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Measuring Risk in Fixed Payment Securities: An Empirical Test of the Structured Full Rank Covariance Matrix

Published online by Cambridge University Press:  06 April 2009

Jimmy E. Hilliard  and
Susan D. Jordan
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Abstract

The appropriate set of parameters determining the volatility of the value of a portfolio of fixed cash flows of arbitrary maturities is the covariance matrix of unexpected interest rate changes over the term. Equilibrium models of the term structure limit the rank of the covariance matrix and implicitly impose restrictions on covariance estimation. The “full information” approach to risk measurement imposes only time stationarity assumptions on covariance matrix estimators and can result in sample matrices of full rank. Hilliard and Jordan (1989) develop a structured full rank covariance matrix that depends on only two parameters. This paper tests the Hilliard-Jordan model using likelihood ratios and criteria of forecast accuracy.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 26 , Issue 3 , September 1991 , pp. 345 - 362
Copyright
Copyright © School of Business Administration, University of Washington 1991

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References

Bierwag, G. O. “Bond Returns, Discrete Stochastic Processes, and Duration.” The Journal of Financial Research, 10 (Fall 1987), 191–209.CrossRefGoogle Scholar
Box, G. E. P. “A General Distribution Theory for a Class of Likelihood Criteria.” Biometrica, 36 (1949), 318–335.CrossRefGoogle ScholarPubMed
Box, G. E. P. “Problems in the Analysis of Growth and Wear Curves. Biometrics, 6 (1950), 362–389.CrossRefGoogle ScholarPubMed
Cox, J. C.; Ingersoll, J. E.; and Ross, S. A. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (03 1985), 385–497.CrossRefGoogle Scholar
Elton, E., and Gruber, M.. “Estimating the Dependence Structure of Share Prices-Implications for Portfolio Selection.” Journal of Finance, 28 (12 1973), 1203–1232.Google Scholar
Elton, E. J.; Gruber, M. J.; and Urich, T. J.. “Are Betas Best?” Journal of Finance, 33 (12 1978), 1375–1384.Google Scholar
Eun, C. S., and Resnick, B.. “Estimating the Correlation Structure of International Share Prices.” Journal of Finance, 39 (12 1984), 1547–1569.CrossRefGoogle Scholar
Graybill, F. A.Matrices with Applications in Statistics. Belmont, CA: Wadsworth Publ. Co. (1983).Google Scholar
Hicks, J. R.Value and Capital. Oxford: Clarendon Press (1939), 72–79.Google Scholar
Hilliard, J. E. “Hedging Interest Rate Risk with Futures Portfolios under Term Structure Effects.” Journal of Finance, 39 (12 1984), 1547–1569.CrossRefGoogle Scholar
Hilliard, J. E., and Jordan, S. D.. “Hedging Interest Rate Risk with Futures Portfolios under Full-Rank Assumptions.” Journal of Financial and Quantitative Analysis, 24 (06 1989), 217–240.CrossRefGoogle Scholar
Ingersoll, J.; Skelton, J.; and Weil, R.. “Duration Forty Years Later.” Journal of Financial and Quantitative Analysis, 13 (11 1978), 627–650.CrossRefGoogle Scholar
Macaulay, F. R.Some Theoretical Problems Suggested by the Movement of Interest Rates, Bonds, Yields, and Stock Prices in the United States since 1865. New York: Columbia Univ. Press (1938), 44–53.Google Scholar
Roll, R.The Behavior of Interest Rates. New York: Basic Books, Inc. (1970).Google Scholar
Samuelson, P. A. “Proof that Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review, 6 (Spring 1965), 13–32.Google Scholar
Sargent, T. J. “Rational Expectations and the Term Structure of Interest Rates.” Journal of Money, Credit, and Banking, 4 (02 1972), 74–97.CrossRefGoogle Scholar
Shiller, R. J. “Rational Expectations and the Term Structure of Interest Rates: A Comment.” Journal of Money, Credit and Banking, 4 (02 1972), 856–860.Google Scholar
Timm, N. H.Multivariate Analysis: With Applications in Education and Psychology. Monterey: Brooks/Cole Publ. Co., Inc. (1975).Google Scholar
Vasicek, O. A. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5 (11 1977), 177–188.CrossRefGoogle Scholar