Portfolio diversification has been a subject frequently addressed since the publications of Markowitz in 1952 and 1959. However, the Modern Portfolio Theory and its mean variance framework have been criticized. The critiques refer to the assumptions that return distributions are normally distributed and the symmetric definition of risk. This paper elaborates on these short comings and applies a heuristic downside risk approach to avoid the pitfalls inherent in the mean variance framework. The result of the downside risk approach is compared and contrasted with the result of the mean variance framework. The return data refers to the real estate sector in Sweden and diversification is reached through property type and geographical location. The result reveals that diversification is reached differently between the two approaches. The downside risk measure applied here frequently diversifies successfully with use of fewer proxies. The efficient portfolios derived also reveals that the downside risk approach would have contributed to a historically higher average total return. This paper outlines a framework for portfolio diversification, the result is empirical and further research is needed in order to grasp the potential of the downside risk measures.

京都大学 / 0048 / 新制・課程博士 / 博士(経済学) / 甲第19953号 / 経博第540号 / 新制||経||279(附属図書館) / 33049 / 京都大学大学院経済学研究科経済学専攻 / (主査)教授 江上 雅彦, 教授 若井 克俊, 教授 原 千秋 / 学位規則第4条第1項該当 / Doctor of Economics / Kyoto University / DFAM

The concept of portfolio optimization has been widely studied in the academy and implemented in the financial markets since its introduction by Markowitz 70 years ago. The problem of the mean-variance optimization framework caused by input uncertainty has been one of the foci in the previous research. In this study, several models (linear shrinkage and Black-Litterman) based on Bayesian approaches are studied to improve the estimation of inputs. Moreover, a new framework based on robust optimization is presented to mitigate the input uncertainty further.  An out-of-sample test is specially designed, and the results show that Bayesian models in this study can improve the optimization results in terms of higher Sharpe ratios (the quotient between portfolio returns and their risks). Both covariance matrix estimators based on the linear shrinkage method contain less error and provide better optimization results, i.e. higher Sharpe ratios. The Black-Litterman model with a proper choice of inputs can significantly improve the portfolio return. The new framework based on the combination of shrinkage estimators, Black-Litterman, and robust optimization presents a better way for portfolio optimization than the classical framework of mean-variance optimization.

Varje investerare vill se sitt kapital växa så mycket som möjligt men samtidigt inte utsätta kapitalet för onödiga risker. Högre risk, högre avkastning är två synonymer inom den finansiella världen. Investerare världen över söker hela tiden nya möjligheter att öka sin avkastning utan att behöva höja sin risk. Optimering av portföljer för att skapa avkastning till låg risk är ett känt fenomen, ofta benämnt som modern portföljteori. Markowitz medel-variansmodell och Black-Litterman modellen är två olika modeller för att optimera en portfölj i aspekten minska risken men behålla avkastningen. En investerare som kan sänka risken på sin investering kan investera ett större kapital och på så sätt skapa större avkastning med tiden. Genom att skapa olika portföljer baserade på de två modellerna och sedan jämföra dem mot varandra samt mot OMXS30 index är syftet att få en inblick i huruvida en investerare kan slå index. Resultatet i studien visat att en investerare med hjälp av optimering kan slå index räknat i avkastning, baserat på historiska kurser. Resultatet visar även att det finns goda skäl till utveckling av modellerna för att få en större säkerhet i att de faktiskt slår index på den verkliga marknaden i realtid. / Every investor seeks to find a way of capital growth combined with the minimization of risk taken. Higher risk and higher reward are synonymous in the financial world. Investors across the globe seek new possibilities to increase their returns without having to take a higher risk. Portfolio optimization to create returns holding low risk is a well-known phenomenon, usually referred to as modern portfolio theory. Markowitz’s mean-variance model and the Black-Litterman model are two different models used to optimize a portfolio in the endeavor of keeping a good return with a lower risk. An investor who can lower risk is an investor who has more free capital to invest and therefore can create a larger return in the future. By creating different portfolios based on the models and then comparing them with one another and the OMXS30 index, the authors seek to get an insight if it’s possible for an investor to beat the index. The result of the study shows that an investor using portfolio optimization can beat the index, calculated in returns, based on historical prices. The results do also show that there are good reasons to develop the models in order to achieve greater security in beating the index on the market and in real-time.

An asset manager's goal is to provide a high return relative the risk taken, and thus faces the challenge of how to choose an optimal portfolio. Many mathematical methods have been developed to achieve a good balance between these attributes and using di erent risk measures. In thisthesis, we test the use of a relatively simple and common approach: the Markowitz mean-variance method, and a more quantitatively demanding approach: the tail optimization method. Using active portfolio based on data provided by the Swedish fund management company Enter Fonderwe implement these approaches and compare the results. We analyze how each method weighs theunderlying assets in order to get an optimal portfolio.

<p>In recent years, considerable effort has been directed toward establishing the nature of the investment behaviour of life insurance companies. In this dissertation an extended portfolio analysis model was developed for the simultaneous determination of the efficient composition of insurance and investment activities of a life insurance company. This was done within a model that takes advantage of the existing finance foundations and the concepts and techniques of modern demand system analysis.</p> <p>Unlike current models which used quadratic programming techniques and are interested in the construction of efficient sets, we have used a utility maximization approach. A two parameter portfolio model was constructed utilizing elements of utility theory and of the theory of insurance. The model provided us with the proportion of assets held in the balance sheet as well as which liabilities are used to raise the necessary capital.</p> <p>The model developed has sufficient empirical content to yield hypotheses' about life insurance portfolio behaviour and thus was tested using appropriate econometric techniques. A comparative static analysis yielded elasticities of substitution between financial assets and liabilities. The estimation of these elasticities in the context of a flexible functional form model, forms a central part of this dissertation. More specifically, by utilizing a mean-variance portfolio framework and a general Box-Cox utility function we were able to model the demand for assets and liabilities by an insurance company. On empirical grounds we found that, in general, the square root quadratic utility function best fits the data. We also tried to evaluate the square root quadratic approximation by showing that, broadly speaking, it yields signs for elasticities of substitution which are consistent with the theory.</p> <p>A by-product of the model developed is the ability to compare stock and mutual life insurance companies. The common belief that mutual companies follow a riskier path in the way they conduct their business was supported by the results in this study.</p> <p>The results obtained from the study are of significant importance since life insurance companies have substantial obligations to millions of households in the economy. Furthermore, despite the extraordinary decline in the importance of the life insurance industry in the bond and mortgage markets during the sixties and the seventies, the industry is still a major supplier of funds to those markets.</p> / Doctor of Philosophy (PhD)

In recent years, considerable effort has been directed toward establishing the nature of the investment behaviour of life insurance companies. In this dissertation an extended portfolio analysis model was developed for the simultaneous determination of the efficient composition of insurance and investment activities of a life insurance company. This was done within a model that takes advantage of the existing finance foundations and the concepts and techniques of modern demand system analysis. Unlike current models which used quadratic programming techniques and are interested in the construction of efficient sets, we have used a utility maximization approach. A two parameter portfolio model was constructed utilizing elements of utility theory and of the theory of insurance. The model provided us with the proportion of assets held in the balance sheet as well as which liabilities are used to raise the necessary capital. The model developed has sufficient empirical content to yield hypotheses about life insurance portfolio behaviour and thus was tested using appropriate econometric techniques. A comparative static analysis yielded elasticities of substitution between financial assets and liabilities. The estimation of these elasticities in the context of a flexible functional form model, forms a central part of this dissertation. More specifically, by utilizing a mean-variance portfolio framework and a general Box-Cox utility function we were able to model the demand for assets and liabilities. by an insurance company. On empirical grounds we found that, in general, the square root quadratic utility function best fits the data. We also tried to evaluate the square root quadratic approximation by showing that, broadly speaking, it yields signs for elasticities of substitution which are consistant with the theory. A by-product of the model developed is the ability to compare stock and mutual life insurance companies. The common belief that mutual companies follow a riskier path in the way they conduct their business was supported by the results in this study. The results obtained from the study are-of significant importance since life insurance companies have substantial obligations to millions of households in the economy. Furthermore, despite the extraordinary decline in the importance of the life insurance industry in the bond and mortgage markets during the sixties and the seventies, the industry is still a major supplier of funds to those markets. / Thesis / Doctor of Philosophy (PhD)

Yes / Although a cornerstone of traditional finance theory, empirical evidence in support of a positive mean-variance relation is far from conclusive, with the behavior of retail investors commonly thought to be one of the root causes of departures from this expected relationship. The behavior of institutional investors, conventionally thought to be sophisticated and rational, has recently come under closer scrutiny, including in relation to investor sentiment. Drawing together these two strands of literature, this paper examines the impact of institutional investor sentiment on the mean-variance relation in six regions, including Asia (excl. Japan), Eastern Europe, Eurozone, Japan, Latin America, and the US, and across thirtyeight markets. Empirical evidence supports the differential impact of institutional investor sentiment on the mean-variance relation (i.e., positive or negative), both across regions and across markets. In particular, for markets with cultural proneness to overreaction and a low level of market integrity institutional investor sentiment tends to distort the risk-return tradeoff.

Portfolio optimization is a process in which the capital is allocated among the portfolio assets such that the return on investment is maximized while the risk is minimized. Portfolio construction and optimization is a complex process and has been an active research area in finance for a long time. For the portfolios with highly correlated assets, the performance of traditional risk-based asset allocation methods such as, the mean-variance (MV) method is limited because it requires an inversion of the covariance matrix of the portfolio to distribute weight among the portfolio assets. Alternatively, a hierarchical clustering-based machine learning method can provide a possible solution to these limitations in portfolio construction because it uses hierarchical relationships between the covariance of assets in a portfolio to distribute the weight and an inversion of the covariance matrix is not required. A comparison of the performance and analyses of the difference in weight distribution of two optimization strategies, the traditional MV method and the hierarchical risk parity method (HRP), which is a machine learning method, on real price historical data has been performed. Also, a comparison of the performance of a simple non-optimization technique called the equal-weight (EW) method to the two optimization methods, the Mean-variance method and HRP method has also been performed. This research supports the idea that HRP is a feasible method to construct portfolios with correlated assets because the performance of HRP is comparable to the performances of the traditional optimization method and the non-optimization method.

Mean variance optimization has shortcomings making the strategy far from optimal from an investor’s perspective. The purpose of the study is to conduct an empirical investigation as to how modern methods of portfolio optimization address the shortcomings associated with mean variance optimization. Equal risk contribution, the Most diversified portfolioand a modification of the Minimum variance portfolio are considered as alternatives to the mean variance model. Portfolio optimization models introduced are explained in detail and solved using the optimization algorithms Cyclical coordinate descent and Alternating direction method of multipliers. Through implementation and backtesting using a diverse set of indices representing various asset classes, the study shows that the mean variance model suffers from high turnover and sensitivity to input parameters in comparison to the modern alternatives. The sophisticated asset allocation models equal risk contribution and the most diversified portfolio do not rely on expected return as an input parameter, which is seen as an advantage, and are not affected to the same extent by the shortcomings associated with mean variance optimization. The paper concludes by discussing the findings critically and suggesting ideas for further research. / Maximering av avkastning i samband med minimering av varians, på engelska kallat Mean variance optimization, är inte optimalt ur en investerares synpunkt. Syftet med denna uppsats är att genomföra en empirisk studie av hur moderna metoder för portföljallokering adresserar de problem som är förknippade med Mean variance optimization. Mer specifikt undersöks allokeringsstrategierna Equal risk contribution, Most diversified portfolio samt en variant av Minimum variance som ersättare till Mean variance optimization. Allokeringsmetoderna beskrivs detaljerat och löses med optimeringsalgoritmerna Cyclical coordinate descent och Alternating direction method of multipliers. Genom implementering och historisk simulering med ett antal index som representerar olika tillgångsslag visar studien att Mean variance optimization innebär hög portföljomsättning och har en större känslighet för ingångsparametrar i jämförelse med de moderna alternativen. De sofistikerade allokeringsmodellerna Equal risk contribution och Most diversified portfolio bygger inte på ingångsparametern förväntad avkastning, vilket ses som en fördel, och drabbas inte i samma utsträckning av problemen associerade med Mean variance optimization. Studien avslutas med att diskutera resultatet kritiskt och ge förslag på vidare studier som bygger på den teori och det resultat som har presenterats.