Historical VaR for Bonds - A New Approach

Abstract

Bonds historical returns cannot be used directly to compute VaR because the maturities of returns implied by the historical prices do not have the relevant maturities to compute VaR. Given the so-called pull-to-par in bonds, with return volatilities necessarily decreasing with diminishing time-to-maturity, direct use of historical returns would lead to overestimation of the true VaR. Market practice deals with the problem of computing VaR for portfolios of bonds or mixed portfolios with cumbersome methods of cash-flow mappings.

In this paper we propose a new approach. We develop a technique to adjust bonds historical prices and extract from them an adjusted history of returns, that can be used directly to compute historical VaR for bonds or bond portfolios. We illustrate the method using one concrete traded market zero-coupon bond, but the simplicity of the method makes this enough to the reader to understand how it would work with coupon bonds, portfolios of bonds or mixed portfolios.