International Workshop

The Physics Approach To Risk:
Agent-Based Models and Networks

October 27-29, 2008, ETH Zurich, Switzerland

Quantifying financial return risk from short time series

Wolfgang Breymann

Zürcher Hochschule Winterthur (Winterthur , Switzerland )

When quantifying financial return risk it is important to take into account the correct form of the return distribution. The family of generalized hyperbolic distributions is able to faithfully describe observed distributions, but fitting requires data sets with several hundred observations. This is not a problem in the case of exchange-traded instruments where daily data is available. Alternative investment opportunities, however, are typically not traded and there value is reported on a monthly (if not quarterly) basis, only, so that for the analysis only about 40 $\sim$ 50 data points are available for a single fund. The challenge then consists in quantifying risk beyond the assumption of normally-distributed returns for small sample sizes. Indeed, this assumption can usually not be rejected for individual monthly return series of that size. We have met the challenge by introducing so-called ``peer groups" of funds whose returns behave similarly. In the case of fund-of-hedge-funds this can be done by means of a style analysis. Then, shape and skewness parameters have been fitted for the peer group, only, while location and scale parameter have been adapted to the individual funds. The fitting procedure has been accomplished iteratively in a self-consisting way using the expectation-maximization algorithm. In this way it could be shown that the return distributions display semi-heavy tails, and the value off the risk measure is about twice as high as under the assumption of normally distributed returns.

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