Bond Talk on May 23

‏If you’re in Denver on May 23 and you’re interested in the bond market, join us for a QWAFAFEW* talk: Predicting the Supply of Long-Term Bonds.  The talk will be based on a new paper by Mattia Landoni, Chris Cameron, and myself. RSVP here.  I hope to see you there!

*Quantitative Work Alliance for Applied Finance, Education, and Wisdom

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New Paper on Bond Portfolio Dynamics

By Sealy j – Own work, CC BY-SA 4.0,


Mattia Landoni (SMU Cox School of Business) and I recently completed a paper on bond portfolio dynamics (now under review at an academic journal). We offer a new theory on the evolution of the maturity structures for rolling bond portfolios inspired by population mathematics, with new tools for evaluating and optimizing government borrowing strategies.  The working paper is available at SSRN (free registration required), or you can contact either of us and we will gladly send you a copy.

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Spam Followers

A wave of spam followers has hit this blog, so I removed the “follow” feature.  If you are sincerely interested in following this blog, please do so by contacting me.  Thank you.

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The Invisible Run-Off

Today, the Alphaville section of the Financial Times published The invisible run-off, in which I discuss a new source of “quantitative tightening” that almost no one seems to have noticed.  I estimate that $350 billion of private funds will be absorbed when the U.S. Treasury refinances its securities that are now in special accounts for state and local government bonds.  The Treasuries are currently held in escrows to secure municipal bonds that have been “advance refunded.”  An advance refunding is a complex refinancing technique for bonds that are months or years away from their first scheduled call date.

The Tax Cuts and Jobs Act prohibits advance refundings going forward because they increase the supply of tax-exempt bonds (at least until the old bonds are called), thereby shaving the revenue to the Treasury.

According to the Joint Committee on Taxation, the end of advance refundings will save the federal government $17 billion over the next ten years:



Of course, that’s not much in comparison to the overall projected effect of tax reform:



Over the next few years, perhaps $350 billion in escrow Treasuries will mature.  These will have to be refinanced without the help of new advance refundings. The run-off from escrows is not as large as the Fed’s expected balance sheet reduction (as much an obsession to the markets as a sizzling steak  to a dog), but the escrow wind-down could match about a third of the Fed’s roughly $1 trillion planned disposal of Treasuries.  The loss of escrow funding to the Treasury, and the additional supply to the market, could be prove significant.


The key to the $350 billion estimate for escrow securities was the S&P Municipal Bond Prerefunded/ETM Index.  The index includes about $190 billion in bonds that have been escrowed to a call date (“ETC”) or to escrowed to maturity (“ETM”).  I scaled up the prerefunded bonds by taking the ratio of the whole S&P municipal bond universe ($2.2 trillion) to the full reported size of the municipal market ($3.8 trillion).

I was interested to see that the average coupon of the prerefunded bonds in the index is 4.9%.  This seems to confirm the prevalence of 5% coupons in recent years.  These high coupons (their yield is now 1.6%) were among the most attractive candidates for refunding.

The escrow Treasuries generally have much lower coupons than the refunded bonds they support, so more than $1 in Treasuries are needed to cover the interest payments on each $1 of refunded bonds.   This relationship implies that $350 billion could be a conservative estimate for Treasuries in advance refunding escrows.  On the other hand, some of the escrows are so short that they are considered to be “current refundings” instead of advance refundings.  Current refundings are still allowed, but their short shelf life has probably limited their impact on the index.  To the extent that some bonds in the index correspond to current refundings, the $350 billion estimate could be on the high side.  Another distortion would be if the prerefunded share of the S&P index universe does not match that of the whole market.


Addendum added January 21, 2018

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My Letter to the Wall Street Journal

The Wall Street Journal just published a letter of mine, Debt Bomb has Shorter Fuse Than Many Citizens Think (credit to them for the snappy title, and to my wife Corrina for invaluable editing).  I respond to the Journal’s recent editorial Obama’s Debt Interest Bomb.

The editorial warned of a growing burden of interest payments on the national debt, due to rising interest rates and the anticipated drawdown of the Fed’s portfolio of Treasury securities.  In my letter, I point out that the problem is exacerbated by two factors.  First, the short maturity structure of the Treasury’s debt offers little protection against higher interest rates.

The second factor is the uneven composition of the securities held by the Fed.  The Fed neutralizes the interest payments it receives by returning them back to the Treasury.  Because the Fed tends to hold the Treasury’s higher-rate securities, the Treasury will sorely miss the Fed’s subsidy when it’s gone.


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Quarter the Cross: An Elegant Construction

Last month, I presented an infinite pattern of nested crosses as a response to the  #QuarterTheCross challenge on Twitter.  The idea is to find interesting ways to shade one-quarter of the area of the cross built from five squares.nested_crossNow David Butler, a math lecturer at the University of Adelaide, has found an elegant way to construct this pattern with the classic tools of compass and straightedge (I used some simple MATLAB code).

As the crosses get smaller, each new one must shrink by \sqrt{3}.

I asked David to explain his construction.

The segment marked “1” is \dfrac{1}{3} of the “radius” from a corner of the outer cross to the center, so the construction generates an inner cross with the required radius, \dfrac{\sqrt{3}}{3}=\dfrac{1}{\sqrt{3}} as long as the original radius.

A nice feature of this construction is that the compass is only used near the beginning.  After that, the construction always provides a scaffold for the next inner cross.


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Quarter the Cross

Yesterday, I noticed that some of the math teachers I follow on Twitter were challenging their students, and themselves, with the #quarterthecross problem.  The problem is simply to find interesting regions of a five-square cross that take up exactly one-quarter of its area.  This looks like a great way to get kids to explore fractions and geometry.


A solution that occurred to me would be to use an infinity of nested crosses.  If the area of the cross shrinks at each step by one-third, then the combined area of the colored regions converges to one-quarter of the large cross.  This works because the alternating geometric series

\dfrac{1}{ 3} - \dfrac{1}{ 3^{2}}+\dfrac{1}{ 3^{3}}- \dfrac{1}{ 3^{4}}+\dfrac{1}{ 3^{5}}...

converges to \dfrac{1}{4}.  Note that if the area shrinks by one-third, the width of the cross must scale down by the square root of 3.  So every two steps the width shrinks by one-third, placing a little cross precisely inside the middle square of a larger cross.

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