Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Essays on pricing of risk and international linkage of Russian stock market

Last two decades have seen a rapid change in the global economic and financial situation; the economic conditions in many small and large underdeveloped countries started to improve and they became recognized as emerging markets. This led to growth in the amounts of global investments in these countries, partly spurred by expectations of higher returns, favorable risk-return opportunities, and better diversification alternatives to global investors. This process, however, has not been without problems and it has emphasized the need for more information on these markets. In particular, the liberalization of financial markets around the world, globalization of trade and companies, recent formation of economic and regional blocks, and the rapid development of underdeveloped countries during the last two decades have brought a major challenge to the financial world and researchers alike. This doctoral dissertation studies one of the largest emerging markets, namely Russia. The motivation why the Russian equity market is worth investigating includes, among other factors, its sheer size, rapid and robust economic growth since the turn of the millennium, future prospect for international investors, and a number of important major financial reforms implemented since the early 1990s. Another interesting feature of the Russian economy, which gives motivation to study Russian market, is Russia’s 1998 financial crisis, considered as one of the worst crisis in recent times, affecting both developed and developing economies. Therefore, special attention has been paid to Russia’s 1998 financial crisis throughout this dissertation. This thesis covers the period from the birth of the modern Russian financial markets to the present day, Special attention is given to the international linkage and the 1998 financial crisis. This study first identifies the risks associated with Russian market and then deals with their pricing issues. Finally some insights about portfolio construction within Russian market are presented. The first research paper of this dissertation considers the linkage of the Russian equity market to the world equity market by examining the international transmission of the Russia’s 1998 financial crisis utilizing the GARCH-BEKK model proposed by Engle and Kroner. Empirical results shows evidence of direct linkage between the Russian equity market and the world market both in regards of returns and volatility. However, the weakness of the linkage suggests that the Russian equity market was only partially integrated into the world market, even though the contagion can be clearly seen during the time of the crisis period. The second and the third paper, co-authored with Mika Vaihekoski, investigate whether global, local and currency risks are priced in the Russian stock market from a US investors’ point of view. Furthermore, the dynamics of these sources of risk are studied, i.e., whether the prices of the global and local risk factors are constant or time-varying over time. We utilize the multivariate GARCH-M framework of De Santis and Gérard (1998). Similar to them we find price of global market risk to be time-varying. Currency risk also found to be priced and highly time varying in the Russian market. Moreover, our results suggest that the Russian market is partially segmented and local risk is also priced in the market. The model also implies that the biggest impact on the US market risk premium is coming from the world risk component whereas the Russian risk premium is on average caused mostly by the local and currency components. The purpose of the fourth paper is to look at the relationship between the stock and the bond market of Russia. The objective is to examine whether the correlations between two classes of assets are time varying by using multivariate conditional volatility models. The Constant Conditional Correlation model by Bollerslev (1990), the Dynamic Conditional Correlation model by Engle (2002), and an asymmetric version of the Dynamic Conditional Correlation model by Cappiello et al. (2006) are used in the analysis. The empirical results do not support the assumption of constant conditional correlation and there was clear evidence of time varying correlations between the Russian stocks and bond market and both asset markets exhibit positive asymmetries. The implications of the results in this dissertation are useful for both companies and international investors who are interested in investing in Russia. Our results give useful insights to those involved in minimising or managing financial risk exposures, such as, portfolio managers, international investors, risk analysts and financial researchers. When portfolio managers aim to optimize the risk-return relationship, the results indicate that at least in the case of Russia, one should account for the local market as well as currency risk when calculating the key inputs for the optimization. In addition, the pricing of exchange rate risk implies that exchange rate exposure is partly non-diversifiable and investors are compensated for bearing the risk. Likewise, international transmission of stock market volatility can profoundly influence corporate capital budgeting decisions, investors’ investment decisions, and other business cycle variables. Finally, the weak integration of the Russian market and low correlations between Russian stock and bond market offers good opportunities to the international investors to diversify their portfolios.

Risk Parity: A Modern Tool for Diversification

The purpose of this study is to examine how well risk parity works in terms of risk, return and diversification relative to more traditional minimum variance, 1/N and 60/40 portfolios. Risk parity portfolios were constituted of five risk sources; three common asset classes and two alternative beta investment strategies. The three common asset classes were equities, bonds and commodities, and the alternative beta investment strategies were carry trade and trend following. Risk parity portfolios were constructed using five different risk measures of which four were tail risk measures. The risk measures were standard deviation, Value-at-Risk, Expected Shortfall, modified Value-at-Risk and modified Expected Shortfall. We studied also how sensitive risk parity is to the choice of risk measure. The hypothesis is that risk parity portfolios provide better return with the same amount of risk and are better diversified than the benchmark portfolios. We used two data sets, monthly and weekly data. The monthly data was from the years 1989-2011 and the weekly data was from the years 2000-2011. Empirical studies showed that risk parity portfolios provide better diversification since the diversification is made at the risk level. Risk based portfolios provided superior return compared to the asset based portfolios. Using tail risk measures in risk parity portfolios do not necessarily provide better hedge from tail events than standard deviation.

The Evolution of Securities Lending and Risk Mitigation: A Finnish Market Case Study

Although securities lending is an important function of the financial markets, it has not received that much academic attention. This study examines the evolution of European securities lending and risk management with an emphasis on the development of collateral management, the function responsible for reducing credit risk. The effects of the recent financial instabilities are also considered. The evolution of the Finnish securities lending market is examined in more detail through a case-study. This study can be classified as a constructive qualitative case study. The initial practical knowledge comes from the author's own experience and additional insight and theoretical background is acquired through a literature review. The case study is based on research, semi-structured interviews and a brief analysis of numerical data. The main observation of this study was that securities lending is now recognized as more of an investment management discipline than an operational support function. The recent financial instabilities have resulted in an increased focus on risk and transparency. In securities lending this is directly reflected in collateral management guidelines and procedures. Collateral management has become increasingly technologically developed and automated. Collateral optimization initiatives have been started to make the process more efficient, liquid, and cost effective. Although securities lending is generally an OTC-market with no standard market place, centralized exchange-like models have been introduced. Finnish securities lending has now shifted towards the more common global OTC model. Although the Finnish securities lending industry has developed, and the main laws governing it (tax legislation) have changed, there is still need for development. There are still not many Finnish participants involved and due to legal issues most securities loans are collateralized with cash and not securities (e.g. government bonds).

Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

On the use of convex underestimators in global optimization

Många kvantitativa problem från vitt skilda områden kan beskrivas som optimeringsproblem. Ett mått på lösningens kvalitet bör optimeras samtidigt som vissa villkor på lösningen uppfylls. Kvalitetsmåttet kallas vanligen objektfunktion och kan beskriva kostnader (exempelvis produktion, logistik), potentialenergi (molekylmodellering, proteinveckning), risk (finans, försäkring) eller något annat relevant mått. I min doktorsavhandling diskuteras speciellt icke-linjär programmering, NLP, i ändliga dimensioner. Problem med enkel struktur, till exempel någon form av konvexitet, kan lösas effektivt. Tyvärr kan inte alla kvantitativa samband modelleras på ett konvext vis. Icke-konvexa problem kan angripas med heuristiska metoder, algoritmer som söker lösningar med hjälp av deterministiska eller stokastiska tumregler. Ibland fungerar det här väl, men heuristikerna kan sällan garantera kvaliteten på lösningen eller ens att en lösning påträffas. För vissa tillämpningar är det här oacceptabelt. Istället kan man tillämpa så kallad global optimering. Genom att successivt dela variabeldomänen i mindre delar och beräkna starkare gränser på det optimala värdet hittas en lösning inom feltoleransen. Den här metoden kallas branch-and-bound, ungefär dela-och-begränsa. För att ge undre gränser (vid minimering) approximeras problemet med enklare problem, till exempel konvexa, som kan lösas effektivt. I avhandlingen studeras tillvägagångssätt för att approximera differentierbara funktioner med konvexa underskattningar, speciellt den så kallade alphaBB-metoden. Denna metod adderar störningar av en viss form och garanterar konvexitet genom att sätta villkor på den perturberade Hessematrisen. Min forskning har lyft fram en naturlig utvidgning av de perturbationer som används i alphaBB. Nya metoder för att bestämma underskattningsparametrar har beskrivits och jämförts. I sammanfattningsdelen diskuteras global optimering ur bredare perspektiv på optimering och beräkningsalgoritmer.

Currency Carry Trades – Excess Returns and Performance Optimization of G10 Currency Carry Trade Strategies during the Euro Era

This study examines the excess returns provided by G10 currency carry trading during the Euro era. The currency carry trade has been a popular trade throughout the past decades offering excess returns to investors. The thesis aims to contribute to existing research on the topic by utilizing a new set of data for the Euro era as well as using the Euro as a basis for the study. The focus of the thesis is specifically on different carry trade strategies’ performance, risk and diversification benefits. The study finds proof of the failure of the uncovered interest rate parity theory through multiple regression analyses. Furthermore, the research finds evidence of significant diversification benefits in terms of Sharpe ratio and improved return distributions. The results suggest that currency carry trades have offered excess returns during 1999-2014 and that volatility plays an important role in carry trade returns. The risk, however, is diversifiable and therefore our results support previous quantitative research findings on the topic.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Distributed energy resources in an electricity retailer’s short-term profit optimization

Liberalization of electricity markets has resulted in a competed Nordic electricity market, in which electricity retailers play a key role as electricity suppliers, market intermediaries, and service providers. Although these roles may remain unchanged in the near future, the retailers’ operation may change fundamentally as a result of the emerging smart grid environment. Especially the increasing amount of distributed energy resources (DER), and improving opportunities for their control, are reshaping the operating environment of the retailers. This requires that the retailers’ operation models are developed to match the operating environment, in which the active use of DER plays a major role. Electricity retailers have a clientele, and they operate actively in the electricity markets, which makes them a natural market party to offer new services for end-users aiming at an efficient and market-based use of DER. From the retailer’s point of view, the active use of DER can provide means to adapt the operation to meet the challenges posed by the smart grid environment, and to pursue the ultimate objective of the retailer, which is to maximize the profit of operation. This doctoral dissertation introduces a methodology for the comprehensive use of DER in an electricity retailer’s short-term profit optimization that covers operation in a variety of marketplaces including day-ahead, intra-day, and reserve markets. The analysis results provide data of the key profit-making opportunities and the risks associated with different types of DER use. Therefore, the methodology may serve as an efficient tool for an experienced operator in the planning of the optimal market-based DER use. The key contributions of this doctoral dissertation lie in the analysis and development of the model that allows the retailer to benefit from profit-making opportunities brought by the use of DER in different marketplaces, but also to manage the major risks involved in the active use of DER. In addition, the dissertation introduces an analysis of the economic potential of DER control actions in different marketplaces including the day-ahead Elspot market, balancing power market, and the hourly market of Frequency Containment Reserve for Disturbances (FCR-D).