M.Sc Student Regev Nitzan Excess Yields in Bond Hedging Department of Industrial Engineering and Management Professor Haim Reisman Abstract

Recent research has explored dynamic term structure affine factor models. These affine models estimate the term structure of interest rates reliably. Litterman and Scheinkman (1991) found that the models can be estimated using Principal Component Analysis. Diebold, Li and Li (2004) suggested using smooth functions in these models. However, affine models using such estimation procedures are not consistent with no-arbitrage assumption in frictionless markets. Of course, in reality bond markets are not frictionless, and so using a no-arbitrage constraint might be restricting. Hence estimating term structure using affine models should be appropriate. Reisman and Zohar (2004) derive a formula for next period expected returns, and test it on processed data. They show that the expected returns perfectly match the returns in practice. Those returns are different from zero, suggesting there are arbitrage opportunities in the bond market. In this paper we expand the Reisman and Zohar formula for coupon-bearing bonds , and test it on unprocessed CRSP treasury bond data .

We first present the multi-factor model, which is a linear combination of some F deterministic functions of time to maturity with stochastic coefficients. Using this model we estimate the term structure. In order to determine the deterministic functions we use

Diebold, Li and Li (2004) factor loadings. We also compute these modes using PCA on the estimated term structure .

In the next step we compare three hedging mechanisms and find that hedging using the multi-factor model outperforms regular duration models. This was previously explored by Diebold et al. (2004), who also found the mean hedging error to be different from zero. Here we explain this using our derived formula .

Next we present how to construct instantaneous risk free portfolios . When testing the performance of these portfolios we find that their returns in practice perfectly match the model predictions .

Finally, we construct optimal portfolios. Again we find that there is excellent agreement between the returns in the data and the theoretical returns. The actual return is 1.35% for a year with a Sharpe ratio of 2.35. We conduct another optimization in the presence of transaction costs . The results show that up to a transaction cost of more than 7 cents we can find positive actual returns .

We conclude that our model is a good predictor of the actual returns in the bond market. These results can be applied to improving hedging, and to finding arbitrage opportunities in the bond market.