Generalized M-Vector Models for Hedging Interest Rate Risk

16 Pages Posted: 9 Jul 2007

See all articles by Sanjay K. Nawalkha

Sanjay K. Nawalkha

University of Massachusetts Amherst - Isenberg School of Management

Gloria M. Soto

University of Murcia - Faculty of Business and Economics

Jun Zhang

affiliation not provided to SSRN

Date Written: January 2003

Abstract

This paper generalizes the M-square and M-vector models (Fong and Fabozzi [1985] and Nawalkha and Chambers [1997]) by using a Taylor series expansion of the bond return function with respect to simple polynomial functions of the cash flow maturities. The classic M-vector computes the weighted averages of the distance between the maturity of each cash flow and the portfolio horizon, raised to integer powers (e.g., (t - H)^1, (t - H)^2, (t - H)^3, etc.). Implementation of the new approach involves computing the weighted averages of the distance between some polynomial function of the maturity of each cash flow and that of the portfolio horizon, raised to integer powers (e.g., (t^0.5 - H^0.5)^1, (t^0.5 - H^0.5)^2, (t^0.5 - H^0.5)^3, etc.). We test six different generalized M-vector models corresponding to six different polynomial functions. It is shown that polynomial functions of lower power (i.e., 0.25 or 0.5) provide significantly enhanced protection from interest rate risk, when higher-order generalized M-vector models are used.

Keywords: immunization, duration, interest rate, risk management, fixed income

JEL Classification: E43, G11

Suggested Citation

Nawalkha, Sanjay K. and Soto, Gloria M. and Zhang, Jun, Generalized M-Vector Models for Hedging Interest Rate Risk (January 2003). Available at SSRN: https://ssrn.com/abstract=998802 or http://dx.doi.org/10.2139/ssrn.998802

Sanjay K. Nawalkha (Contact Author)

University of Massachusetts Amherst - Isenberg School of Management ( email )

Amherst, MA 01003-4910
United States
413-687-2561 (Phone)

Gloria M. Soto

University of Murcia - Faculty of Business and Economics ( email )

Spain

Jun Zhang

affiliation not provided to SSRN ( email )

No Address Available

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