Saturday, August 24, 2019

Why stop at 100? The case for perpetuities

Issue 100-year Treasurys, advocates the Wall Street Journal.  It mentions a short note deep on the Treasury website that
Treasury’s Office of Debt Management is conducting broad outreach to refresh its understanding of market appetite for a potential Treasury ultra-long bond (50- or 100-year bonds). 
My 2 cents: Why stop at 100? Issue perpetuities! 

(I wrote a whole paper on this a while ago, if you want lots of detail and answers to practical questions. Unfortunately the Treasury website does not say how to send in suggestions, and nobody outreached to me, so this blog post is it.)

Perpetuities are bonds with no principal payment. Each perpetuity pays $1 forever.  If interest rates are 3%, to borrow $100, the government would sell three perpetuities, and then pay investors $3 each year. When the government wants to pay back the debt, it simply buys back the perpetuities on the open market.

A 100 year bond is almost a perpetuity. If the government issues a $100 100 year bond at 3%, only 100/(1.03)^100 = $5.20 of that value comes from the $100 principal payment. 95% of the value of a 100 year bond is already in the stream of coupons. For the investor, they are practically the same security. In particular they have nearly the same sensitivity to interest rate changes.

But perpetuities are better. Most of all: Perpetuities would be much more liquid -- easy to buy, sell, and use as collateral.  The reason is simple. Once 100 year bonds get going, there would be 100 separate and distinct issues outstanding. The 2123 2.6% 100 year bond is a different bond from the 2124 2.7% 100 year bond. If a dealer has an order for the first and an offer for the second, he or she cannot make the trade. If you borrow and sell short the first, you cannot deliver the second in return. This segmentation would make the markets for each bond thinner, and the bid ask spread larger. It would keep a lot of dealers and traders and market makers needlessly in business, which may  be one good reason the financial industry seems largely against the idea.

Perpetuities, by contrast, are a single security. When the government borrows more next year, it is borrowing more of the same security.  There is one, thick, transparent, low-spread market.

A more liquid market would pay lower rates.  Much of the point is for the government to borrow at low rates. Much of the reason government debt has such low interest rates is that it is very liquid -- easy to buy and sell, the "safe haven" in bad  times and so forth. Government debt is somewhat like money, and like money pays less interest in return for its liquidity. Well, then, the more liquid the better!

A 100 year bond would make sense if there were a group of investors sitting around who really wanted to have $3 coupons for 100 years, and then $100 exactly in 100 years, not 101 years, and they were not planning to buy or sell in the meantime. That is not remotely the case. Long term bonds are actively traded. Perpetuities match the varied investment horizons of ultimate investors, and by being more liquid are more flexible.

There is plenty of historical precedent. Perpetuities actually came before long-term bonds. They were the cornerstone of UK finance for the entire 19th century.

One can raise a bunch of practical objections, and if you have them go check out the paper.

Lower costs? The WSJ only advocates 100 year debt on the notion it would give the Treasury a lower borrowing cost when yield curves are inverted. This is a good argument, but more difficult and subtle than the WSJ lets on. The current yield is not the lifetime cost.  The 100 year cost of borrowing with short term bonds depends on what short term interest rates do in the future. If rates go up, it costs eventually more to borrow short. If rates go down it costs less, even if the current yield curve is inverted. In the benchmark "expectations model" yields have already adjusted so the expected cost is the same. The issue is the same to a household deciding between an ARM and a fixed rate mortgage. Even if the current ARM rate is higher than the fixed, if ARM rates go down in the future, the ARM could end up being better.

My paper was part of a conference at Treasury, published by Brookings.  I had a good debate with Robin Greenwood, Sam Hanson, Joshua Rudolph, and Larry Summers who wrote The Optimal Maturity of Government Debt (available here). They argued for borrowing short, not long. A the time the yield curve was steeply upward sloping, and in their simulations they opined that the chance of short rates rising and long rates declining to the point that the cost advantage would invert was small. The current reality has changed that conclusion as now it is the short rates that are higher.

Still, I think this is the wrong way to look at it. The Treasury is not in a great position to play bond trader and figure out where small variations in the yield curve reflect profitable opportunities.

Risk management. Like all investors, though, the Treasury's first question should be risk management, not profit. And there is a great risk facing the US Treasury. We are clearly going to run up a lot more debt before sanity sets in. Go look at the just released CBO Long Term Debt Outlook.

Net interest is already large. What happens if interest rates go up? Yes, they are unbelievably low now. But nobody really knows why. Between "secular stagnation" and "r* has declined" and "savings glut" you can see economists making things up right and left. So, you should not have huge confidence that we will not  return to historically normal interest rates of the last few centuries, or moreover that we will never suffer the kinds of interest rate spikes that happen to highly indebted countries trying to roll over 100% of  GDP  or so debt in a recession,  financial crisis, or war. If interest rates rise sharply, the US Treasury, having borrowed  short, is screwed.  We bought the ARM at a teaser rate.

This,  to me, is the real argument that  the  government should issue lots more long-term debt; 100 years if needed (but please, only every 10 years or so!) or, much better, perpetuities. Buy the fixed rate mortgage, and you keep the house no matter what happens to rates. Let's keep the house. In this discussion with Greenwood et al, they argued that the chance of such an interest rate spike is low. Perhaps, but the insurance is cheap -- and with a flat or inverted yield  curve it's even cheaper.

Borrow long to buy insurance, not just for a good deal.


In response to a few comments. In the paper I proposed that the Treasury issue 1)  fixed-rate perpetuities -- a security that pays one  dollar forever -- 2) floating-rate perpetuities -- just like Fed reserves, the interest rate adjusts  daily  and the price is always exactly $1.00 3) indexed perpetuities  -- it pays one dollar adjusted for  the CPI (or one of its improved versions) forever. The first eventually replaces all long  term debt, the second eventually replaces all short term debt, and the third replaces TIPS.

The second is really more  important, and I'll do a separate post eventually. If the treasury offered a fixed-value floating-rate instantly transferrable security just like reserves, it would do wonders for the  financial system.


  1. Interesting. I am not so sure about whether this is a good idea. When I traded corporate bonds the existence of roll-over / re-financing risk seemed to play a large role in constraining the behavior of corporate debtors and limiting the amount of debt they take on (sometimes excessively so given financing availability and probability). Looking at all those zeros on the balance sheet and contemplating the markets rejecting your new issue is a healthy scare. Also they seemed to do more prudent management of debt overall e.g. scheduling calls and re-issues during periods of low stress for the company, and doing a better job integrating it into planning.

    Logically, as a bond owner you would think that that reducing risk of future re-financing options for a company reduces your risk of not getting paid. Ditto government. But the corporate market went the other way with increased restrictions on covenants and more hoops to jump through to defease or re-issue debt.

    Of course US government does not have an external minder as yet (congress does not count) and mechanisms and options such as taxing authority are significantly different.

    But remove this risk for government and I suspect will just move elsewhere, likely higher debt and spending levels -- just making the coupon means everything is a-ok now. Tell an AOC you don't have to roll existing debt and watch her double down on spending.

    Perhaps this is one of those cases for a behavioral economics study: offer a borrower a perpetual or offer them one with periodic principal repayment with almost guaranteed rollover absent blatant stupidity and see what debt level they are willing to take on.

    Also reminds me a bit of the mortgage boom in 2007 -- at least amongst my family (narrow sample) the older generation viewed a mortgage as something one should pay back in their lifetime, while amongst the younger generation (unfortunately more educated and able to run spreadsheets), they bought more house that they could ever own just modeling cashflow, and when the market changed *unthinkably* -- well... hard to move if you will be immediately bankrupt if you sell the house. So yes, as you point out, you own the house and catastrophe averted if you pay the mortgage but you may lose hidden optionality.

    At least that is the intuition, although to be honest I find it hard to get a quick back-of-the-envelope mathematical sketch for it and I confess I have not worked through your papers. So put this at the 5% informed level. But I thought I would comment while this post is up - just trash it if non-sensical.

    1. RFC123, your most interesting remark is about how managers are disciplined by having to roll over bonds. It would be interesting to flesh that out. I guess with an old issue, the rating agencies don't pay a lot of attention so they downgrade rarely, but with a new issue, there is both more attention in rating and there is scrutiny from the investment bankers and the buyers. The immediate interest rate is like an employment evaluation for Management, and maybe the Board of Directors will get a report on it (will they?) so they'll care a lot, compared to the market prices of seasoned bonds.

  2. The Bank of England started issuing consols in 1751 and subsequent years and redeemed them in 1923. It would make sense for the Treasury to issue these no maturity instruments at market rates and redeem them when there is a budget surplus. In 1923,The UK showed primary budget surpluses.

  3. I think this is a good idea. But, there a raft of questions. here are just a few:

    Should the perpetuals (perps?, consols in memory of the 19th Century British bonds?) be fixed rate or floating rate?

    If fixed, should they be issued at different rates depending on the market? I took it that your thought was that they would be issued at one fixed rate. But, if market rates went up, the Federal Government would have to give huge discounts to sell new issues, and they might not want to do that. I think this was pretty common in 19th Century Europe. There would pressure to issue them at higher rate. OTOH, if they are issued at market rates, then the advantage of market depth will be vitiated.

    If the perps are floating rate, what should the basis of the adjustment? Short term or long term rates? If they float, some of the advantage of fixed in terms of locking in future interest costs will be lost.

    This discussion raises the question of the nature of currency. One perspective is that paper currency is a zero coupon perpetual. The Federal Reserve has issued 1.75 T$ of currency. (H.4.1) About 1.34 T$ of that is Benjamins. Chicago Fed says*: "more than 60% of all U.S. bills and nearly 80% of $100 bills are now overseas ... economic and political instability contribute to this demand." *Chicago Fed Letter, No. 396 (2018) Additional factors that might contribute to the demand for US currency might be avoiding a negative interest rate environment for people who do not have the wherewithal to access T-Bill markets. Of course there is always the issue of criminality and terrorism funding.

    The Fed could increase overseas demand for US currency by issuing notes in denominations higher than $100, such as $1,000 and $10,000. They were issued until 1946, and after 1969, they were officially discontinued, and the Fed began removing them from circulation. Only a few are left. "As of May 30, 2009, only 336 $10,000 bills were known to exist; 342 remaining $5,000 bills; and 165,372 remaining $1,000 bills.*" Because of their rarity, their numismatic value exceeds their face value. If you find one while cleaning out Grandma's attic. Don't take it to a bank,. Take it to a coin dealer. * Large_denominations_of_United_States_currency.

    If the Fed were to resume issuing high denomination bills, it would be money in our pockets, but foreign central banks would scream bloody murder. I think it is most unlikely.

    There are also interesting questions about the Fed's balance sheet. Should the Fed be permitted to buy them? Should the Fed be required to buy them? If the Fed can deal in them, they could buy when rates go up (driving the market value of fixed rate perps down), which would expand the money supply. Is that pro-cyclical or anti-cyclical? Should banks be allowed to hold them in lieu of reserve account deposits? If so should they be valued at face value or market value? Would that be pro- or anti-cylical?

    One more question while we are at it. If the US is issuing perpetuals which are IOs, should it limit other issuances to POs (zero coupon bonds which are Principal only)? That would solve the off run problem. Should the US sell inflation protection on the POs in the form of transferable put options? Of course the index should not be CPI. A trading market in those options would give us better clarity about what inflation really is.

  4. Perhaps it's a stupid question, but is there a difference between perpetuities and just plain money? Except for the diminished liquidity, that is. To me, it seems there is no principal difference.

    1. If "money" is understood to be "anything that extinguishes a debt (denominated in the same units of 'money')," then the new T-Perps would be such close substitutes for the large currency notes a statistical M-sum aggregation surely ought to include their sum too (if these aggregates matter, as Cochrane also seems to doubt).
      Not issuing T-Perps in paper format might be a solution to the black market detail.

    2. Federal Reserve Note are the non-coin portion of the circulating money of the United States and are legal tender in the US for all debts public and private. They are zero coupon perpetuals that are not subject to call, and may be put at par at any time.

      As I noted above, almost 1 T$ of Benjamins circulates abroad and may be considered to be an important (about 15% of the total outstanding) and cheap form of finance for the US government.

  5. I should add that the Federal Reserve Note derives no value from its coupon which is zero or its principal value which is at infinity and is therefore also zero. The free transferability and complete call protection are elements of value, but at least 80% of its value derives from the right to put it at face value to any creditor.

  6. Govt debt is simply base money that is locked up for some period of time. Why should anyone be rewarded just for hoarding money? That reward / interest comes from taxpayers, thus the whole process boils down to subsidising the rich at the expense of the less well off.

  7. There are quite a few differences. Perpetuities would pay interest, which money does not. Also, the market value of a perpetuity can change, and these changes gains will have taxable consequences in a realization or a mark-to-market regime.

    But, yes, there are elements of the perpetuity security -- for both issuers and buyers -- that make them akin to money. Yet, from the issuer perspective, issuing the perpetuity foregoes the value of seigniorage. From the buyers', out goes anonimity. So neither would see perpetuities as a good substitute for cash. Though that does not mean that they could pave the way to digital, interest paying, money.

  8. There is a very cool video on the topic of British perpetual bonds:

    1. Actually, Dutch. But what's a hundred miles and a bunch of extra consonants among friends?

  9. Great post. I've often wondered about this. The discussion forum for my online MBA's this week is on century bonds. The big thing is transaction costs from having to retire and reissue. Could that be the real reason we don't have perpetuities--- the investment banks and traders like having lots of different securities? (Note that they'd still be able to *create* fixed-length securities for customers who wanted them-- you probably said this somewhere.)

  10. One interesting thing about perpetuities is that you could buy them to offset your (expected) property taxes, meaning that a house with a lower tax burden would be functionally the same as a house with a higher tax burden + a perpetuity. (This depends a little on how expectations of future property taxes are set.) The price of a perpetuity could then be used in comparing house prices.

  11. Summers has a notoriously poor record of interest rate forecasting, as evidenced by the Harvard swap debacle ( ) - but I would expect him to reverse his position now that the curve has inverted, since his main article of faith seems to be that a massive fiscal stimulus is what is needed...

  12. The chart embedded in your article (see above) puts a nail through the heart of your argument--it projects negative primary deficits and an increasing total deficit (primary deficit + interest payments) without prospect of a surplus in any year out to 2049. What lies beyond 2049? More deficits, almost surely. Absence a sustainable run of surpluses sufficient to retire outstanding perpetuties, what would induce Congress to budget for the retirement of the outstanding obligations? Not the so-called 'debt ceiling', as we have seen the 'ceiling' is raised whenever the debt outstanding rises to the 'ceiling' thus rendering it ineffectual as a means of limiting U.S. government debt obligations.

    A floating rate perpetuity? Impossible to value, absent a retraction provision (i.e., a put option held by the holder of the perpetuity).

    A declining coupon payment perpetuity? Worth less than the fixed rate perpetuity--why would one buy it? At some point it would be effectively worthless, so the discount rate applied would exceed r+g (r the nominal rate of interest, g the rate of coupon value depreciation), say, r+g+d with d >0 varying with market sentiment.

    A fixed rate, continuously issued, perpetuity would suffer if supply exceeded demand. The applied discount rate, r* would exceed the nominal coupon rate desired by the government, r. If the coupon payment is optional and non-cumulative, you have a situation in which Congress might issue a large quantity of such securities and then suspend payment on them without causing a legal default. What's not to like (on the part of Congress)? Congress could always promise to resume payments next period, or next year, and then come up with a reason (excuse) not to resume payments. The Treasury could repeat this gambit endlessly (or at least until the markets baulked at which point the Treasury would resume payments on the suspended perpetuities until the new issue sold, and then turnaround again and suspend payments citing "economic conditions". It would be a game. The discount rate applied to the perpetuity would factor in the likelihood of payment suspension so that instead of r, the rate would be r + p, with p equal to the probability of suspension.

    Corporate debt would soon look very attractive to the market. Government debt would become less suitable for the purposes it is now used for. The government would find it less able to fund its needs from the market; taxes of all types would increase to offset the reduced access to debt market funding. Default risk would rise.

    Interesting to contemplate and discuss, but not practicable.

  13. >The issue is the same to a household deciding between an ARM and a fixed rate mortgage. Even if the current ARM rate is higher than the fixed, if ARM rates go down in the future, the ARM could end up being better.

    The mortgage is significantly more complicated than a bond, since the mortgagor has the right to buy back the mortgage at par. This embedded call option to close the short bond position has significant value, and could get exercised via refinance if rates fall.

    If the fixed rate is lower than the ARM, it's almost always correct to take the fixed rate and refinance if and when the expected future rate decrease happens.

  14. Old Eagle Eye:
    (1) What's the problem with valuing a floating rate perpetuity?
    (2) Why do you think Congress would make the coupon optional on debt? That would indeed be crazy.

  15. A bit off-topic but probably of interest to the same people as perpetual bonds: Gulati and Kahan, Sleeping Giant Contracts, .

    From my notes: The situation is that something like that which incidentally violates a bond covenant but might well have a real business purpose. This triggers immediate repayment at par. But bond indentures often have clauses that say that the borrower can redeem the bonds any time it wants, but if it does, it has to pay a premium. This is to prevent refinancing any time the interest rate drops. The big question in Sharon Steel and in Case America is whether the borrower must not only pay par, but the premium, in a case of "voluntary default" like this. The parties can of course contract to make what happens completely clear, but suppose they don't. In Sharon Steel, Ralph Winter said they have to pay the premium.

  16. The two hundred year trend in real rates appears to be down. That makes sense given richer societies, longer life spans, a long peace and more and more efficient markets.

  17. Turn it into a security token; would make the trading even easier. Might even clear on a blockchain and then you'd know exactly who had what when

  18. Why not tokenize it, clear it on a blockchain and make it even easier to trade?

  19. This is entirely true:

    "They were the cornerstone of UK finance for the entire 19th century."

    So, Chesterton's Fence. Why did they stop being so? Why did the UK govt buy them back a few years ago? And what is it that has changed to make them a good idea again?

    There also being another point. As you say the change would make it easier for government to borrow. Given the spendthrift nature of politics this is a good idea why?

  20. Why not perpetuities? Because they never go away. After 100, 1000, or 100,000 years you're still servicing them, whether you still need to be in debt or not. One of the nice features of term debt is that eventually you pay it off.

    The solution to that is to make them callable, but callable perpetuities can be less attractive to investors who want to lock in a yield they perceive as high, and do not want the bond called when yields go down.

  21. Why not perpetuities? Because they never go away. After 100, 1000, or 100,000 years you're still servicing them, whether you still need to be in debt or not. One of the nice features of term debt is that eventually you pay it off.

    The solution to that is to make them callable, but callable perpetuities can be less attractive to investors who want to lock in a yield they perceive as high, and do not want the bond called when yields go down.

  22. John-should the Treasury issue 40TR in perpetual bonds now, refinancing the current 20TR debt, due to extraordinarily low interest rates resulting from Fed intervention on Corona?


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