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Abstract:
This paper explores the possible advantages of introducing observable state variables into risk management models as a strategy for modeling the evolution of second moments. A simulation exercise demonstrates that if asset returns depend upon a set of underlying state variables that are autoregressively conditionally
heteroskedastic (ARCH), then a risk management model that fails to take account
of this dependence can badly mismeasure a portfolio's "Value-at-Risk" (VaR),
even if the model allows for conditional heteroskedasticity in asset returns.
Variables measuring macroeconomic news are constructed as the orthogonalized
residuals from a vector autoregression (VAR). These news variables are found
to have some explanatory power for asset returns. We also estimate a model of
asset returns in which time variation in variances and covariances derives only
from conditional heteroskedasticity in the underlying macroeconomic shocks.
Although the data give some support for several of the specifications that we
tried, neither these models nor GARCH models that used only asset returns
appear to have much ability to forecast the second moments of returns.
Finally, we allow asset return variances and covariances to depend directly on
unemployment rates -- proxying for the general state of the economy -- and find
fairly strong evidence for this sort of specification relative to a null
hypothesis of homoskedasticity.
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