Time Varying Covariance Structures in Financial Markets

Frank Gerhard and Dieter Hess
Faculty of Economics and Statistics, Universtity of Konstanz
Frank.Gerhard@Uni-Konstanz.de
Dieter.Hess@Uni-Konstanz.de

Abstract

Reliable estimates of variances and covariances are crucial for portfolio management and risk controlling. This paper investigates alternative methods to estimate time varying variance-covariance matrices: first, ordinary estimates as a baseline, second, exponentially weighted moving averages (EWMA) being used widely by practioners, third, Markov switching models as an alternative appearing to be better adapted to certain time series properties and to the needs of portfolio management.

We use different benchmarking concepts to compare the point estimators. First, econometric tests are implemented for the dynamic specification. In addtition estimators are compared on the basis of bootstrapped standard deviations and confidence intervals. Furthermore, the problem of dimensioning the state space is addressed. Bootstrap results are also provided for ordinary and EWMA estimates. Second, we evaluate the performance of these estimation concepts from their ability to select portfolios according to the minimum-variance criterium which is a meaningful benchmark concept since it is able to infer the estimators' ability to capture diversification benefits without the need to produce an inference about expected returns.

EWMA estimators perform slightly better in terms of ex-post portfolio variance. However, the high variability of EWMA parameters lead to large and frequent portfolio adjustments, resulting in high transaction costs. Markov switching as well as ordinary estimates cause less portfolio revisions whereas ex-post portfolio variances do not differ significantly.

As an additional benefit Markov switching models provide the probability to switch to a shock state and thus allow the ex-post identification of significant events from time-series information only. Such `events' may well be interpreted as the arrival of unanticipated information.