Measuring the Volatility in US Treasury Benchmarks and Debt Instruments

Abstract

As U.S. Treasury securities carry the full faith and credit of the U.S. government, they are free of default risk. Thus, their yields are risk-free rates of return, which allows the most recently issued U.S. Treasury securities to be used as a benchmark to price other fixed-income instruments. This article analyzes the time series properties of interest rates on U.S. Treasury benchmarks and related debt instruments by modelling the conditional mean and conditional volatility for weekly yields on 12 Treasury Bills and other debt instruments for the period January 8, 1982 to August 20, 2004. The conditional correlations between all pairs of debt instruments are also calculated. These estimates are of interest as they enable an assessment of the implications of modelling conditional volatility on forecasting performance. The estimated conditional correlation coefficients indicate whether there is specialization, diversification, or independence in the debt instrument shocks. Constant conditional correlation estimates of the standardized shocks indicate that the shocks to the first differences in the debt instrument yields are generally high and always positively correlated. In general, the primary purpose in holding a portfolio of Treasury Bills and other debt instruments should be to specialize on instruments that provide the largest returns. Tests for Stochastic Dominance are generally consistent with these findings, but find somewhat surprising rankings between debt instruments, with implications for portfolio composition. Thirty year treasuries, Aaa bonds, and mortgages tend to dominate the other instruments, at least to the second order.