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Review of Business and Economics Studies / Вестник исследований бизнеса и экономики, 2015, том 3, № 2

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Review of Business and Economics Studies / Вестник исследований бизнеса и экономики. - Москва : Финансовый университет при Правительстве Российской Федерации, 2015. - Т. 3, № 2. - 68 с. - ISSN 2308-944X. - Текст : электронный. - URL: https://znanium.ru/catalog/product/1014584 (дата обращения: 05.09.2026). – Режим доступа: по подписке.
Фрагмент текстового слоя документа размещен для индексирующих роботов
Review of 
Business and
Economics 
Studies

EDITOR-IN-CHIEF
Prof. Alexander Ilyinsky
Dean, International Finance Faculty, 
Financial University, Moscow, Russia
ailyinsky@fa.ru 

EXECUTIVE EDITOR
Dr. Alexander Kaffka

EDITORIAL BOARD

Dr. Mark Aleksanyan
Adam Smith Business School, 
The Business School, University 
of Glasgow, UK

Prof. Edoardo Croci
Research Director, IEFE Centre for 
Research on Energy and Environmental 
Economics and Policy, Università 
Bocconi, Italy

Prof. Moorad Choudhry
Dept.of Mathematical Sciences, Brunel 
University, UK

Prof. David Dickinson 
Department of Economics, Birmingham 
Business School, University of 
Birmingham, UK

Prof. Chien-Te Fan
Institute of Law for Science and 
Technology, National Tsing Hua 
University, Taiwan

Prof. Wing M. Fok
Director, Asia Business Studies, College 
of Business, Loyola University New 
Orleans, USA

Prof. Konstantin P. Gluschenko
Faculty of Economics, Novosibirsk State 
University, Russia

Prof. George E. Halkos
Associate Editor in Environment and 
Development Economics, Cambridge 
University Press; Director of Operations 
Research Laboratory, University of 
Thessaly, Greece

Dr. Christopher A. Hartwell
President, CASE - Center for Social and 
Economic Research, Warsaw, Poland

Prof. S. Jaimungal
Associate Chair of Graduate 
Studies, Dept. Statistical Sciences 
& Mathematical Finance Program, 
University of Toronto, Canada

Prof. Bartlomiej Kaminski
University of Maryland, USA; 

Rzeszow University of Information 
Technology and Management, 
Poland

Prof. Vladimir Kvint 
Chair of Financial Strategy, Moscow 
School of Economics, Moscow State 
University, Russia

Prof. Alexander Melnikov 
Department of Mathematical and 
Statistical Sciences, University of 
Alberta, Canada

Prof. George Kleiner
Deputy Director, Central Economics and 
Mathematics Institute, Russian Academy 
of Sciences, Russia

Prof. Kwok Kwong
Director, Asian Pacifi c Business 
Institute, California State University, Los 
Angeles, USA

Prof. Dimitrios Mavrakis
Director, Energy Policy and 
Development Centre, National and 
Kapodistrian University of Athens, 
Greece

Prof. Steve McGuire
Director, Entrepreneurship Institute, 
California State University, Los Angeles, 
USA

Prof. Rustem Nureev
Head of the Department of Economic 
Theory, Financial University, 
Russia

Dr. Oleg V. Pavlov
Associate Professor of Economics and 
System Dynamics, Department of Social 
Science and Policy Studies, Worcester 
Polytechnic Institute, USA

Prof. Boris Porfi riev
Deputy Director, Institute of Economic 
Forecasting, Russian Academy of 
Sciences, Russia

Prof. Svetlozar T. Rachev
Professor of Finance, College of 
Business, Stony Brook University, USA

Prof. Boris Rubtsov
Chair of Financial Markets and 
Financial Engineering, Financial 
University, Russia

Dr. Minghao Shen
Dean, Center for Cantonese Merchants 
Research, Guangdong University of 
Foreign Studies, China

Prof. Dmitry Sorokin
Deputy Rector for Research, Financial 
University, Russia

Prof. Robert L. Tang
Vice Chancellor for Academic, De La 
Salle College of Saint Benilde, Manila, 
The Philippines

Dr. Dimitrios Tsomocos 
Saïd Business School, Fellow in 
Management, University of Oxford; 
Senior Research Associate, Financial 
Markets Group, London School 
of Economics, UK

Prof. Sun Xiaoqin
Dean, Graduate School of Business, 
Guangdong University of Foreign 
Studies, China

REVIEW OF BUSINESS 
AND ECONOMICS STUDIES 
(ROBES) is the quarterly peerreviewed scholarly journal published 
by the Financial University under 
the Government of Russian 
Federation, Moscow. Journal’s 
mission is to provide scientifi c 
perspective on wide range of topical 
economic and business subjects.

CONTACT INFORMATION
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Russian Federation
Telephone: +7(499) 277-28-19
Website: www.robes.fa.ru

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by electronic mail to robes@fa.ru.

COPYRIGHT AND PHOTOCOPYING 
© 2015 Review of Business and 
Economics Studies. All rights 
reserved. No part of this publication 
may be reproduced, stored 
or transmitted in any form or by any 
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in writing from the copyright holder. 
Single photocopies of articles may 
be made for personal use as allowed 
by national copyright laws. 
ISSN 2308-944X

Вестник
исследований
бизнеса и 
экономики

ГЛАВНЫЙ РЕДАКТОР
А.И. Ильинский, профессор, декан 
Международного финансо вого факультета Финансового университета 

ВЫПУСКАЮЩИЙ РЕДАКТОР
А.В. Каффка

РЕДАКЦИОННЫЙ СОВЕТ

М.М. Алексанян, профессор Бизнесшколы им. Адама Смита, Университет 
Глазго (Великобритания)

К. Вонг, профессор, директор Института азиатско-тихоокеанского бизнеса 
Университета штата Калифорния, 
Лос-Анджелес (США)

К.П. Глущенко, профессор экономического факультета Новосибирского 
госуниверситета

С. Джеимангал, профессор Департамента статистики и математических финансов Университета Торонто 
(Канада)

Д. Дикинсон, профессор Департамента экономики Бирмингемской бизнесшколы, Бирмингемский университет 
(Великобритания)

Б. Каминский, профессор, 
Мэрилендский университет (США); 
Университет информационных 
технологий и менеджмента в Жешуве 
(Польша)

В.Л. Квинт, заведующий кафедрой 
финансовой стратегии Московской 
школы экономики МГУ, профессор 
Школы бизнеса Лассальского университета (США)

Г. Б. Клейнер, профессор, член-корреспондент РАН, заместитель директора Центрального экономико-математического института РАН

Э. Крочи, профессор, директор по 
научной работе Центра исследований 
в области энергетики и экономики 
окружающей среды Университета 
Боккони (Италия)

Д. Мавракис, профессор, 
директор Центра политики 
и развития энергетики 
Национального университета 
Афин (Греция)

С. Макгвайр, профессор, директор Института предпринимательства 
Университета штата Калифорния, 
Лос-Анджелес (США)

А. Мельников, профессор 
Депар та мента математических 
и ста тистических исследований 
Университета провинции Альберта 
(Канада)

Р.М. Нуреев, профессор, заведующий 
кафедрой "Экономическая теория" 
Финансового университета

О.В. Павлов, профессор 
Депар та мента по литологии 
и полити ческих исследований 
Ворчестерского политехнического 
института (США) 

Б. Н. Порфирьев, профессор, 
член-корреспондент РАН, заместитель директора Института 
народнохозяйственного прогнозирования РАН

С. Рачев, профессор Бизнес-колледжа Университета Стони Брук 
(США) 

Б.Б. Рубцов, профессор, заведующий 
кафедрой "Финансовые рынки и финансовый инжиниринг" Финансового 
университета

Д.Е. Сорокин, профессор, членкорреспондент РАН, проректор 
Финансового университета 
по научной работе

Р. Тан, профессор, проректор 
Колледжа Де Ла Саль Св. Бенильды 
(Филиппины) 

Д. Тсомокос, Оксфордский университет, старший научный сотрудник 
Лондонской школы экономики (Великобритания)

Ч.Т. Фан, профессор, Институт 
права в области науки и технологии, 
национальный университет Цин Хуа 
(Тайвань)

В. Фок, профессор, директор по 
исследованиям азиатского бизнеса Бизнес-колледжа Университета 
Лойола (США)

Д.Е. Халкос, профессор, Университет 
Фессалии (Греция)

К.А. Хартвелл, президент Центра 
социальных и экономических исследований CASE (Польша)

М. Чудри, профессор, Университет 
Брунеля (Великобритания)

Сун Цяокин, профессор, декан Высшей школы бизнеса Гуандунского 
университета зарубежных исследований (КНР)

М. Шен, декан Центра кантонских 
рыночных исследований Гуандунского университета (КНР)

Издательство Финансового 
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Тел. 8 (499) 277-28-19.
Интернет: www.robes.fa.ru.

Журнал "Review of Business and 
Economics Studies" ("Вест ник 
исследований бизнеса и экономики") зарегистрирован 
в Федеральной службе по надзору в сфере связи, информационных технологий и массовых 
коммуникаций 9 июля 2013 г. 
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Подписано в печать: 19.06.2015.
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Отпечатано в ООП Издательства 
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(Ленинградский проспект, д. 49).
16+

CONTENTS

Editorial

Alexander Didenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Using Intrinsic Time in Portfolio Optimization

Boris Vasilyev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Is There a Dividend Month Premium? Evidence from Japan

Cong Ta  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Analysis of Investors’ Strategies Using Backtesting and DEA Model

Dina Nasretdinova, Darya Milovidova, Kristina Michailova . . . . . . . . . . . . . . . . . . . 21

Using Elliott Wave Theory Predictions as Inputs 

in Equilibrium Portfolio Models With Views

Nurlana Batyrbekova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Some Stylized Facts about Analyst Errors

Oleg Karapaev  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Productivity Spillovers from Foreign Direct Investment in Vietnam

Thu Trang Le  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Exchange Rate Management in Vietnam 

for Sustaining Stable and Long-Term Economic Growth

Nguyen Hai An . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Infographics: Patterns of Information Flows 

Sharing and Volatility Spillovers

Valery Barmin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Review of 
Business and
Economics 
Studies

Volume 3, Number 2, 2015

CОДЕРЖАНИЕ

От редакции

Александр Диденко . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Использование внутреннего времени ценовых рядов 

в портфельной оптимизации

Борис Васильев  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Существует ли премия дивидендного месяца? Пример из Японии

Конг Та  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Анализ стратегий инвесторов с помощью 

использования бэктеста и DEA-модели

Дина Насретдинова, Дарья Миловидова, Кристина Михайлова  . . . . . . . . . . . . 21

Использование предсказаний волновой теории Эллиотта 

в моделях равновесных портфелей с суждениями

Нурлана Батырбекова  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Несколько стилизованных фактов об аналитических ошибках

Олег Карапаев . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Переливы продуктивности от прямых иностранных 

инвестиций во Вьетнаме

Тху Чанг Ле  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Управление обменным курсом для поддержки стабильности 

экономического роста во Вьетнаме

Нгуен Хаи Ань . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Инфографика: разделение информационных потоков 

и переливы волатильности

Валерий Бармин  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Вестник
исследований
бизнеса и 
экономики

№ 2, 2015


 

Editorial*

*От редакции.

Importance of information value issues in finance and 
economics can hardly be overestimated. Information is 
reflected (or not) in market prices; price itself could be 
used to predict major turmoils in economy; information 
use (or misuse) determines asset managers performance 
(or underperformance); market participants use 
information about central banks’ actions and econometric 
links between major macroeconomic variables to form 
their expectations about inflation and exchange rates; 
investment bankers use information about firm’s past 
fundamentals to hypothesize on its future value; local 
fi rms can learn from actions of multinational enterprises –
i.e. copy information – to increase productivity, etc. 
Coincidence or not, but each paper in the current, 7th, issue 
of Review of Business and Economic Studies is somehow 
related to various aspects of the information impact on 
performance of fi rms, markets, its actors, and economy as a 
whole. And this is the reason why we’ve chosen to dedicate 
infographics on the second page of the cover to the topic of 
stock market information fl ows impact on each other. The 
model, outputs of which are visualized by Valery Barmin, 
allows to capture some aspects of information sharing 
regime changes as a result of crises. In fact, during major 
economic turmoils, regional information sets (i.e. sets 
that are supposed to be relevant only for regional stocks) 
become more globalized, market participants are sharing 
the same news flow. We can hypothesize, that under 
extreme uncertainty traders (probably, irrationally) are 
looking for any additional information piece, which could 
shed light on future. In turn, that leads to spontaneous 
coordination of market participants, which makes assets 
co-move together in times of fi nancial turmoil. Further, we 
can observe some signs of habit formation: there is some 
evidence, though weak, that when situation stabilizes, 
information fl ow sharing decreases, but general patterns 
sustain, leading to more co-movement between assets. 
Assets co-movement, especially during crises, 
brings its own risks, creating huge obstacle to 
diversifi cation. Quality of diversifi cation is obviously 
one of the most disputable topics in modern 
quantitative finance. Boris Valilyev’s piece "Using 
Intrinsic Time in Portfolio Optimization" in current 
issue of our journal contributes to the field in two 
important ways. He uses mixture of distribution 
hypothesis to obtain nearly-normal returns, which 
then can be used to calculate historical estimates 
of market returns. His approach assumes applying 
concept of intrinsic time, which became well-known 
since seminal work by Clark, published in 1973 in 

Econometrica1. Boris Vasilyev deforms return series 
timescale across volume domain. By doing that he 
obtains series, that are slightly asynchronous in time 
domain, but instead synchronous in volume domain. 
According to mixture of distribution hypothesis, 
volume could be regarded as proxy for information 
arrival process, and information is regarded as 
the sum of all the forces, that drive prices. Returns 
are almost normal, but can we use asynchronous 
returns when building portfolio, which assumes 
simultaneity in trading? Boris Vasilyev offers his 
own solution to the problem; and by doing it, he, at 
the same time, develops his own way of covariance 
matrices robust estimation, which has solid ground 
in economic science. Empirical analysis performed 
by Vasilyev shows, that raw estimates of covariance 
matrices, obtained through this procedure, appear 
to be superior in terms of diagonality even to 
shrinked estimates. Efficiency frontiers built with 
these estimates strongly dominate frontiers build 
using all traditional approaches. This is defi nitely a 
breakthrough in portfolio management science. 
Another important and disputable issue in 
finance is what part of information set is reflected 
in prices. Ta Cong in his paper "Is There a Dividend 
Month Premium? Evidence from Japan" discusses, 
how stock market responds to news about firm’s 
dividend distribution decisions. Although he uses 
standard approach of building with-dividends and 
without-dividends portfolios and regressing its 
returns in CAPM, Fama-French and Carhart models, 
his findings contradict to previous evidence. He 
postulates regional differences in market reaction 
to dividend announcements. Dividend payers have 
always been regarded as value companies, paying 
to investor a premium over growth firms; but on 
Japanese market, as Ta Cong shows, dividend payers 
have negative premium over dividend non-payers. 
In fact, this means that information about dividends 
have negative value to investors in Japanese market –
a puzzling fi nding. 
The paper "Analysis of Investors’ Strategies Using 
Backtesting and DEA Model" by Dina Nasretdinova, 
Darya Milovidova and Kristina Michailova approaches 
issues of fi rm fundamentals relevance from completely 
different angle. They analyse stock market public 
strategies of 30 investment "gurus", as they were 
popularized in their books. These strategies use 

1 Clark, P.K. (1973), "A Subordinated Stochastic Process 
Model with Finite Variance for Speculative Prices", Econometrica, 41, 135–155.


 

various sets of fundamentals to build portfolios 
of stocks. Common sense would suggest that this 
information has no value at all, since strategies were 
made public long ago, and all possible excess profi ts 
could easily be wiped by rational arbitragers. 
Approach of Nasretdinova, Milovidova and 
Mikhailova assumes using simulation of trades of 
famous market forecasters, inferred from description 
of their strategies; their goal is to determine, which 
strategy of information set usage (if any) is superior 
to others. Instead of relying to one of the classic 
parametric approaches (like regressing returns in 
CAPM/Fama-French/Carhart, as in Ta Cong’s paper), 
they use data envelopment analysis to determine 
strategies’ relative superiority in multi-criterial 
KPI-like sense. Authors have found, that some 
strategies do demonstrate sustainable superiority in 
performance, and, moreover, these strategies could be 
exposed either to value or growth risks, or even both; 
hence not information set itself, but the strategy 
of its usage contributes to performance. We can 
mention at least one seminal paper, which supports 
that result from different point of view, namely 
series of papers by Brinson, Hood and Beebower on 
importance of investment policy of funds2. 
Nurlana Batyrbekova in her paper "Using Elliott 
Wave Theory Predictions as Inputs in Equilibrium 
Portfolio Models With Views" uses approach, 
similar to the one taken by authors of previous 
piece. She studies, whether market revelations of 
one of the Elliott Wave Theory proponents, Robert 
Prechter, do have some real value for predicting 
the market. Conceptually, she paves the way of 
Brown, Goetzmann, and Kumar3, who used to 
backtest predictions of Dow Theory proponent, 
William Peter Hamilton. Further, she augments their 
approach with Bayesian portfolio decision using 
Black-Litterman portfolio optimization framework. 
She fi nds that while overly concentrated, high-risk 
portfolios are underperforming the benchmark, 
combining predictions with diversifi cation beats both 
the benchmark and diversified portfolios without 
Prechter’s simulated views. Hence, Prechter’s market 
ruminations, despite all the haziness and adhocism 
inherent to Elliott Wave Theory, could bring some 
value to market participants. 
Oleg Karapaev further contributes to information 
value issues in the following way. In his paper, "Some 
Stylized Facts about Analyst Errors", he questions 

2  Gary P. Brinson, L. Randolph Hood, and Gilbert L. Beebower, "Determinants of Portfolio Performance," Financial 
Analysts Journal (1995): 133–138.
3  Stephen J Brown, William N. Goetzmann, and Alok Kumar, "The Dow Theory: William Peter Hamilton’s Track Record Reconsidered," The Journal of Finance 53, no. 4 (1998): 
1311–1333.

possible reasons of low accuracy of broker sell-side 
recommendations. Brokers are supposed to use all 
relevant information, be it publicly available or 
insider, to estimate future stock prices and market 
fundamentals; they use the latter to build discounted 
cash flows models, and to infer fair price from it. 
Sometimes brokers fail to forecast prices; sometimes 
they fail to forecast fundamentals as well. Possible 
questions here could be: is there some significant 
difference in forecast errors for fundamentals as 
compared to prices? If so, the reason of error could be 
in denominator of DCF model, i.e. in discount term, 
which incorporates time-varying risks perception. 
Further, are there some differences in errors across 
industries or investment styles? In other words, 
can we say that some fundamentals are harder to 
predict due to specifi c uncertainties of the industry 
or business model or fi rm lifecycle period? Do errors 
of consensus forecast depend upon the number of 
brokers covering the stock? This is a sketch of a grand 
research programme, and Oleg Karapaev in his paper 
formulates just some stylized facts and makes fi rst 
attempt of conceptualization. 
Le Thu Trang takes completely different angle in 
"Productivity Spillovers from Foreign Direct Investment 
in Vietnam", researching how information about best 
practices in industry affects firm productivity and 
hence – economic growth. She applies classic approach 
– total factor productivity estimation through data 
envelopment analysis, with subsequent regression 
of panel of various factors to TFP – to Vietnamese 
data, and contributes to evidences of positive impact 
of foreign direct investments by multinational 
corporations on local industries. 
Finally, we close the 7th issue of ROBES with 
paper "Exchange Rate Management in Vietnam for 
Sustaining Stable and Long-Term Economic Growth" 
by Nguyen Hai An. His findings are complementary 
to results of Le Thu Trang. Nguyen Hai An builds 
macroeconometric model linking inflation and 
trade balance with exchange rate, price for credit, 
and money supply. Author fi nds that while currency 
depreciation impacts inflation, information about 
exchange rate alone could not explain trade balance 
change. Hence, policy advice could be inferred, that 
government should focus on stabilizing exchange 
rate to make inflation more predictable for firms, 
and on enhancing the quality of exported goods to 
improve fi rms competitiveness. Probably, that could be 
achieved, among other measures, by creating stimuli 
for multinational enterprises to be more active in 
direct investments to industries.
Alexander DIDENKO, Ph.D.
Head of Research Planning and Support
Financial University, Moscow 


 

INTRODUCTION

Soon after the publication of "Portfolio Selection" by 
Harry Markowitz (1952) that is mostly referred to as 
a seminal work for modern portfolio theory based on 
mean-variance analysis (referred herein after to as 
"MVO"), it became evident that the original method 
presented therein resulted in low-diversifi ed and unstable portfolios leading to overtrading and excessive 
risks. Along with increasing the number of assets in 
optimization universe these drawbacks even aggravated, and that most probably motivated Markowitz to introduce initial linear constraints to the process which 
were described in his work (1956) published several 
years later and gave ground to numerous modifi cations 
and developments to the MVO process ever since.

OVERTRADING

With respect to MVO excessive trading activity is 
mainly stemmed from frequent portfolio rebalancing 

that leads to placing additional open or close market 
orders to meet new assets allocation. A major cause 
of such instability is a combination of factors comprising unavoidable presence of estimation errors 
within input data from one hand, and high sensitivity of MVO to even minor changes in inputs, from 
the other. Hypothetically, if input data would be free 
of such errors inside, the optimization would definitely provide effi cient or optimal portfolio composition. In reality the inputs are statistical estimates 
derived from or generated on the basis of historical 
data and bear some portion of disturbance inside. 
Michaud (1986) posited such inaccuracy results in 
overinvestment in some securities or assets and underinvestment in others. For example, with two assets like A and B, such as A’s true expected return is 
slightly lower than that of B, but standard deviation 
is slightly higher, and provided both assets returns 
have identical correlations with the returns for each 
of the other assets the portfolio universe, asset B is 
preferred among these two, and if the inputs are free 

Using Intrinsic Time 
in Portfolio Optimization*

Boris VASILYEV
International Financial Laboratory, Financial University, Moscow
b_va@hotmail.com

Abstract. The concept of intrinsic time was introduced in Mandelbrot’s paper circa 1963 and further developed 
in discussion paper by Muller et al. (1993).  As reported by Didenko et al. (2014), there are some evidences 
that sampling price series in volume domain results in almost normal returns, which could help to overcome 
some common issues in portfolio optimisation. First, we briefl y survey fl aws of classic approach to portfolio 
optimisation, then we test for statistical properties of intrinsic-time sampled return series, theorize on how 
intrinsic time could help in handling issues of portfolio optimisation, and then empirically test our guesses. We 
show that using intrinsic time helps in overcoming such fl aws of Modern Portfolio Theory as poor diversifi cation 
and reliance on normality of returns.

Аннотация. Концепция внутреннего времени была введена в работе Mandelbrot 1963 года и далее 
развита в докладе Muller с соавторами (1993). Недавнее исследование Диденко с соавторами (2014) 
предоставило  ряд свидетельств о том, что свертка ценовых рядов по объемам приводит к квазинормальности доходностей активов. Этот феномен можно использовать в портфельной оптимизации. 
Наша работа начинается с краткого обзора основных проблем современной портфельной теории. Далее мы 
тестируем нормальность рядов при различных параметрах свертки по объемам и эмпирически тестируем 
пригодность такой свертки в портфельной оптимизации. Наши результаты показывают, что свертка 
по объемам позволяет преодолеть такие недостатки СПТ, как слабая диверсификация и предположение 
о нормальности доходностей.

Key words: Intrinsic time, modern portfolio theory, portfolio optimisation, returns normality.

* Использование внутреннего времени ценовых рядов в портфельной оптимизации.