Review of Business and Economics Studies, 2015, том 3, № 2
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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 Financial University Oleko Dundich St. 23, 123995 Moscow Russian Federation Telephone: +7(499) 277-28-19 Website: www.robes.fa.ru AUTHOR INQUIRIES Inquiries relating to the submission of articles can be sent 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 means without the prior permission 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
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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)
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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
Review of Business and Economics Studies Volume 3, Number 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.
Review of Business and Economics Studies Volume 3, Number 2, 2015 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
Review of Business and Economics Studies Volume 3, Number 2, 2015 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.
Review of Business and Economics Studies Volume 3, Number 2, 2015 of estimation error, it dominates A. But if such errors resides the input data, asset A may have an estimated expected return that is higher, and an estimated standard deviation hat is lower than that of B. In this case, portfolio optimization will erroneously assign a higher weight for A than for B. Moreover, estimation error may fl uctuate around zero over time, and having the same true expected values for A and B in future, the optimizer may generate the opposite result affected by changing estimation error that will lead to dramatic rebalancing of portfolio. High MVO sensitivity to a minor change in the data for input can therefore lead to a dramatic change in overall portfolio composition. Thus, an update that bears a slight change in expected return or standard deviation for one asset can result in radical portfolio reconstruction, rebalancing weight not only for this particular asset, but reallocating all the assets from the universe under consideration. Such potential recomposition results in excessive trading on the portfolio deemed necessary to meet new allocations each time the inputs change. Overtrading is usually associated with two main problems such as increased possibility of capital loss and excessive transaction costs. First mainly results from overinvestment in few assets that is evident for low-diversifi ed concentrated portfolios. The inputs for MVO are always estimates that may be quite far from the true values in future. Thus, if the market turns against the investor, low portfolio diversifi cation, i. e. allocation into fewer assets, will increase potential losses. In this case if the investor utilizes the leverage the losses are even magnifi ed and may exceed investor’s capital. Another issue is transaction costs. They are often fi xed, and in total therefore dependant on the number of trades executed. Frequent assets re-allocation results in higher transaction costs that harmfully affect the return of the portfolio and hence overall profi tability of the investment. The problem of excessive turnover and overinvestment in fewer assets can be settled by introduction of specifi c constraints into MVO process. These may limit minimum and maximum weights for one asset (or class of assets) and/or preset minimum number of assets to be included in the portfolio to ensure proper level of its diversifi cation. Transaction costs may be reduced by composition of more stable portfolios. For example, Lummer et al. (1994) proposed for this purpose to use sensitivity analysis allowing to diminish dramatic changes in recommended portfolio due to minor changes in inputs. This method implies selecting an effi cient portfolio and then altering the MVO inputs to construct a set of portfolios with new inputs, and then to examine how close they are to the initial effi cient one. The goal is to fi nd a set of asset weights that will be close to effi cient proportion under several different sets of plausible inputs. On the other hand, expected benefi t from any reallocation advised by MVO can be assessed with respect to relevant transaction costs necessary for its execution. EXPECTED RETURNS Yet another question for MVO is that the theory implies expected returns as an input. They cannot be known directly from the market, but only estimated commonly on the basis of its past data, that leads to unstable portfolio weights. MVO would generate a perfect solution if the inputs would be true expected returns and the variance matrix. In reality the estimates of expected returns mostly consist of noise and estimates of the variance matrixes are very noisy too. Scherer (2002) noted that "mean-variance optimization is too powerful tool for the quality of our data". The main problem is to estimate expected returns with suffi cient accuracy. There are several main methods published to resolve this issue. For example, Black and Litterman (1992) proposed to estimate the expected returns by combining Capital Asset Pricing Model (CAPM) equilibrium and subjective investor views. However, investor’s assumptions for the market must be also specifi ed with numbers for both the expected returns and the uncertainty that may be considered as a drawback for this approach. Another way is the Arbitrage Pricing Theory (APT) that was described by Ross (1976) and was intended to model returns of the assets (for the discrete time) as a linear combination of independent factors. The APT constructs expected returns as statistical estimates to fi t historical data that in turn may also lead to unstable allocations. Another empirical way of expected returns estimation is to apply for consensus forecasts of professionals participating in market activity. Informational vendors (such as Bloomberg) provide this opportunity to its subscribers. However, the experience proves their expectations are usually drop far from true values, at least as far as single assets predicts are concerned. Meanwhile, the empirical expectations with respect to cumulative indexes prove to be much more accurate. This allows to use a single index model as an instrument of expected return estimations using index estimation as the only macroeconomic parameter to influence particular asset expected return. Multifactor models are not that simplifi ed and imply regression analysis based on several factors such as, for example, indexes by various industry sectors. They are more detailed in assessment of expected returns
Review of Business and Economics Studies Volume 3, Number 2, 2015 than single index models as consider any stock dependence not on general index, but on the index of corresponding sector. However, multifactor models also provide quite rough estimations within wide confi dence intervals. Following MVO routine, once input parameters have been estimated, it performs optimization assuming all inputs are certain and estimation errors are introduced into the process of allocation. Various approaches exist to stabilize the optimization results with respect to estimation errors, which can be distinguished in two main ways. The fi rst approach implies to reduce the estimation errors of the input parameters via econometric methods. For example, to reduce the impact of noise estimation Michaud (1998) used the resampling method. The idea behind it is that real returns are very noisy. As the optimization procedure is very unstable depending on small changes in inputs, the portfolio should be optimized over sets of similar return series that are randomly generated following some preset parameters. On average, noise should be evened out. Thus, starting with original return series, some new series are generated with small amounts of noise to the original series. Then MVO procedure runs over all series and eventually results in a set of different optimal portfolios composed for a same expected returns level. The average over all optimal portfolios is expected to be more stable with respect to errors in the input data. The second way is to shrink directly the weights in portfolio using bounds, penalties for the objective function or regularization of input parameters. Jagannathan and Ma (2003) showed that imposing constraints on the mean-variance optimization can be interpreted as a modification of the covariance matrix. In particular, lower (upper) bounds decrease (increase) the variances of asset returns. Thus, constraints imposed on weights can reduce the degree of freedom of the optimization, and the allocation remains then within certain intervals. But the correction of estimation errors proved to be such difficult task that some studies were devoted to show that heuristic allocations perform even better than MVO-generated ones with respect to Sharpe ratio. For example, DeMiguel et al. (2009) assessed the performances of 14 different portfolio models and the equally-weighted portfolio on different datasets and come to conclusion that detailed and sophisticated models did not produce a better optimization than the naïve equally-weighted portfolio. As a result, Lindberg (2009) mentioned one more way to deal with the problem of expected returns estimation that is simply ignoring them. This method is stemmed from the classical 1/n strategy, which simply puts 1/n of the investor’s capital in each of n available assets. No doubt, this strategy should be well diversified. However, covariation between different assets may refrain this from being the case, and as it is possible to obtain rather good estimates of covariations between assets returns, this information can be also used in portfolio construction. Later, Fernholz (2002) has proposed to consider expected returns as dependant on ranks. These ranks can be established, for example, based on the market capital distribution. Thus, rank 1 can be assigned to the asset with the highest market capitalization, rank 2 to the next highest, and so far. A paper by Almgren and Chriss (2005) presented a portfolio optimization method which utilized such ordering information instead of expected returns. It uses information about the order of the expected returns as the MVO inputs instead of the very estimates. This approach also benefi ts from extended use of covariance information. NORMALITY OF RETURNS Assets returns follow some statistical distribution and its form is an issue of highest importance for fi nancial modeling in general and MVO in particular. Basic assumptions on market prices behavior are required to perform a testing of asset pricing models, to optimize portfolios by computation of risk/return effi cient frontiers, to assess derivatives and determine the hedging strategy over time, as well as to measure and manage financial risks. However, neither economic nor statistical theory appears to succeed in determination of exact type of returns distribution. Thus, distributions used in empirical and theoretical research are commonly derived from an assumption or estimation of data used. The overall belief adopted in fi nances is that this is the normal (Gaussian) distribution. Although returns normality is the standard in fi nancial modeling, some alternatives have been also considered mainly due to evidence that the Gaussian distribution tends to underestimate the weight of the extreme returns contained in the distribution tails as well as the returns fallen around the mean. For example, Longin (2005) noted that during the stock market crashes (such as in 2008) daily market drops can exceed 20% that can hardly be explained within normality universe. In response, several other distributions have been proposed by the scholars, who tried to apply them, however without evident success: a mixture of Gaussian distributions, stable Paretian distributions, Student t-distributions and the class of ARCH processes. Main shortcoming of all these alternatives is that they are not nested and their adequacy
Review of Business and Economics Studies Volume 3, Number 2, 2015 therefore cannot be directly compared, for example, by a likelihood ratio test. On the other hand, MVO’s intended outcome is to fi nd an optimal portfolio that means to maximize investor’s utility function. In case this utility function is not quadratic, but generally represented with any upward concave form, expected utility function should depend on the portfolio return’s values only. Such distributions must be the two-parameter ones, i. e. should be fully explained by their fi rst two moments — mean and variance, which are also implied to express the higher order moments, e. g. skewness and kurtosis. Several distributions, such as the normal, lognormal, or gamma ones satisfy this criterion well. However, with respect to the problem of portfolio optimization, the distribution in question should also satisfy one more criterion. Portfolio optimization deals with a universe of assets (or other portfolios), and an investor selects which assets to include into portfolio. Thus, all portfolios composed by combination of individual assets must also follow some distribution that can be fully explained by their means and variances. The distribution therefore must comply with a criterion that both individual assets’ returns distribution should depend on just their mean and variance, and the distribution of returns of a portfolio (combination) of these assets meets the same requirement. The only distribution that is suitable to comply with it and has fi nite variance is the normal Gaussian one. As a result, the paradigm in fi nance is that MVO can be successfully applied only provided asset returns follow the normal distribution that is determined by its two first moments, means of returns and their variances. The third and fourth moments of distribution, that are, in particular, the skewness and kurtosis can be also theoretically added to the utility to refl ect and explain a non-normality of returns, but it is believed that skewness is close to impossible to predict and the predictability of kurtosis is considerably limited, either. INTRINSIC TIME MVO is intended to answer a very natural question: if the exact parameters are known, which portfolio maximizes the expected return for pre-specifi ed level of risk, or which portfolio minimizes the risk for prespecifi ed rate of expected return? This would be all the investor would need to have an optimal portfolio and be happy enough with it. However, among others, the issues described above bring some bitter stuff into reality. "Exact parameters" that are needed ad hoc, proved to be uncertain, noisy and lead the optimizer to unstable results with underestimated risks. However, it becomes evident the main problem for all these issues is that asset returns are not normally distributed. This is a reason why the investor cannot accurately estimate expected returns, has problems with unstable solutions, rebalancing, and hence with overtrading and other bad things. Realized returns values refrains the investor from a clear view of true normal distribution that exists in the market, but is hidden by noise. It is widely assumed that this is the way things are, and for the purpose of this work, in particular, it is implied as a true. Based on inherent normality of returns distribution, most of the scholars propose various approaches how to adjust realized market returns to suit Gaussian framework by introducing new parameters that make the models more and more complicated. At some extent, it becomes evident that many of such sophisticated models perform worse than simplest naïve portfolios, and hence are discarded. But one point remains unchanged: the source data is taken from the market and then is converted into returns addressed for statistical manipulations. On the other hand, it is known that the proximity of returns distribution to Gaussian normality is not stable over different time intervals and commonly increases with decrease of the frequency. For example, the distribution of monthly returns is closer to the normal one than that of days, hours or minutes. The cause is deemed to be that the higher time intervals have relatively lower proportion of noise within the returns, but anyway it is obvious the proximity of returns distribution to the normal on depends on time. It fl ows constantly by seconds, minutes, etc. And it is also obvious, but not for the market! One minute at the middle of trading day is not the same as one minute right before it is being closed. Hence, a question: how can one consider all time spans during the day in the same manner? This understanding may explain (at least partially) the non-normality that all involved have got accustomed to observe. Next question is what can be used to measure this difference in the same intervals of time, or to tick market intrinsic time clock. Volatility is usually higher during periods of active trading (when our time should go "faster") and, conversely, is lower over nonactive trading ones (when our time goes "slower"). But it is not so easy to estimate it independently, and its value represents the situation non-equally depending on volumes traded, that seems itself to be much more interesting to implement. Traded volumes can generally refl ect the level of market activity and this parameter is usually available as provided among common market data. The bars can be now formed as based not on astronomic time interval expiration (end of second,
Review of Business and Economics Studies Volume 3, Number 2, 2015 minute, hour, etc.), but when the traded volume achieves certain pre-set value since last closed bar formed by the same method. It can be considered as market intrinsic time. Such time dimension — cumulative volume bar (referred hereinafter to as "CVB"), will not coincide with astronomic time, but is expected to better refl ect the nature and the mood of the market. The CVB returns are expected to achieve closer proximity to normal distribution as much of usual noise may prove to be in fact the messed data of neighbor conventional (astronomic timed) bars, that is going to disappear in case of CVB accounting for market activity. CVB approach as market intrinsic time can potentially provide a better solution for all of above described issues. And the most interesting is that it may allow to use MVO it its original form, without complicated modifi cations and add-ons. More stable portfolios avoid overtrading, expected returns have lower estimation errors as returns distribution is close to the normal one, realized returns noise is diminished. CVB PROXIMITY TO NORMAL DISTRIBUTION Although the data generated by the market is believed to be normally distributed, it is full of noise that prevents investors from gaining benefi ts associated with this normality. The proportion of such disturbances, however, in overall price movements tends to decrease along with increasing of time intervals size taken for consideration. It mainly results from the magnitude of the market swings that are evidently bigger within less frequent intervals, while the noise component rises slower and steadily fades out. The returns for yearly intervals are much closer to normally distributed data than the returns for minute frequency. Higher intervals, however, cannot often be useful enough for active trading and this makes it clear that normalization of more frequent data would be a matter of the highest interest for investors. As the returns derived from CVB are believed to be closer to normal distributed data than the regular ones (based on conventional astronomic time bars — referred hereinafter to as "conventional returns"), we have conducted a comparison of both types. CVB concept posits that the bar is closed not with a tick of a clock as usual, but when the volume of trades for particular asset achieved certain preset value. Thus, such intrinsic time is individual for every asset as particular trading volumes are believed impossible to coincide across the market. To fulfi ll an experiment we have taken one minute data for a period of one year 2013 for top ten assets of Russian stock market1 and have compared the proximity to normal distribution for the returns generated by conventional bars data and CVBs. CVB composition is performed as iterations for trading volumes increasing from 100,000 to 40,000,000 with a step of 100,000. For every asset, one minute bars volumes from original source data files are added up until the sum achieves the value of current iteration. Then the current CVB is considered as closed, and the loop starts the same routine for next CVB. Any next iteration obviously produces less bars than the previous one as it collects more conventional bars to achieve increased target volume, i. e. generates higher intervals that may itself bring the results closer to normality. To offset this infl uence and to assess the contribution of the very CVB concert rather than the benefi t of a scale, we also generate conventional bars of similar range. When any iteration if fi nished, it brings the fi nite number of CVBs generated. Dividing original source data fi le length by this number we can obtain the number of conventional bars in the interval that corresponds to one newly generated CVB. Then we compose new conventional bars dataset relevant to this particular 1 Data is available at: http: //www. fi nam. ru/analysis/profi le041CA00007/, [accessed 25 February 2015]. Figure 1. Deviation of observed returns from normally distributed data.
Review of Business and Economics Studies Volume 3, Number 2, 2015 CVB set and compare proximity to normally distributed data with the same mean and standard deviation for both generated datasets. Figure 1 presents the results for common shares of GAZP (Gazprom) and SBER (Sberbank). Other assets examined provide similar pictures. Deviation from normal distribution diminishes with interval rise for returns based on both conventional bars and CVBs, but the latter present higher rate and gets times lower in the left part of the charts. By the end of iterations the conventional returns row tends to reach CVB ones, although CVBs still provide lower values within the range of observation. As a result we may posit that CVB approach allows obtaining returns that are closer to normally distributed than the conventional bars. This advantage becomes specifi cally evident on smaller time intervals, but proceeds even further, although not that dramatically. The application of CVB may encounter some complexities stemmed from the fact that every asset now exists in the market at its own time. But this problem may be solved for practical purposes of optimization as described below. PORTFOLIO OPTIMIZATION USING CVB Portfolio Theory by Harry Markowitz gives ground to numerous mean-variance optimizers most of which attempt to improve the method and to bypass its known drawbacks as described above. Thus, we believe it is interesting to compare portfolio optimization by original mean-variance analysis performed on conventional and CVB based data, as CVB brings no modifi cation to optimization process itself, but just rearranges the data to input. For this purpose we take one minute interval data (also provided by Finam) for a period from June 2008 till end of December 2014 for top ten Russian stocks. The start date was taken that as one of the participants (particularly HYDR — Rushydro) was listed just at the end of May 2008, and we have no data for processing beyond this point. The portfolio is intended to be rebalanced on a weekly or monthly basis. Here we encounter a problem rising from individual CVB time for each participant of our universe to optimize. Going common way we cannot rebalance the portfolio based on CVB as the bars of all participating assets close differently, and there is no conventional uniform cut-off time. This issue can be solved by several means, but we use one as follows. As CVB is intended to arrange the data in a more natural way, there is no difference which direction such a composition goes to. In other words, returning back to the Figure 1 above, CVB construction performed from the last data point backward to the first one would produce the same result in the chart. Thus, we can perform portfolio optimization at any point of conventional time if constructing CVB row backward from this point. Similar to the way we used in the experiment on proximity to normal distribution, at every point of portfolio optimization we imitate conventional row by CVBs one to compare with the most suitable. For example, if we perform monthly optimization for the point X of conventional data and use therefore X months of previous data, we adjust CVB dataset accordingly. Particularly, we derive total trading volume for each asset for whole the period till point X, and then we divide it by X — the number of months taken for optimization. It results in the value of average volume per month which becomes a target volume for CVB composition. It is defi nitely the easiest way that does not take into account, for example, global changes in volumes across all periods that may be signifi cant for Russian market and can be introduced by averages, but we leave it out of this research for the sake of simplicity. Once we have the target value for volume, we can construct CVBs starting from X point. The number of CVBs is also X that is the last point of both conventional and CVB datasets that are now equally sized and ready for input to the optimizer. Figure 2. Static Transition Maps.