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Tests of International CAPM with Time-Varying Covariances

  • Charles Engel
  • Anthony P. Rodrigues

We perform maximum likelihood estimation of a model of international asset pricing based on CAPM. We test the restrictions imposed by CAPM against a more general asset pricing model. The "betas" in our CAPM vary over time from two sources -- the supplies of the assets (government obligations of France, Germany, Italy, Japan, the U.K. and the U.S.) change over time, and so do the conditional covariances of returns on these assets. We let the covariances change over time as a function of macroeconomic data. We also estimate the model when the covariances follow a multivariate ARCH process. When the covariance of forecast errors are time-varying, we can identify a modified CAFM model with measurement error -- which we also estimate. We find that the model in which the CAPM restrictions are imposed (which involve cross-equation constraints between coefficients and the variances of the residuals) perform much better when variances are not constant over time. Nonetheless, the CAPM model is rejected in favor of the less restricted model of asset pricing.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 2303.

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Date of creation: Jul 1987
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Publication status: published as Journal of Applied Econometrics, Volume 4, April-June 1989, 119-138
Handle: RePEc:nbr:nberwo:2303
Note: ITI IFM
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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  1. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
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  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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  7. Domowitz, Ian & Hakkio, Craig S., 1985. "Conditional variance and the risk premium in the foreign exchange market," Journal of International Economics, Elsevier, vol. 19(1-2), pages 47-66, August.
  8. Frankel, Jeffrey A., 1988. "Recent estimates of time-variation in the conditional variance and in the exchange risk premium," Journal of International Money and Finance, Elsevier, vol. 7(1), pages 115-125, March.
  9. Frankel, Jeffrey A., 1986. "The implications of mean-variance optimization for four questions in international macroeconomics," Journal of International Money and Finance, Elsevier, vol. 5(1, Supple), pages S53-S75, March.
  10. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
  11. Branson, William H. & Halttunen, Hannu & Masson, Paul, 1979. "Exchange rates in the short run : Some further results," European Economic Review, Elsevier, vol. 12(4), pages 395-402, October.
  12. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  13. Lars Peter Hansen & Robert J. Hodrick, 1983. "Risk Averse Speculation in the Forward Foreign Exchange Market: An Econometric Analysis of Linear Models," NBER Chapters, in: Exchange Rates and International Macroeconomics, pages 113-152 National Bureau of Economic Research, Inc.
  14. Stanley W. Black, 1972. "International money markets and flexible exchange rates," Staff Studies 70, Board of Governors of the Federal Reserve System (U.S.).
  15. Hsieh, David A., 1984. "Tests of rational expectations and no risk premium in forward exchange markets," Journal of International Economics, Elsevier, vol. 17(1-2), pages 173-184, August.
  16. Cumby, Robert E & Obstfeld, Maurice, 1981. "A Note on Exchange-Rate Expectations and Nominal Interest Differentials: A Test of the Fisher Hypothesis," Journal of Finance, American Finance Association, vol. 36(3), pages 697-703, June.
  17. Branson, William H. & Halttunen, Hannu & Masson, Paul, 1977. "Exchange rates in the short run: The dollar-dentschemark rate," European Economic Review, Elsevier, vol. 10(3), pages 303-324.
  18. Hamilton, James D, 1985. "Uncovering Financial Market Expectations of Inflation," Journal of Political Economy, University of Chicago Press, vol. 93(6), pages 1224-41, December.
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  20. Giovannini, Alberto & Jorion, Philippe, 1987. "Interest rates and risk premia in the stock market and in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 6(1), pages 107-123, March.
  21. Giovannini, Alberto & Jorion, Philippe, 1988. "Foreign exchange risk premia volatility once again," Journal of International Money and Finance, Elsevier, vol. 7(1), pages 111-113, March.
  22. Jeffrey A. Frankel & Charles Engel, 1982. "Do Asset-Demand Functions Optimize over the Mean and Variance of Real Returns? A Six-Currency Test," NBER Working Papers 1051, National Bureau of Economic Research, Inc.
  23. Geweke, John F & Feige, Edgar L, 1979. "Some Joint Tests of the Efficiency of Markets for Forward Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 61(3), pages 334-41, August.
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