Portfolio selection is a financial decision problem faced by all investors. Private investors, companies or financial institutions need to decide on how to invest in assets by selecting a portfolio according to some optimality criterion and under possible constraints. Expressed in mathematical terms, the portfolio optimization problem involves quantities which are usually estimated from historical data. Such estimates are accompanied by uncertainty which, via the optimization process, is transferred to the investment decisions, thus rendering many portfolio estimators unstable or unreliable. This thesis approaches the problem from two angles. On the one hand, we propose an improvement of the sample moments plug-in estimator through its bootstrap distribution. A robust measure of location of this distribution results, on average, in better out-of-sample performance, especially when the original estimator exhibits high instability, as illustrated by simulations. On the other hand we propose an alternative way of choosing the optimal intensity of two shrinkage estimators. These estimators stabilize the portfolio by applying shrinkage towards desirable targets. In the first case, these targets are the conventional ones for the mean and the covariance matrix, whereas in the second case we allow for additional market information to be included. Our method again uses bootstrap resamples to account for each estimator's possible out-of-sample performance. Finally, we consider the problem from a practitioner's perspective by including transaction costs. We exploit a striking similarity between the new optimization problem and the lasso estimator, a variation of the ordinary least squares estimator. We modify accordingly and extend further an existing algorithm for the solution of this problem and present the results. The new algorithm allows for additional constraints on the model coefficients and could be useful in a regression framework when assumptions on the coefficients' sign or magnitude are made.

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This thesis is concerned with forecasting the variance covariance matrix (VCM) for a range of financial assets and investigating whether combining the elements of such forecasts result in more accurate predictions of portfolio volatility than those obtained from univariate models of aggregate volatility. There are three substantive chapters in the thesis; two introduce new methods for forecasting the VCM, while the third examines the accuracy of the techniques available for forecasting overall portfolio volatility. The first chapter introduces a model labelled the CD-MIDAS model, designed to improve the forecasting of the VCM at frequencies lower than a single day, for example we focus on predicting the VCM for a 22 day (monthly) horizon. The CD-MIDAS model uses the approach of Chiriac and Voev (2010) in forecasting the elements of the Cholesky decomposition of the VCM, rather than attempting to directly forecast elements of the matrix which are subject to restrictions ensuring that the forecast VCM is symmetric and positive definite. The elements of the Cholesky decomposition are modelled using the mixed data sampling (MIDAS) methodology introduced in Ghysels, Santa-Clara and Valkanov (2004,2006) which allows for the use of data observed at a high frequency (i.e. daily) to forecast the same variable observed at a lower frequency (i.e. monthly). The forecasting performance of this model is compared to that of other popular multivariate models and evidence is found, in both simulations and applied experiments, that the CD-MIDAS model is able to produce forecasts of the monthly VCM that are more accurate than its competitors. The second substantive chapter builds on findings in the univariate volatility forecasting literature that the level of return volatility for financial assets can be related to observations of certain economic variables. The kernel technique introduced in this chapter uses a multiplicative kernel to compare the characteristics of past periods with those at the point when the forecast of the VCM is being made. A weighting is then assigned to each point of time depending on how the historical economic and VCM characteristics compare to those at the point of forecast, the more similar the two points are, the higher the weight will be. All weights are positive and are applied to historical realizations of the VCM, thus the resulting forecast is guaranteed to be symmetric and positive definite, while the calculation method avoids the curse of dimensionality. In applied investigations it is shown that versions of the kernel technique produce the most accurate forecasts of those considered at horizons of 1, 5 and 22 days. In addition it is shown that the addition of the economic data to the kernel produces a statistically significant improvement in the accuracy of the forecasts generated. The final chapter considers which models provide the best forecasts when we are interested in forecasting overall portfolio volatility. This question can be seen as an extension of the aggregation vs. disaggregation literature in which we are essentially testing whether the aggregation error, cause by modelling an aggregate of several time series, is more or less important than the misspecification error caused by having a disaggregated model. While the latter can potentially capture idiosyncrasies of individual component series, it also may contain a larger number of misspecified representations and may suffer from increased parameter uncertainty due to the large number of parameters requiring estimation. Hence this chapter examines whether it is best to use multivariate models, using individual stock data, or univariate models, using portfolio level data, when the aim is to generate forecasts of total portfolio return volatility. An applied experiment shows that the best performing models are univariate models based on realized measures of portfolio variance. It is also apparent that any model, univariate or multivariate that does not make use of realized data, computed from high frequency returns data is significantly handicapped in terms of forecasting performance when compared to those that do. Hence the results imply that the misspecification errors in currently available multivariate models are of more concern to those wishing to forecast total portfolio return volatility than the misspecification inherent in modelling the aggregate of a number of variables.

This thesis investigates the relative merits of econometric modeling, statistical and judgmental techniques for predicting debt crises and assessing the risk of credit migration. The increased reliance on econometric or statistical approaches and credit rating systems in risk management has intensified the need for more rigorous analysis of their finite sample properties. A better understanding of the available tools has implications for credit risk management, regulation and policy decision-making. The thesis contributes to the extant sovereign risk literature in three areas. First, it addresses the question of whether controlling for unobserved heterogeneity is important for predicting debt crises and explores a pervasive inference problem in Early Warning Systems (EWSs). Second, it addresses the development of an `optimal' EWS for sovereign debt crises that accommodates the decision maker's preferences. Third, it considers the measurement of sovereign credit migration matrices using different estimators and explores non Markov effects in the rating dynamics. Chapter 2 confronts competing models of sovereign default that differ in how country-, region- and time-specific effects are treated. Statistical tests and information criteria overwhelmingly favour more complex models with country heterogeneity that possibly changes over time. However, simplicity beats complexity in terms of forecasting. Simple pooled logit parameterization, that control either for regional heterogeneity or for time effects produce the most accurate forecasts and outperform several naive predictors. Chapter 3 investigates the severity of the autocorrelation problem in EWS of sovereign default. This stems from seeking to provide crisis warnings over a horizon that is longer than the frequency at which the forecasts are updated and from the sluggishness of the typical exogenous indicators. Neglecting residual serial autocorrelation in such models is shown to be far from innocuous. Inferences are overturned when using a correction. This phenomenon is generally clearer for the macroeconomic ratios that are more persistent. Chapter 4 combines three fundamentally different classification techniques - econometric, statistical and judgmental- to produce an EWS for sovereign default. The optimal choice of crucial EWS elements is shown to depend on the decision-makers' preferences. The forecast ranking of classifiers is found to be unstable and overall the classifiers appear to have different strengths. Payoffs from forecast combination are documented and the combining scheme is shown to depend on the decision-makers' loss function. Chapter 5 turns to the estimation of sovereign transition probability matrices and evaluates the popular discrete multinomial estimator against two continuous hazard rate methods that differ in their treatment of time-heterogeneity. Bootstrap simulations of the rating generating process reveal interesting insights. Hazard rate estimators yield more reliable default probabilities. Efficiency is further enhanced upon relaxing homogeneity. Downgrade momentum and duration effects are found to be present in the rating process.

This thesis extends the dynamic conditional correlation (DCC) model proposed in Engle (2002) to the case of conditional returns supposed to follow an asymmetric multivariate Laplace (AML) distribution as presented in Kotz, Kozubowsky and Podgorski (2003). We prove that maximum likelihood estimator provides optimal estimates of the relevant parameters estimated. We show the applicability of our approach in a comprehensive set of risk management implementations where we compute Value-at-Risk and Expected-Shorfall measures for portfolios composed by a large number of assets.

This thesis investigates the predictive power of six bivariate GARCH-CCC (constant conditional correlation) models; the GARCH (1, 1), BEKK GARCH (1, 1), GARCH-X (1, 1), BEKK-X (1, 1), GARCH-GJR (1, 1) and QGARCH (1, 1) based on both normal and student’s t distributions. Empirical investigations are conducted by forecasting the daily hedge ratios from agricultural futures markets using one-step-ahead over 1 year and 2 year out-of-sample period. The forecasting of OHR in agricultural and commodities’ futures markets has not been studied thoroughly and few publications are available in literature. My work enriches the literature and will hopefully provide guidance for hedging in these markets. To forecast the OHR, we apply data from three storable commodities, coffee, wheat and soybean and two non-storable commodities, live cattle and live hog. Four tests are conducted to evaluate the forecasting errors of out-of-sample forecasted return of the portfolio based on the forecasted OHR. Our study shows that the asymmetric GARCH model outperforms other models, and the standard GARCH is the weakest for 1-year forecast. However, the standard GARCH model performs well for 2-year forecast of live cattle with student’s t distributed residuals. More generally, the BEKK and asymmetric GJR and QGARCH models are recommended to forecast OHR on both 1-year and 2-year horizons with normal and student’s t distributions for storable products and the asymmetric models for non-storable commodities. Furthermore, our study demonstrates that the predictive power of GARCH models depends on the distribution of residuals, the commodity and also the length of the forecast horizons. This result is consistent with the those from Poon and Granger (2003) and Chen et.al (2003). Given accurately forecasted OHR, investors can determine appropriate hedging strategies for portfolio management to reduce or transfer risks, and prepare for the capital needed for hedging.

Η παρούσα εργασία πραγματεύεται το θέμα των χρηματοοικονομικών περιορισμών που καλούνται να αντιμετωπίσουν οι επιχειρήσεις προτού πάρουν την απόφαση ή όχι να αναλάβουν μια επένδυση. Συγκεκριμένα θα μελετήσουμε πως το μέγεθος μιας επιχείρησης και η μόχλευση επηρεάζουν την επενδυτική της απόφαση ή καλύτερα πώς η εσωτερική χρηματοδότηση επιδρά στην επένδυση σε διαφορετικά επίπεδα μόχλευσης και μεγέθους της επιχείρησης. Η εργασία αποτελείται από εφτά(7) κεφάλαια. Το πρώτο κεφάλαιο αποτελεί την εισαγωγή μας η οποία παραθέτει εν συντομία αυτά που θα δούμε στα επόμενα έξι(6) κεφάλαια. Το δεύτερο κεφάλαιο είναι μια επισκόπηση της βιβλιογραφίας. Παρουσιάζονται οι δύο διαφορετικές απόψεις όσον αφορά τις επενδύσεις, η νεοκλασική η οποία υποθέτει οποία υποθέτει πλήρη ανταγωνισμό στην αγορά κεφαλαίου και πλήρη πληροφόρηση και άρα οι επενδυτικές αποφάσεις δεν υπόκεινται σε περιορισμούς και η εναλλακτική άποψη η οποία υποθέτει ότι βρισκόμαστε σε ατελείς αγορές και άρα η χρηματοοικονομική κατάσταση της επιχείρησης επηρεάζει την επενδυτική της απόφαση. Το κεφάλαιο ολοκληρώνεται με μια εκτενής παρουσίαση των προηγούμενων εμπειρικών μελετών. Στο τρίτο κεφάλαιο γίνεται μια παρουσίαση των δεδομένων καθώς και μια ανάλυση της μεθόδου GMM με την οποία θα εκτιμήσουμε την συνάρτηση επένδυσης. Στο κεφάλαιο αυτό γίνεται επίσης μια αναφορά της βάσης δεδομένων BACH από την οποία αντλήσαμε τα δεδομένα μας. Τέλος, παραθέτουμε και κάποια ενδιαφέρονται στατιστικά χαρακτηριστικά των μεταβλητών μας. Στο τέταρτο κεφάλαιο, το οποίο είναι και το ουσιαστικότερο, παρουσιάζουμε τα εμπειρικά μας αποτελέσματα. Συγκεκριμένα με την βοήθεια του οικονομετρικού προγράμματος STATA είδαμε πώς τον μέγεθος της επιχείρησης και η μόχλευση επηρεάζουν την επενδυτική της απόφαση, πώς δηλαδή η εσωτερική χρηματοδότηση επιδρά στην επένδυση σε διαφορετικά επίπεδα μόχλευσης και μεγέθους της επιχείρησης. Να σημειώσουμε ότι για το μέγεθος της επιχείρησης έχουν γίνει τρεις(3) διαφορετικές μετρήσεις οι οποίες και παραθέτονται λεπτομερώς. Το πέμπτο κεφάλαιο αποτελεί τα συμπεράσματά μας δηλαδή γίνεται μια σύνοψη όσων έχουν αναφερθεί στα προηγούμενα κεφάλαια και καταλήγουμε ότι τα εμπειρικά μας αποτελέσματα συμφωνούν πλήρως τόσο με την υπάρχουσα βιβλιογραφία όσο και με τις προηγούμενες εμπειρικές μελέτες. Τέλος η παρούσα εργασία ολοκληρώνεται με τα κεφάλαια έξι και εφτά όπου παραθέτουμε την βιβλιογραφία που έχουμε χρησιμοποιήσει, καθώς και ένα παράρτημα όπου παρουσιάζονται τα διαγράμματα οι πίνακες που έχουμε χρησιμοποιήσει στην εργασία. / This work deals with the issue of financial constraints facing undertakings before take the decision or not to take an investment. In particular we consider that the size of the company and the leverage affecting the investment decision or how cash flow affects investment at different levels of leverage and firm’s size The work consists of seven(7) chapters. The first chapter is the introduction us which sets out briefly what we will see in the coming six(6) Chapters The second chapter is an overview of the literature. Presented the two different views as regards the investment, neoclassical, which assumes full competition to the capital market and full information and therefore the investment decisions not subject to restrictions and the alternative view, which assumes that we are in an environment of uncertainty and hence the financial situation of the firm affects the investment decision. The chapter ends with an extended presentation of the previous empirical studies In the third chapter there is a presentation of our data and an analysis of the method GMM with the aid of it, we will estimate the relation investment. In this chapter there is also a reference of the BACH database from which we took our data. Finally, we hold some interested statistical characteristics of our variables. In the fourth chapter, which is the most meaningful, we are presenting our empirical results. In particular, with the assistance of the econometric program STATA we have seen that the size of the firm and the leverage affects its investment decision how cash flow affects investment at different levels of leverage and firm’s size. It’s worth noting that, concerning the size of the firm, we have made three (3) different measurements which are presented in detail. The fifth chapter presents our conclusions. There is a summary of what has been reported in the previous chapters and we conclude that our empirical results agree fully with both the literature and previous empirical studies. Finally, this paper concludes with chapters six and seven, where we present the literature we have used, as well as an appendix showing charts and tables we have used in this paper.