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

36 Pages Posted: 28 Dec 2006 Last revised: 7 Sep 2010

See all articles by Robert F. Engle

Robert F. Engle

New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER); New York University (NYU) - Volatility and Risk Institute

Victor Ng

University of Michigan at Ann Arbor

Michael Rothschild

Princeton University; National Bureau of Economic Research (NBER)

Date Written: November 1988

Abstract

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.

Suggested Citation

Engle, Robert F. and Ng, Victor and Rothschild, Michael, Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills (November 1988). NBER Working Paper No. t0065, Available at SSRN: https://ssrn.com/abstract=579752

Robert F. Engle

New York University (NYU) - Department of Finance

Stern School of Business
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New York, NY 10012-1126
United States

National Bureau of Economic Research (NBER)

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New York University (NYU) - Volatility and Risk Institute ( email )

44 West 4th Street
New York, NY 10012
United States

Victor Ng

University of Michigan at Ann Arbor ( email )

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Ann Arbor, MI 48109
United States

Michael Rothschild (Contact Author)

Princeton University ( email )

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Oakland, CA California 94611
United States
5102509635 (Phone)

National Bureau of Economic Research (NBER) ( email )

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Cambridge, MA 02138
United States

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