Choix de portefeuille de grande taille et mesures de risque pour preneurs de décision pessimistes

Cette thèse de doctorat consiste en trois chapitres qui traitent des sujets de choix de portefeuilles de grande taille, et de mesure de risque. Le premier chapitre traite du problème d’erreur d’estimation dans les portefeuilles de grande taille, et utilise le cadre d'analyse moyenne-variance. Le second chapitre explore l'importance du risque de devise pour les portefeuilles d'actifs domestiques, et étudie les liens entre la stabilité des poids de portefeuille de grande taille et le risque de devise. Pour finir, sous l'hypothèse que le preneur de décision est pessimiste, le troisième chapitre dérive la prime de risque, une mesure du pessimisme, et propose une méthodologie pour estimer les mesures dérivées. Le premier chapitre améliore le choix optimal de portefeuille dans le cadre du principe moyenne-variance de Markowitz (1952). Ceci est motivé par les résultats très décevants obtenus, lorsque la moyenne et la variance sont remplacées par leurs estimations empiriques. Ce problème est amplifié lorsque le nombre d’actifs est grand et que la matrice de covariance empirique est singulière ou presque singulière. Dans ce chapitre, nous examinons quatre techniques de régularisation pour stabiliser l’inverse de la matrice de covariance: le ridge, spectral cut-off, Landweber-Fridman et LARS Lasso. Ces méthodes font chacune intervenir un paramètre d’ajustement, qui doit être sélectionné. La contribution principale de cette partie, est de dériver une méthode basée uniquement sur les données pour sélectionner le paramètre de régularisation de manière optimale, i.e. pour minimiser la perte espérée d’utilité. Précisément, un critère de validation croisée qui prend une même forme pour les quatre méthodes de régularisation est dérivé. Les règles régularisées obtenues sont alors comparées à la règle utilisant directement les données et à la stratégie naïve 1/N, selon leur perte espérée d’utilité et leur ratio de Sharpe. Ces performances sont mesurée dans l’échantillon (in-sample) et hors-échantillon (out-of-sample) en considérant différentes tailles d’échantillon et nombre d’actifs. Des simulations et de l’illustration empirique menées, il ressort principalement que la régularisation de la matrice de covariance améliore de manière significative la règle de Markowitz basée sur les données, et donne de meilleurs résultats que le portefeuille naïf, surtout dans les cas le problème d’erreur d’estimation est très sévère. Dans le second chapitre, nous investiguons dans quelle mesure, les portefeuilles optimaux et stables d'actifs domestiques, peuvent réduire ou éliminer le risque de devise. Pour cela nous utilisons des rendements mensuelles de 48 industries américaines, au cours de la période 1976-2008. Pour résoudre les problèmes d'instabilité inhérents aux portefeuilles de grandes tailles, nous adoptons la méthode de régularisation spectral cut-off. Ceci aboutit à une famille de portefeuilles optimaux et stables, en permettant aux investisseurs de choisir différents pourcentages des composantes principales (ou dégrées de stabilité). Nos tests empiriques sont basés sur un modèle International d'évaluation d'actifs financiers (IAPM). Dans ce modèle, le risque de devise est décomposé en deux facteurs représentant les devises des pays industrialisés d'une part, et celles des pays émergents d'autres part. Nos résultats indiquent que le risque de devise est primé et varie à travers le temps pour les portefeuilles stables de risque minimum. De plus ces stratégies conduisent à une réduction significative de l'exposition au risque de change, tandis que la contribution de la prime risque de change reste en moyenne inchangée. Les poids de portefeuille optimaux sont une alternative aux poids de capitalisation boursière. Par conséquent ce chapitre complète la littérature selon laquelle la prime de risque est importante au niveau de l'industrie et au niveau national dans la plupart des pays. Dans le dernier chapitre, nous dérivons une mesure de la prime de risque pour des préférences dépendent du rang et proposons une mesure du degré de pessimisme, étant donné une fonction de distorsion. Les mesures introduites généralisent la mesure de prime de risque dérivée dans le cadre de la théorie de l'utilité espérée, qui est fréquemment violée aussi bien dans des situations expérimentales que dans des situations réelles. Dans la grande famille des préférences considérées, une attention particulière est accordée à la CVaR (valeur à risque conditionnelle). Cette dernière mesure de risque est de plus en plus utilisée pour la construction de portefeuilles et est préconisée pour compléter la VaR (valeur à risque) utilisée depuis 1996 par le comité de Bâle. De plus, nous fournissons le cadre statistique nécessaire pour faire de l’inférence sur les mesures proposées. Pour finir, les propriétés des estimateurs proposés sont évaluées à travers une étude Monte-Carlo, et une illustration empirique en utilisant les rendements journaliers du marché boursier américain sur de la période 2000-2011.

On the design of customized risk measures in insurance, the problem of capital allocation and the theory of fluctuations for Lévy processes

Dans cette thèse, nous étudions quelques problèmes fondamentaux en mathématiques financières et actuarielles, ainsi que leurs applications. Cette thèse est constituée de trois contributions portant principalement sur la théorie de la mesure de risques, le problème de l’allocation du capital et la théorie des fluctuations. Dans le chapitre 2, nous construisons de nouvelles mesures de risque cohérentes et étudions l’allocation de capital dans le cadre de la théorie des risques collectifs. Pour ce faire, nous introduisons la famille des "mesures de risque entropique cumulatifs" (Cumulative Entropic Risk Measures). Le chapitre 3 étudie le problème du portefeuille optimal pour le Entropic Value at Risk dans le cas où les rendements sont modélisés par un processus de diffusion à sauts (Jump-Diffusion). Dans le chapitre 4, nous généralisons la notion de "statistiques naturelles de risque" (natural risk statistics) au cadre multivarié. Cette extension non-triviale produit des mesures de risque multivariées construites à partir des données financiéres et de données d’assurance. Le chapitre 5 introduit les concepts de "drawdown" et de la "vitesse d’épuisement" (speed of depletion) dans la théorie de la ruine. Nous étudions ces concepts pour des modeles de risque décrits par une famille de processus de Lévy spectrallement négatifs.

A note on estimating market–based minimum capital risk requirements: a multivariate GARCH approach

Internal risk management models of the kind popularized by J. P. Morgan are now used widely by the world’s most sophisticated financial institutions as a means of measuring risk. Using the returns on three of the most popular futures contracts on the London International Financial Futures Exchange, in this paper we investigate the possibility of using multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models for the calculation of minimum capital risk requirements (MCRRs). We propose a method for the estimation of the value at risk of a portfolio based on a multivariate GARCH model. We find that the consideration of the correlation between the contracts can lead to more accurate, and therefore more appropriate, MCRRs compared with the values obtained from a univariate approach to the problem.

On the determinants of derivative usage by Australian companies

This paper provides an examination of the determinants of derivative use by Australian corporations. We analysed the characteristics of a sample of 469 firm/year observations drawn from the largest Australian publicly listed companies in 1999 and 2000 to address two issues: the decision to use financial derivatives and the extent to which they are used. Logit analysis suggests that a firm's leverage (distress proxy), size (financial distress and setup costs) and liquidity (financial constraints proxy) are important factors associated with the decision to use derivatives. These findings support the financial distress hypothesis while the evidence on the underinvestment hypothesis is mixed. Additionally, setup costs appear to be important, as larger firms are more likely to use derivatives. Tobit results, on the other hand, show that once the decision to use derivatives has been made, a firm uses more derivatives as its leverage increases and as it pays out more dividends (hedging substitute proxy). The overall results indicate that Australian companies use derivatives with a view to enhancing the firms' value rather than to maximizing managerial wealth. In particular, corporations' derivative policies are mostly concerned with reducing the expected cost of financial distress and managing cash flows. Our inability to identify managerial influences behind the derivative decision suggests a competitive Australian managerial labor market.

Low-frequency volatility of yen interest rate swap market in relation to macroeconomic risk

Using ‘low-frequency’ volatility extracted from aggregate volatility shocks in interest rate swap (hereafter, IRS) market, this paper investigates whether Japanese yen IRS volatility can be explained by macroeconomic risks. The analysis suggests that this low-frequency yen IRS volatility has strong and positive association with most of the macroeconomic risk proxies (e.g., volatility of consumer price index, industrial production volatility, foreign exchange volatility, slope of the term structure and money supply) with the exception of the unemployment rate, which is negatively related to IRS volatility. This finding is fairly consistent with the argument that the greater the macroeconomic risk the greater is the use of derivative instruments to hedge or speculate. The relationship between the macroeconomic risks and IRS volatility varies slightly across the different swap maturities but is robust to alternative volatility specifications. This linkage between swap market and macroeconomy has practical implications since market makers and hedgers use the swap rate as benchmark for pricing long-term interest rates, corporate bonds and various other securities.

Selection of the right risk measures for portfolio allocation

 An optimisation framework is proposed to enable investors to select the right risk measures in portfolio selection. Verification is deployed by performing experiments in developed markets (e.g., the US stock market), emerging markets (e.g., the South Korean stock market) and global investments. A preselection procedure dealing with large datasets is also introduced to eliminate stocks that have low diversification potential before running the portfolio optimisation model. Portfolios are evaluated by four performance indices, i.e., the Sortino ratio, the Sharpe ratio, the Stutzer performance index, and the Omega measure. Experimental results demonstrate that high performance and also well-diversified portfolios are obtained if modified value-at-risk, variance, or semi-variance is concerned whereas emphasising only skewness, kurtosis or higher moments in general produces low performance and poorly diversified portfolios. In addition, the preselection applied to large datasets results in portfolios that have not only high performance but also high diversification degree.

Fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio

A new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper. Beyond the well-known Sharpe ratio (i.e., the reward-to-variability ratio) in modern portfolio theory, we initiate the so-called fuzzy Sharpe ratio in the fuzzy modeling context. In addition to the introduction of the new risk measure, we also put forward the reward-to-uncertainty ratio to assess the portfolio performance in fuzzy modeling. Corresponding to two approaches based on TM and TW fuzzy arithmetic, two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized, while the fuzzy Sharpe ratio is maximized. These models are solved by the fuzzy approach or by the genetic algorithm (GA). Solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean-variance optimization (MVO) model used prevalently in the financial literature. In terms of portfolio performance evaluated by the fuzzy Sharpe ratio and the reward-to-uncertainty ratio, the model using TW fuzzy arithmetic results in higher performance portfolios than those obtained by both the MVO and the fuzzy model, which employs TM fuzzy arithmetic. We also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using GA, although GA can offer a series of well-diversified portfolio solutions diagrammed in a Pareto frontier.

O método das opções reais aplicado na avaliação das oportunidades de investimento no setor de seguros

Esta dissertação tem como objetivo demonstrar a validade do método de análise da avaliação das oportunidades de investimentos que utiliza a Teoria das Opções Reais. De forma a demonstrar a aplicabilidade desta metodologia de avaliação, será exemplificado, com base no modelo das opções reais, uma oportunidade de investimento no setor de seguros. As opções reais fecham a brecha entre as finanças e o planejamento estratégico introduzindo um meio para incorporar o impacto da incerteza implícita nas oportunidades de investimento, e ao mesmo tempo considerando como as ações gerenciais podem limitar as possíveis perdas ou capitalizar os possíveis ganhos nos projetos de investimento. Este processo de avaliação não direciona somente os administradores a focar suas atenções nas diferentes oportunidades e alternativas estratégicas, mas fornece também uma metodologia sistemática para medir a influencia das ações contingentes sobre o próprio risco e valor do projeto. Os métodos tradicionais de avaliação dos investimentos assumem que os administradores adotem um comportamento passivo à implementação dos projetos, considerando somente o valor dos fluxos de caixa esperados dos mesmos. A partir da teoria de precificação das opções financeiras, as opções reais expandem o valor global do projeto incorporando os potenciais ganhos e limitando as possíveis perdas. O modelo de opções reais permite aos administradores alavancar o valor do acionista em um ambiente de negócios dinâmico considerando a possibilidade de uma gestão ótima das opções estratégicas e operacionais existentes. Tipicamente, o ativo subjacente é o valor bruto dos fluxos de caixa esperados do projeto, mas considerando a incerteza, o valor total do projeto deve considerar o valor implícito das opções reais presentes nas oportunidades de investimento. A flexibilidade gerencial, que permite adaptar as decisões futuras as mudanças inesperadas do mercado, representa um fonte crucial de valor agregado em um ambiente dinâmico. Muitas opções reais presentes nos projetos e que interagem entre si, podem ocorrer em paralelo ou seqüencialmente, de maneira que o valor combinado destas opções seja diferente da simples soma algébrica das opções individuais.

Nonparametric tail risk, macroeconomics and stock returns: predictability and risk premia

This paper proposes a new novel to calculate tail risks incorporating risk-neutral information without dependence on options data. Proceeding via a non parametric approach we derive a stochastic discount factor that correctly price a chosen panel of stocks returns. With the assumption that states probabilities are homogeneous we back out the risk neutral distribution and calculate five primitive tail risk measures, all extracted from this risk neutral probability. The final measure is than set as the first principal component of the preliminary measures. Using six Fama-French size and book to market portfolios to calculate our tail risk, we find that it has significant predictive power when forecasting market returns one month ahead, aggregate U.S. consumption and GDP one quarter ahead and also macroeconomic activity indexes. Conditional Fama-Macbeth two-pass cross-sectional regressions reveal that our factor present a positive risk premium when controlling for traditional factors.

The effect of default risk on trading book capital requirements for public equities : an irc application for the Brazilian market

Esse é um dos primeiros trabalhos a endereçar o problema de avaliar o efeito do default para fins de alocação de capital no trading book em ações listadas. E, mais especificamente, para o mercado brasileiro. Esse problema surgiu em crises mais recentes e que acabaram fazendo com que os reguladores impusessem uma alocação de capital adicional para essas operações. Por essa razão o comitê de Basiléia introduziu uma nova métrica de risco, conhecida como Incremental Risk Charge. Essa medida de risco é basicamente um VaR de um ano com um intervalo de confiança de 99.9%. O IRC visa medir o efeito do default e das migrações de rating, para instrumentos do trading book. Nessa dissertação, o IRC está focado em ações e como consequência, não leva em consideração o efeito da mudança de rating. Além disso, o modelo utilizado para avaliar o risco de crédito para os emissores de ação foi o Moody’s KMV, que é baseado no modelo de Merton. O modelo foi utilizado para calcular a PD dos casos usados como exemplo nessa dissertação. Após calcular a PD, simulei os retornos por Monte Carlo após utilizar um PCA. Essa abordagem permitiu obter os retornos correlacionados para fazer a simulação de perdas do portfolio. Nesse caso, como estamos lidando com ações, o LGD foi mantido constante e o valor utilizado foi baseado nas especificações de basiléia. Os resultados obtidos para o IRC adaptado foram comparados com um VaR de 252 dias e com um intervalo de confiança de 99.9%. Isso permitiu concluir que o IRC é uma métrica de risco relevante e da mesma escala de uma VaR de 252 dias. Adicionalmente, o IRC adaptado foi capaz de antecipar os eventos de default. Todos os resultados foram baseados em portfolios compostos por ações do índice Bovespa.

Flexibility and firm value: the role of inventories

In the present thesis I study the contribution to firm value of inventories management from a risk management perspective. I find a significant contribution of inventories to the value of risk management especially through the operating flexibility channel. In contrast, I do not find evidence supporting the view of inventories a reserve of liquidity. Inventories substitute, albeit not perfectly, derivatives or cash holdings. The substitution between hedging with derivatives and inventory is moderated by the correlation between cash flow and the underlying asset in the derivative contract. Hedge ratios increase with the effectiveness of derivatives. The decision to hedge with cash holdings or inventories is strongly influenced by the degree of complementarity between production factors and by cash flow volatility. In addition, I provide a risk management based explanation of the secular substitution between inventories and cash holdings documented, among others, in Bates et al. (2009), Journal of Finance. In a sample of U.S. firms between 1980 and 2006, I empirically confirm the negative relation between inventories and cash and provide evidence on the poor performance of investment cash flow sensitivities as a measure of financial constraints also in the case of inventories investment. This result can be explained by firms' scarce reliance on inventories as a reserve of liquidity. Finally, as an extension of my study, I contrast with empirical data the theoretical predictions of a model on the integrated management of inventories, trade credit and cash holdings.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

A fuzzy risk attitude classification based on prospect theory

Traditional methods do not actually measure peoples’ risk attitude naturally and precisely. Therefore, a fuzzy risk attitude classification method is developed. Since the prospect theory is usually considered as an effective model of decision making, the personalized parameters in prospect theory are firstly fuzzified to distinguish people with different risk attitudes, and then a fuzzy classification database schema is applied to calculate the exact value of risk value attitude and risk be- havior attitude. Finally, by applying a two-hierarchical clas- sification model, the precise value of synthetical risk attitude can be acquired.

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.

Temporal variability of damage potential on roads as a conceptual contribution towards a short-term avalanche risk simulation

The fatality risk caused by avalanches on road networks can be analysed using a long-term approach, resulting in a mean value of risk, and with emphasis on short-term fluctuations due to the temporal variability of both, the hazard potential and the damage potential. In this study, the approach for analysing the long-term fatality risk has been adapted by modelling the highly variable short-term risk. The emphasis was on the temporal variability of the damage potential and the related risk peaks. For defined hazard scenarios resulting from classified amounts of snow accumulation, the fatality risk was calculated by modelling the hazard potential and observing the traffic volume. The avalanche occurrence probability was calculated using a statistical relationship between new snow height and observed avalanche releases. The number of persons at risk was determined from the recorded traffic density. The method resulted in a value for the fatality risk within the observed time frame for the studied road segment. The long-term fatality risk due to snow avalanches as well as the short-term fatality risk was compared to the average fatality risk due to traffic accidents. The application of the method had shown that the long-term avalanche risk is lower than the fatality risk due to traffic accidents. The analyses of short-term avalanche-induced fatality risk provided risk peaks that were 50 times higher than the statistical accident risk. Apart from situations with high hazard level and high traffic density, risk peaks result from both, a high hazard level combined with a low traffic density and a high traffic density combined with a low hazard level. This provided evidence for the importance of the temporal variability of the damage potential for risk simulations on road networks. The assumed dependence of the risk calculation on the sum of precipitation within three days is a simplified model. Thus, further research is needed for an improved determination of the diurnal avalanche probability. Nevertheless, the presented approach may contribute as a conceptual step towards a risk-based decision-making in risk management.