002d01040004000000
2d010000050000000102ffffff0005000000090200008000040000002c01000007000000
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050000000102ffffff0005000000090200008000040000002c010000070000001604c200
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0500040000002d010200040000002d010300040000002d010600040000002701ffff0300
00001e00040000002d010500040000002d010400040000002d010000050000000102ffff
ff0005000000090200008000040000002c010000070000001604a60041019100d7000500
00000902000000000400000004010d00040000000201010025000000320a9400d9001400
000079203d20302c3237393478202b2031332c3037340600030006000300060003000600
0600060006000600030006000300060006000300060006000600040000002d0106000400
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ffff030000001e00040000002d010500040000002d010400040000002d01000005000000
0102ffffff0005000000090200000000040000002c010000070000001604c20046010000
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00001e00040000002d010500040000002d010400040000002d010000050000000102ffff
ff0005000000090200000000040000002c010000070000001604c2004601000000000400
000004010d0004000000020101000a000000320a74002700020000003132060006000a00
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050000000102ffffff0005000000090200000000040000002c010000070000001604c200
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ffff030000001e00040000002d010500040000002d010400040000002d01000005000000
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09000000320a8400580001000000375a060009000000320a8400780001000000385a0600
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06000a000000320a8400d50002000000313106000600040000002d010200040000002d01
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2d010400040000002d010000050000000102ffffff000500000009020000000004000000
2c010000070000001604c2004601000000001c000000fb02f5ff000000000000bc020000
00cc00000000417269616c20437972000000000000000000000000000000000000000000
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ffff030000001e00040000002d010700040000002d010400040000002d01000005000000
0102ffffff0005000000090200000000040000002c010000070000001604ab0094009600
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0600040000002d010600040000002d010700040000002d010200040000002d0103000400
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0600040000002d010700040000002d010200040000002d010300040000002d0106000400
00002701ffff030000001e00040000002d010700040000002d010400040000002d010000
050000000102ffffff0005000000090200000000040000002c0100000700000016046300
2500590010000400000004010d0004000000020101001c000000fb02f5ff000084038403
bc02000000cc00100000417269616c204379720000000000000000000000000000000000
000000000000040000002d01080009000000320a6100130001000000465a070004000000
2d01070004000000f0010800040000002d010600040000002d010700040000002d010200
040000002d010300040000002d010600040000002701ffff030000001e00040000002d01
0700040000002d010400040000002d010000050000000102ffffff000500000009020000
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2d010300040000002d010600040000002701ffff030000001e00040000002d0107000400
00002d010400040000002d010000050000000102ffffff00050000000902000000000400
00002c010000070000001604c20046010000000008000000fa0200000000000000000000
040000002d01080004000000f0010000040000002d010400050000000902ffffff000500
00000102000000000400000004010d000400000002010200070000001b04be0041010500
050007000000fc020000000000000000040000002d010000040000002d01020004000000
f0010800040000002d010600040000002701ffff030000001e0005000000010200000000
050000000902ffffff00040000002701ffff030000001e00050000000102000000000500
00000902ffffff00040000002701ffff030000000000

Рис. 3.5 – Изменение доходности рынка за счет изменения доходности
ценных бумаг Центрэнерго

Регрессия d на f имеет вид: d = 0.2794f + 13.074. Следовательно,
случайная величина остаточных колебаний е есть d – 0.2794f -13.074.
Найдем вариации остатков, составив ряд значений е (табл. 3.3):

Таблица 3.3. Вариации остаточных колебаний курса ценных бумаг
Центрэнерго

03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.0214.02–
21.02-100-1011

Среднее, естественно, равно 0, и потому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.

Далее,picscalex100010009000003cd0000000200150000000000050000000902000000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0,279,
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,

picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000=13,074+19
(0,279–1)=-0,626.

Таблица 3.4. Данные по доходности финансового рынка и акций Днепрэнерго
за определенный период

Период03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.02
14.02–21.02F14151615151617x26674467

picscalex100010009000003971f000009001610000000001610000026060f002220574d
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20454d4600000100bc2700003a0200000500000000000000000000000000000000040000
0003000040010000f000000000000000000000000000000000e2040080a9030046000000
2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
60000000460000005c00000050000000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c00000000000000044000000c00000000000000180000000c00000000000000
190000000c000000ffffff00140000000c0000000d000000120000000c00000002000000
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190000000c000000ffffff00180000000c000000000000001e0000001800000000000000
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0000090200008000040000002c0100000700000016046d00da003a003700050000001402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Рис. 3.6 – Изменение доходности финансового рынка за счет изменения
доходности акций Днепрэнерго.

Регрессия d на f имеет вид: d=0.4091f+13.091. Следовательно, случайная
величина остаточных колебаний е есть d-0.4091f-13.091. Найдем вариации
остатков, составив ряд значений е (табл. 3.5):

Таблица 3.5

Вариации остаточных колебаний курса ценных бумаг Днепрэнерго

03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.0214.02–
21.02-1,5-0,500,20,30,51

Среднее, естественно, равно 0, и потому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.

Далее,picscalex100010009000003cd0000000200150000000000050000000902000000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0,409,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,
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2c000000200100008c0100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000=1,861.

Таблица 3.6. Данные по доходности финансового рынка и акций Киевэнерго
за определенный период

Период03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.02
14.02–21.02F14151615151617x35765457
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ffffff000400000004010d000400000002010200030000001e00040000002701ffff0300
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3e00f800040000002d010200040000002d010300040000002701ffff030000001e000400
00002d010400040000002d010000050000000102ffffff00050000000902ffffff000400
00002c010000070000001604a9003f01000000000500000014023e003a00040000000401
0d0004000000020101000500000013023e00f8000500000013026700f800050000001302
67003a000500000013023e003a0005000000130267003a001c000000fb02f5ff00000000
00009001000000cc00000000417269616c20437972000000000000000000000000000000
0000000000000000040000002d0105000500000014026700370005000000130267003a00
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3a000500000013026700f8000500000014026a003a0005000000130267003a0005000000
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1c000000fb021000070000000000bc02000000cc0102022253797374656d000000000000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ffff030000001e00040000002d010500040000002d010400040000002d01000005000000
0102ffffff0005000000090200000000040000002c010000070000001604a9003f010000
00001c000000fb02f5ff000000000000bc02000000cc00000000417269616c2043797200
00000000000000000000000000000000000000000000040000002d010700040000002d01
0600040000002d010700040000002d010600040000002d010700040000002d0102000400
00002d010300040000002d010600040000002701ffff030000001e00040000002d010700
040000002d010400040000002d010000050000000102ffffff0005000000090200000000
040000002c0100000700000016049700a200820091000400000004010d00040000000201
01000a000000320a8500930002000000643307000600040000002d010600040000002d01
0700040000002d010200040000002d010300040000002d010600040000002701ffff0300
00001e00040000002d010700040000002d010400040000002d010000050000000102ffff
ff0005000000090200000000040000002c010000070000001604a9003f01000000000400
00002d010600040000002d010700040000002d010600040000002d010700040000002d01
0200040000002d010300040000002d010600040000002701ffff030000001e0004000000
2d010700040000002d010400040000002d010000050000000102ffffff00050000000902
00000000040000002c010000070000001604570024004d000f000400000004010d000400
0000020101001c000000fb02f5ff000084038403bc02000000cc00100000417269616c20
4379720000000000000000000000000000000000000000000000040000002d0108000900
0000320a5500120001000000466b0700040000002d01070004000000f001080004000000
2d010600040000002d010700040000002d010200040000002d010300040000002d010600
040000002701ffff030000001e00040000002d010700040000002d010400040000002d01
0000050000000102ffffff0005000000090200000000040000002c010000070000001604
a9003f0100000000040000002d010200040000002d010300040000002d01060004000000
2701ffff030000001e00040000002d010700040000002d010400040000002d0100000500
00000102ffffff0005000000090200000000040000002c010000070000001604a9003f01
0000000008000000fa0200000000000000000000040000002d01080004000000f0010000
040000002d010400050000000902ffffff00050000000102000000000400000004010d00
0400000002010200070000001b04a5003a010500050007000000fc020000000000000000
040000002d010000040000002d01020004000000f0010800040000002d01060004000000
2701ffff030000001e0005000000010200000000050000000902ffffff00040000002701
ffff030000001e0005000000010200000000050000000902ffffff00040000002701ffff
030000000000

Рис. 3.7 – Измерение доходности финансового рынка за счет изменения
доходности акций Киевэнерго.

Регрессия d на f имеет вид: d=0.4259f+13.056. Следовательно, случайная
величина остаточных колебаний е есть d-0.4259f-13.056. Найдем вариации
остатков, составив ряд значений е (табл. 3.7).

Таблица 3.7. Вариации остаточных колебаний курса ценных бумаг Киевэнерго

03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.0214.02–
21.02-1-100011

Среднее, естественно, равно 0, и потому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.

Далее,picscalex100010009000003cd0000000200150000000000050000000902000000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0,426,
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,

picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000=2,15.

Таблица 3.8. Данные по доходности финансового рынка и акций Укрнафта за
определенный период

Период03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.02
14.02–21.02F14151615151617x46575677

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00002d010200040000002d010300040000002d010600040000002701ffff030000001e00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Рис. 3.8 – Изменение доходности финансового рынка за счет изменения
доходности акций Укртатнафта

Регрессия d на f имеет вид: d=0.7353f+10.912. Следовательно, случайная
величина остаточных колебаний е есть d-0.7353f-10.912. Найдем вариации
остатков, составив ряд значений е (табл. 3.9).

Таблица 3.9. Вариации остаточных колебаний курса ценных бумаг
Укртатнафты

03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.0214.02–
21.02-1000001

Среднее, естественно, равно 0, и потому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.

Далее,picscalex100010009000003cd0000000200150000000000050000000902000000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0,735,
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,

picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000=5,876.

Таблица 3.10. Данные по доходности финансового рынка и акций Турбоатом
за определенный период

Период03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.02
14.02–21.02F14151615151617x58976679
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Рис. 3.9 – Изменение доходности финансового рынка за счет изменения
доходности акций Турбоатом

Регрессия d на f имеет вид: d=0.1765f+14.119. Следовательно, случайная
величина остаточных колебаний е есть d-0.1765f-14.119.

Найдем вариации остатков, составив ряд значений е (табл. 3.11):

Таблица 3.11. Вариации остаточных колебаний курса ценных бумаг
Турбоатома

03.01–10.0111.01–17.0118.01–24.0125.01–01.0201.02–07.0208.02–14.0214.02–
21.02-2-110011

Среднее, естественно, равно 0, и потому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.

Далее,picscalex100010009000003cd0000000200150000000000050000000902000000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0,176,
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,

picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000=-1,539.

Эффективность ценных бумаг удобно отсчитывать от эффективности
безрискового вклада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. Итак,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, где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. Превышение эффективности ценной бумаги над безрисковой
эффективностью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 называется премией за риск. Таким образом, эта премия за риск в
основном линейно зависит от премии за риск, складывающейся для рынка в
целом, и коэффициентом является «бета» данной бумаги. Это, однако,
верно, если
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000=0. такие ценные
бумаги называются «справедливо» оцененными. Те же бумаги, у которых
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000>0, рынком
недооценены, а если
picscalex100010009000003880000000200120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02600160011200000026060f001a00ffffffff00001000
0000c0ffffff2600000020010000860100000b00000026060f000c004d61746854797065
0000300010000000fb0280fe0000000000009001010000020002001053796d626f6c0002
040000002d01000008000000320a000116000100000061000a00000026060f000a00ffff
ffff01000000000010000000fb021000070000000000bc02000000cc0102022253797374
656d00cc040000002d01010004000000f0010000030000000000

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