Choosing the Weighting Coefficients for Estimating the Term Structure from Sovereign Bonds

Estimates of the term structure of interest rates depend heavily on the quality of the market data from which it is constructed. Estimated rates can be incorrect because of observation errors and omissions in the data. The usual way to deal with the heteroscedasticity of observation errors is by introducing weights in the fitting procedure. There is currently no consensus in the literature about the choice of such weights. We introduce a non-parametric bootstrap-based method of introducing observation errors drawn from the empirical distribution into the model data, which allows us to perform a comparison test of different weighting schemes without implicitly favoring one of the contesting models – a common design flaw in comparison studies. We use government bonds from several countries with examples of both liquid and illiquid bond markets. We show that realistic observation errors can greatly distort the estimated yield curve. Moreover, we show that using different weights or other modifications to account for observation errors in bond price data does not always improve the term structure estimates, and often worsens the situation. Based on our comparison, we advise to either use equal weights or weights proportional to the inverse duration in practical applications