## Introduction

##### Abstract

The international workshop “Finance and Decisions 05” was organized by the School of Economics and Management of the Free University of Bolzano – Bozen. During three days, from the 28th till the 30th of April of 2005, 15 presentations have been made by leading experts of financial modeling. This volume includes some of these papers. They focus on the three aspects: (1) dependence and correlation (of risk factors), (2) heavy tail effects and (3) numerical schemes. The editing process has been supported by quite a number of referees, their help is highly appreciated.
The paper by J. Abaffy et al. analyzes the two factors that affect the dynamics of bond prices: the transition between different rating classes and the correlation risk. The dynamics is modeled by a lattice structure. The theoretical predictions are compared with the real data that concern 928 securities. The paper treats the risk factors separately, a natural next step would be to analyze their interaction.
Based on the mean-variance approach and discretization of the corresponding random variables, a numerical optimization scheme for portfolio selection is suggested by K. Frauendorfer and U. Jacoby. Aimed for pension funds, it entails a multi period setting. There are two regimes characterizing the overall situation: a bear market and a bull one. The switching between them is governed by a time homogeneous Markov chain. Then, being a mixture of two normal distributions, the excess return exhibits some features similar to heavy tails. Also the phenomenon of volatility clusters is modeled.
A highly important methodologically contribution by M. Kallio and W.T. Ziemba uses Tucker’s theorem of the alternative to develop a unified and simple treatment for known arbitrage pricing results in frictionless and friction cases in a numerical setting. (That is, time is discrete and finite. Realizations of uncertainties over time are represented by a scenario tree with a finite number of nodes and branches.) Uncertainty concerns the total returns (including the asset price, price increment, interest payments, dividends, etc.) of financial instruments. The following market imperfections may be analyzed simultaneously: transaction costs; an interest rate spread between borrowing and lending; charges for short positions; and restricted short selling.
Y.M. Kaniovski and G.Ch. Pflug develop a Markov Chain model, which uses a given transition probability matrix as the marginal law, but introduces correlation coefficients within and between industry sectors and between rating classes for the joint law of migration of all components of the portfolio. Since the migration probabilities and pairwise correlations do not define uniquely a joint distribution, a quadratic minimization problem is solved to choose one of them. A generating function for the one step joint distribution of all assets having non-default credit ratings and a generating function of the loss distribution are found. The numerical simulations presented demonstrate that the average number of defaults is not affected by the correlation coefficients, but the percentiles of the number of defaults are heavily dependent upon them. In particular, for strongly correlated assets, the distribution of the number of defaults follows a “cascade” picture nesting in non-overlapping intervals. A pattern similar to heavy tails emerges: the probability of a large number of defaults is higher for correlated assets than for non-correlated ones. This approach provides a method for modeling the transition risk treated in the paper by J. Abaffy et al.
S. Rachev et al. analyze momentum strategies based on reward–risk stock selection criteria against ordinary momentum strategies based on a cumulative return criterion. The former include the standard Sharpe ratio with variance as a risk measure, and alternative reward–risk ratios with the expected shortfall as a risk measure. 517 stocks in the S&P 500 universe in the period from 1996 to 2003 are used. Although the ordinary momentum strategies based on a cumulative return criterion provide the highest average monthly momentum profits of 1.3% compared to the monthly profit of 0.86% for the best alternative criterion, the latter provide better risk-adjusted returns measured on an independent risk-adjusted performance measure. The findings may indicate that extreme momentum portfolio returns have non-normal distribution and thus contain an additional risk component due to heavy tails.
Copyright © 2007 Published by Elsevier B.V.

##### URI

http://dx.doi.org/10.1016/j.jbankfin.2007.02.001http://www.sciencedirect.com/science/article/pii/S0378426607000647?via=ihub

http://hdl.handle.net/10863/3639