Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills

Robert F. Engle, Victor Ng, Michael Rothschild

NBER Technical Working Paper No. 65
Issued in November 1988
NBER Program(s):Monetary Economics

Asset pricing relations are developed for a vector of assets with a time varying covariance structure. Assuming that the eigenvectors are constant but the eigenvalues changing, both the Capital Asset Pricing Model and the Arbitrage Pricing Theory suggest the same testable implication: the time varying part of risk premia are proportional to the time varying eigenvalues. Specifying the eigenvalues as general ARCH processes. the model is a multivariate Factor ARCH model. Univariate portfolios corresponding to the eigenvectors will have (time varying) risk premia proportional to their own (time varying) variance and can be estimated using the GARCH-M model. This structure is applied to monthly treasury bills from two to twelve months maturity and the value weighted NYSE returns index. The bills appear to have a single factor in the variance process and this factor is influenced or "caused in variance" by the stock returns.

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Document Object Identifier (DOI): 10.3386/t0065

Published: Journal of Econometrics, Vol. 45, No. 1/2, pp. 213-237, (July/August 1990).

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