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Aggregating Risk Across Multiple Asset Classes, Chapter 2
Jan 1, 2002
The first article in this series defined the business role of the enterprise risk management and the need for consistency between the analysis on a small set of assets and an aggregated analysis across the enterprise. We concluded that a consistent analysis requires a covariance matrix for factors across many asset classes. This article will evaluate the two challenges presented by the business case. First, the length of the time series of factor realizations is frequently different for different asset classes. If all series are reduced to the length of the shortest series then we are effectively discarding information present in longer time series. A similar problem, that of missing observations, has a known solution in the EM algorithm. We apply this solution to estimate a preliminary factor covariance matrix across multiple asset classes. The second challenge arises because the covariance matrix for any given asset class that is produced by the EM algorithm may not correspond to the covariance matrix that is produced when we consider that asset class alone. For example, the volatility of the U.S. equity market has often been described using variants of GARCH models, which we can incorporate into a robust covariance matrix for U.S. equity factors. In general, however, this covariance matrix will differ from the covariance matrix for U.S. equity factors produced by the EM algorithm. The result of this difference is that risk predictions at the asset class level will be inconsistent with the risk predictions across asset classes.
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