Generating interest-rate scenarios for fixed-income portfolio optimisation

Abstract

One of the main sources of uncertainty in the analysis of the risk and return properties of a portfolio of fixed-income securities is the stochastic evolution of the shape of the yield curve. The authors have estimated a model that fits the South African yield curve, using a Kalman filter. The model includes four latent factors and three observable macroeconomic variables (capacity utilisation, inflation and the repo rate). The goal is to capture the dynamic interactions between the macroeconomy and the yield curve in such a way that the resulting model can be used to generate interest-rate scenario trees that are suitable for fixed-income portfolio optimisation. An important input into the scenario generator is the investor’s view on the future evolution of the repo rate. In this paper, details of the model are provided and the results of the estimation and scenario generation are reported.

KEYWORDS Term structure; yield curve; Kalman filter; macroeconomic; scenario generation; Nelson–Siegel curve; Svensson curve