Abstract

The optimal Debt Management (DM) literature concludes that the covariance of long bond prices with fiscal deficits justifies a dominant role for long bonds and that when long and short bond positions are time varying they are negatively correlated. An important, but unheralded, assumption in this literature is that each period governments repurchase all outstanding long bonds and immediately reissue (r/r) new long bonds. We show that all these features are in sharp contrast to basic features of observed DM in the US where the share of short bonds is large and persistent, short and long bond positions are positively correlated and r/r operations have been very rare. From the DM literature one could derive the normative implications that governments should issue fewer short bonds and they should engage in r/r operations but these implications would only be valid if they are robust to reasonable variations in market settings.To investigate this we systematically examine optimal DM under various reasonable market frictions. We find that under incomplete markets and small transaction costs, calibrated to observed data, there is no role for repurchases and the share of short bonds should be significant and stable. Under no buyback long bonds introduce volatility of cash payments whilst short bonds are desirable as they smooth cash flows. We find a robust result that optimal DM under no buyback resembles the data much more closely than the conventional modelling assuming r/r. Solving incomplete market models with large dimensional state spaces is challenging so we introduce a computational method that enables the efficient global solution of optimal portfolio models under incomplete markets with multiple assets.