Measuring Bond Portfolio Value at Risk and Expected Shortfall in US Treasury Market

Abstract

This paper measured the value at risk (VaR) and expected shortfall (ES) of the US Treasury yield changes. The US Treasury yield data were tested and found to be not normally distributed. Consequently, the mixture normal model (MNM) was used to improve the delta normal VaR and ES measures. It performed extraordinarily well in all cases, based on bootstrapping and mean square error tests. In addition, the key rate model (KRM) for the risk measure of portfolios showed that VaRs but not ESs exhibited non-subadditivity at a 99% confidence level. This could be attributed to the fact that the diversification effect is weak in the US Treasury portfolios. At the same time, level, slope, and curvature (LSC) factor models as well as structural equation models (SEM) were applied for the risk sensitivity analysis of portfolios. For an investment worth $1,000 within a one-month horizon, MNM of key rates showed that the barbell portfolio had the lowest VaR ($1.398) and ES ($1.858) of all the portfolios at a 95% confidence level. On the other hand, the historical simulation of key rates revealed that at a 95% confidence level, the barbell portfolio had VaR of $1.396 and ES of $2.097 while LSC and SEM showed VaR of $1.122 and ES of $1.434, and VaR of $1.179 and ES of $1.505, respectively. According to LSC and SEM, the barbell was affected the most by level, and long-term factors. It was also found that the bullet was affected by curvature, level, and medium-term factors.