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A man walks away from the U.S Treasury Department in Washington, U.S., August 6, 2018.     REUTERS/Brian Snyder - RC1FD03EA500

Optimizing the maturity structure of U.S. Treasury debt: A model-based framework

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Editor's Note:

Code that replicates part of the model described in this paper is available on GitHub. (The optimization module will be added in the near future.) This code was written for the Hutchins Center by Lorenzo Rigon of Stanford University.

Brian Sack

Director of Global Economics - The D. E. Shaw group

The U.S. Treasury doesn’t decide how much money to borrow each year; that depends on the gap between federal spending and revenues. The Treasury does decide how to borrow – that is, how much short-term and how much long-term and how much in between.  These decisions typically involve a trade-off between minimizing expected costs of borrowing and minimizing fiscal risks.

For years, the U.S. Treasury has focused primarily on maintaining a “regular and predictable” pattern of debt, while several other countries rely on analytical frameworks or models to guide their decisions.  In a paper commissioned by the Hutchins Center on Fiscal and Monetary Policy at Brookings, six Wall Street economists – Terry Belton, Huachen Li, and Srini Ramaswamy of JPMorgan Chase, Kristopher Dawsey and Brian Sack of The D. E. Shaw Group, and David Greenlaw of Morgan Stanley – describe a framework to guide Treasury decisions.  Their paper – “Optimizing the Maturity Structure of U.S. Treasury Debt: A Model-Based Framework” – presents a model that can be used to assess the trade-offs between various debt issuance strategies and to explore the sensitivity of those trade-offs to different assumptions.

The model — originally developed by several members of the Treasury Borrowing Advisory Committee, a private-sector panel that advises Treasury debt managers – captures an important trade-off between short-term and long-term financing. In general, the authors write, short-term financing is relatively inexpensive but can complicate budget planning by increasing the volatility of interest expenses. Longer-term borrowing mitigates the volatility of financing costs, but typically at a higher expected cost, because long-term interest rates tend to be higher than shorter-term rates.  A debt manager concerned with managing debt-service costs must strike a balance between these competing considerations when determining the optimal issuance profile across all maturities.

The authors demonstrate this trade-off by examining debt management decisions made from 2007 to 2015 that extended the projected weighted average maturity of Treasury debt from six to seven years. Their model shows that this maturity extension increased expected debt service costs, costing the Treasury around $10 billion a year, but reduced the variability of debt service costs.

The model also highlights the potential cost of failing to optimize the maturity structure of debt issuance. For instance, in 2007, the authors say, the Treasury could have reduced its expected debt service costs by just over 0.2 percent of GDP, or about $40 billion per year based on current GDP, without increasing the variation in debt service costs, by following the model’s analytical approach to optimizing the Treasury’s debt structure.

The authors suggest that issuing debt at intermediate maturities – particularly two-, three-, and five-year securities – is appealing, as those securities do not involve high expected costs and yet are effective at smoothing variation of interest expenses over time. Issuing too much on the long end – 10 years and beyond – is particularly unattractive, as this increases debt service costs without reducing variability. However, the exact optimal maturity profile depends on the risk aversion of the issuer. A risk neutral or moderately risk averse debt manager would prefer to skew issuance towards the short end, producing a larger concentration of debt with maturities of five years or less than observed in the current U.S. Treasury debt stock; while a highly risk averse debt manager would choose to issue fewer short-term and more long-term securities.

A debt issuance strategy that responds dynamically to the level of the short-term interest rate, the term premium, and the size of the budget deficit can further improve outcomes. For instance, the model suggests that increases in the term premium and the real two-year rate generally favor moving into short-term bills from medium- and long-term securities, while rising deficits should result in increases in medium-term securities offset by borrowing less at the at the long and short end.

Read the full paper here.

Belton, Greenlaw, and Sack are members of the Treasury Borrowing Advisory Committee — a committee composed of senior representatives from investment funds and banks that meets quarterly with the Treasury Department. This paper was prepared to further discussion of potential changes to the model that informs the U.S. Treasury’s debt management choices. The authors are employees of investment funds and banks, however, they did not receive financial support for their work on this paper. 

The authors would like to thank participants from an authors’ workshop held at The Hutchins Center on Fiscal and Monetary Policy at Brookings in May 2018 for their helpful feedback, and Colin Kim for his helpful comments. The authors would also like to thank Jason Cummins for suggesting this project, and Walter Mueller for providing guidance in its early stages. All views expressed in this paper are those of the authors and do not represent the views of JPMorgan Chase, The D. E. Shaw Group, Morgan Stanley, or the Brookings Institution.

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