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on Risk Management |
| By: | Jeroen V.K. Rombouts (IEA, HEC Montréal); Marno Verbeek |
| Abstract: | In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, we specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. Finally, we examine the economic value of the multivariate GARCH models by determining optimal portfolios based on maximizing expected returns subject to a VaR constraint, over a period of 500 consecutive days. Again, the superiority and robustness of the semi-parametric model is confirmed. |
| Keywords: | multivariate GARCH, semi-parametric estimation, Value-at-Risk, asset allocation. |
| Date: | 2004–12 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0414&r=rmg |
| By: | Peter Hecht; Tuomo Vuolteenaho |
| Abstract: | Stock returns are correlated with contemporaneous earnings growth, dividend growth, future real activity, and other cash-flow proxies. The correlation between cash-flow proxies and stock returns may arise from association of cash-flow proxies with one-period expected returns, cash-flow news, and/or expected-return news. We use Campbell's (1991) return decomposition to measure the relative importance of these three effects in regressions of returns on cash-flow proxies. In some of the popular specifications, variables that are motivated as proxies for cash-flow news also track a nontrivial proportion of one-period expected returns and expected-return news. As a result, the R2 from a regression of returns on cash-flow proxies may overstate or understate the importance of cash-flow news as a source of return variance. |
| JEL: | E44 G10 G12 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11169&r=rmg |
| By: | Thibault Gajdos (CREST); Jean-Marc Tallon (EUREQua); Jean-Christophe Vergnaud (EUREQua) |
| Abstract: | We provide a model of decision making under uncertainty in which the decision maker reacts to imprecision of the available data. Data is represented by a set of probability distributions. We axiomatize a decision criterion of the maxmin expected utility type, in which the revealed set of priors explicitly depends on the available data. We then characterize notions of comparative aversion to imprecision of the data as well as traditional notions of risk aversion. Interestingly, the study of comparative aversion to imprecision can be done independently of the utility function, which embeds risk attitudes. We also give a more specific result, in which the functional representing the decision maker's preferences is the convex combination of the minimum expected utility with respect to the available data and expected utility with respect to a subjective probability distribution, interpreted as a reference prior. This particular form is shown to be equivalent to some form of constant aversion to imprecision. We finally provide examples of applications first to unanimity rankings of imprecision and risk and then to optimal risk sharing arrangements. |
| Keywords: | Imprecision; ambiguity; uncertainty; decision; multiple priors |
| JEL: | D81 |
| Date: | 2004–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:v04056&r=rmg |
| By: | Torben G. Andersen (Kellogg School of Management, Northwestern University); Tim Bollerslev (Department of Economics, Duke University); Peter F. Christoffersen (Faculty of Management, McGill University); Francis X. Diebold (Department of Economics, University of Pennsylvania) |
| Abstract: | Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. |
| JEL: | C10 C53 G1 |
| Date: | 2005–02–22 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:05-011&r=rmg |