Macroeconomic state variables as determinants of asset price covariances

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.