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Hedging Interest Rate Risk with Futures Portfolios under Full-Rank Assumptions

Published online by Cambridge University Press:  06 April 2009

Abstract

A spot portfolio of rate-sensitive assets can be hedged by a portfolio of interest-sensitive futures contracts. The hedge ratios of minimum-variance portfolios are unique when the fixed cash flows of underlying instruments are linearly independent and when the covariance matrix of unexpected changes in spot rates over the term of the cash flows is of full rank. Hilliard's (1984) full-rank model has produced smaller portfolio variances than a duration model in a short-term hedging context. However, the methodology typically requires extensive econometric analysis. This paper develops a structured covariance matrix of full rank that requires only one parameter estimate. Hedging examples are provided.

Type
Research Article
Copyright
Copyright © School of Business Administration, University of Washington 1989

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References

Bierwag, G. O.Bond Returns, Discrete Stochastic Processes, and Duration.” The Journal of Financial Research, 10 (Fall 1987), 191209.CrossRefGoogle Scholar
Bierwag, G. O.; Kaufman, G. C. and Toevs, A.. “Duration: Its Development and Use in Bond Portfolio Management.” Financial Analysts Journal, 15 (0708 1983), 15–35.Google Scholar
Bierwag, G. O.; Kaufman, G. C. and Khang, C.. “Duration and Bond Portfolio Analysis: An Overview.” Journal of Financial and Quantitative Analysis, 13 (11 1978), 671685.CrossRefGoogle Scholar
Boyle, P. O.Immunization, Duration, and the Term Structure of Interest Rates.” Journal of the Institute of the Actuaries, 105 (1977), 177187.CrossRefGoogle Scholar
Brennan, M. J., and Schwartz, E. S.. “Duration, Bond Pricing, and Portfolio Management.” In Innovations in Bond Portfolio Management, Kaufman, et al. Greenwich, CT: JAI Press (1983), 336.Google Scholar
Campbell, J. Y.A Defense of Traditional Hypotheses about the Term Structure of Interest Rates.” Journal of Finance, 41 (03 1986), 183193.Google Scholar
Cox, J; Ingersoll, J. E. and Ross, S. A.. “Duration and Measurement of Basis Risk.” Journal of Business, 52 (01 1979), 5761.Google Scholar
Cox, J; Ingersoll, J. E. and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (03 1985), 385407.Google Scholar
Chambers, D. R.; Carleton, W. T. and McEnally, R. W.. “Immunization Default-Free Bond Portfolios with a Duration Vector.” Journal of Financial and Quantitative Analysis, 23 (03 1988), 89104.CrossRefGoogle Scholar
Ederington, L.The Hedging Performance of the New Futures Markets.” Journal of Finance, 34 (03 1979), 157170.CrossRefGoogle Scholar
Elton, E., and Gruber, M.. “Estimating the Dependence Structure of Share Prices—Implications for Portfolio Selection.” Journal of Finance, 28 (12 1973), 12031232.Google Scholar
Elton, E.; Gruber, M. and Urich, T.. “Are Betas Best?Journal of Finance, 33 (12 1978), 13751384.Google Scholar
Eun, C. S., and Resnick, B.. “Estimating the Correlation Structure of International Share Prices.” Journal of Finance, 39 (12 1984), 13111324.Google Scholar
Fisher, L., and Weil, R. L.. “Coping with the Risk of Interest Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies.” The Journal of Business, 44 (10 1971), 408431.Google Scholar
Gay, G. D., and Kolb, R. W.. “Interest Rate Futures: A New Perspective on Immunization.” Journal of Portfolio Management, 10 (Fall 1983), 6570.CrossRefGoogle Scholar
Graybill, F. A.Matrices with Applications in Statistics. Belmont, CA: Wadsworth Publ. Co. (1983).Google Scholar
Gultekin, G. R., and Rogalski, R. J.. “Alternative Duration Specifications and the Measurement of Basis Risk: Empirical Tests.” The Journal of Business, 57 (10 1985), 241264.Google Scholar
Hilliard, J. E.Hedging Interest Rate Risk with Futures Portfolios under Term Structure Effects.” Journal of Finance, 39 (12 1984), 15471569.CrossRefGoogle Scholar
Ingersoll, J. E. Jr, “Is Immunization Feasible? Evidence from the CRSP Data.” In Innovations in Bond Portfolio Management, Kaufman, et al. Greenwich, CT: JAI Press (1983), 163182.Google Scholar
Ingersoll, J.; Skelton, J. and Weil, R.. “Duration Forty Years Later.” Journal of Financial and Quantitative Analysis, 13 (11 1978), 627650.Google Scholar
Kaufman, G. C.; Bierwag, G. O.; and Toevs, A., eds. Innovations in Bond Portfolio Management. Greenwich, CT: JAI Press (1983).Google Scholar
Kolb, R. W., and Chaing, R.. “Improving Hedging Performance Using Interest Rate Futures.” Financial Management, 10 (Autumn 1981), 7279.CrossRefGoogle Scholar
Kolb, R. W.; Gay, G. D. and Corgel, J.. “Effective Hedging of Mortgage Interest Rate Risk.” The Housing Review, 20 (1982), 13351346.Google Scholar
Leibowitz, M. L.The Dedicated Bond Portfolio in Pension Funds—Part II: Immunization, Horizon Matching and Contingent Procedures.” Financial Analysts Journal, 42 (0304 1986), 4757.CrossRefGoogle Scholar
Meiselman, D.The Term Structure of Interest Rates. Englewood Cliffs, NJ: Prentice Hall (1962).Google Scholar
Merton, R. C.Optimum Consumption and Portfolio Rules in a Continuous-Time Model.” Journal of Economic Theory, 3 (12 1971), 373413.CrossRefGoogle Scholar
Nelson, J., and Schaefer, S.. “Dynamics of the Term Structure and Alternative Portfolio Immunization Strategies.” In Innovations in Bond Portfolio Management, Kaufman, et al. Greenwich, CT: JAI Press (1983), 61101.Google Scholar
Richard, S. F.An Arbitrage Model of the Term Structure of Interest Rates.” Journal of Financial Economics, 6 (03 1978), 3357.Google Scholar
Roll, R.The Behavior of Interest Rates. New York: Basic Books, Inc. (1970).Google Scholar
Sargent, T. J.Rational Expectations and the Term Structure of Interest Rates.” Journal of Money, Credit, and Banking, 4 (02 1972), 7497.Google Scholar
Samuelson, P. A.Proof that Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review, 6 (Spring 1965), 4149.Google Scholar
Schaefer, S. M.Immunisation and Duration: A Review of Theory, Performance and Applications.” Midland Corporate Finance Journal, 2 (Fall 1984), 4158.Google Scholar
Shiller, R. J.Rational Expectations and the Term Structure of Interest Rates, A Comment.” Journal of Money, Credit and Banking, 5 (08 1973), 856860.CrossRefGoogle Scholar
Smith, C. W., and Stulz, R.. “The Determinants of Firms' Hedging Policies.” Journal of Financial and Quantitative Analysis, 20 (12 1985), 391405.Google Scholar
Trainer, F. H. Jr, “The Uses of Treasury Bond Futures in Fixed Income Portfolio Management.” Financial Analysts Journal, 39 (0201 1983), 2734.CrossRefGoogle Scholar
Vasicek, O.An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5 (11 1977), 177188.Google Scholar
Wold, H.A Study in the Analysis of Stationary Time Series. Stockholm, Sweden: Almqvist and Wiksell (1938).Google Scholar
Yawitz, J. B., and Marshall, W. B.. “The Use of Futures in Immunized Portfolios.” Journal of Portfolio Management, 11 (Winter 1985), 5155.Google Scholar