Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

Negative swap spread

The fact that the 30 year US dollar swap rate is lower than the
interest rate on the 30 year US treasury bond was till recently
something that only fixed income specialists worried about. Sure, the
Across the Curve blog has
been putting NEGATIVE in capital letters in each of his daily blog
posts on the swap spread for several months now, but the mainstream
financial media did not bother much about it. Last week, however,the
Financial Times carried a detailed story (“Negative 30-year rate swap
spread linger,” September 9, 2009) on the subject.

Under the current view that financial markets have normalized, the
negative swap spread is an embarrassment because it suggests that even
a year after Lehman, simple arbitrage trades are not happening because
of a paucity of the balance sheets required to put on the
trades. Alternative explanations are being sought for the phenomenon,
and the report states that “questions are being asked in the
market about the assumption governing whether a 30-year swap is
riskier than a 30-year bond.”

In this post (necessarily long and highly technical), I shall try
to examine this question. I shall initially assume that the interest
rate swaps have no counterparty risk because of high degree of
collaterilization. This is very different from asserting that the swap
rate is a risk free rate.

I shall assume that the Libor rate on the floating leg of the
interest rate swap is a rate that includes a default risk component. I
shall also assume that the default risk inherent in Libor is greater
than that of US Treasury. More precisely, I shall assume that the TED
spread (the excess of Libor over the T-Bill yield at the same
maturity) is expected to remain positive. I shall also assume that the
positive TED spread reflects the greater credit risk of Libor as
compared to the T-Bill. Before the crisis, it was fashionable in the
CDS market to assume that Libor and swap rates were risk free rates
and the TED spread was due to liquidity and tax effects. I believe
that this claim is untenable today.

Since banks are afloat today with huge government support, I think
it is reasonable to assume that the government is more credit worthy
than the banks. But I do not assume that the US government is risk free
either. It too can default, but the probability of this default is
lower than that of the banks.

Libor is the borrowing rate of a bank with what is often called a
“refreshed Libor rating.” On every day that Libor is
polled, only a sample of “sound” banks is
considered. Therefore, the default risk inherent in three-month Libor
is that of a bank defaulting in the next three months given that it
meets the Libor creditworthiness standard today. Libor exceeds a
hypothetical three month risk free rate by a compensation for this
possibility of default.

Assuming that the interest rate swap itself has no default risk,
the fixed rate payer should be willing to pay a fixed rate that
exceeds the risk free rate because what he receives on the floating
leg is higher than the risk free rate. He should also be willing to
pay more than he would on a swap in which the floating leg was the US
T-bill yield instead of Libor because I am assuming that the TED
spread (T-bill yield minus Libor) is expected to be positive. The
T-Bill yield itself exceeds a hypothetical risk free rate because of
the the possibility of default by the US government.

Unfortunately, even from all these assumptions, it does not follow
that the 30 year UST yield should be less than the 30 year swap rate
without some further assumptions that we will come to at the end. The
problem is that the interest rate swap is not terminated by the
default by one or more of the Libor rated banks or by the default of
the US government. Several banks may fail and Libor may still be
computed the next day based on the few banks that remain. The floating
rate payer on the swap would have to make floating leg payments at
this Libor rate, and the fixed rate payer would have to make fixed leg
payments at the fixed rate.

The holder of the 30 year bond however will not continue to receive
coupons if the US government has defaulted. To eliminate the default
risk of the US Treasury, we must consider a hypothetical asset swap on
the 30 year bond. Consider an asset swap in which (a) the owner of a
newly minted bond sells it to an asset swap buyer at par, (b) the
buyer agrees to make fixed rate payments at the coupon rate of the
bond, and (c) the seller agrees to make a floating rate payment at
Libor +/- a spread.

Assuming that the asset swap is risk free, the asset swap seller
now has a risk free stream of payments equal to the coupon of the 30
year UST bond. If it were true that the floating leg payment would be
equal to the T-bill yield, then we can immediately conclude that the
30 year bond must yield less than the fixed rate of the 30 year interest
rate swap. If not an arbitrageur would enter into an asset swap as a
seller and simultaneously enter into an interest rate swap as a fixed
rate payer. It would be left with two sources of profit from these two

  1. the fixed rate it receives on the asset swap would exceed the
    fixed rate that it pays on the interest rate swap because the 30 year
    bond yields more than the swap rate
  2. the floating rate it pays on the asset swap (T-bill yield) would
    be less than what it pays in the interest rate swap (Libor) because
    the TED spread is expected to be positive.

If US Treasury were risk free, it is evident that the floating leg
would be equal to the T-Bill yield. We just add a notional exchange of
principal at the end (which simply cancels out). The fixed leg must be
worth par because it is economically the same as the newly minted 30
year Treasury (par) bond. Therefore the floating leg payment including
the notional payment must also be worth par, but this “floating
rate bond” can be worth par only if the floating rate is the
risk free rate which is the T-Bill yield.

This equivalence breaks down when US Treasury can default. To
understand this consider a modified asset swap which terminates
without any termination payments if and when US government
defaults. In this case, it is easy to see that the modified asset swap
floating leg must equal the T-Bill yield. The case where the US
government does not default has already been analyzed above, so
consider what happens if there is a default.

In this case, we add a notional exchange between the swap buyer and
the swap seller not of the principal value of the bond but of the
recovery value of the defaulted bond. With this notional payment
included, the fixed leg again is the same as the US treasury bond. It
must therefore be worth par because the Treasury bond is a par
bond. The floating leg must therefore also be worth par which means
that it (including the notional payment at default of the recovery
value) must be a par floater. But the T-Bill yield is precisely the
yield on a par floater of the US government.

With this understanding in place, let us now return to the only
possible explanation for the swap rate being less than the UST rate in
a perfect market – the asset swap floating leg must exceed Libor
(or the asset swap spread must be positive). In this case, in a
perfect market the fixed leg (which is the UST bond yield) must also
exceed the swap rate – the asset swap seller receives a larger
fixed leg than in an interest rate swap but also pays a higher
floating rate.

So the position is that for the current interest rates to be
consistent with a perfect market, the asset swap spread should be
positive while we know that the modified asset swap spread (the one
that terminates on default by the US government) is the negative of
the TED spread and is therefore expected to be negative. The
difference between the asset swap and the modified asset swap is that
after default by the US government, the modified swap terminates while
the ordinary asset swap subsists.

Everything now depends on what Libor is likely to be after the
default by the US government. If Libor is expected to be high, the
asset swap seller would have to make large floating rate payments in
return for the fixed rate payment from the asset swap buyer. The
subsisting swap would therefore be a liability to the asset swap
seller and he would therefore insist on paying a lower (more negative)
spread in the asset swap than in the modified asset swap where this
liability would not exist. This would imply that the asset swap
floating leg would be even lower than the T-Bill yield and therefore
much lower than Libor. The 30 year UST yield must therefore be less
than the swap rate.

For the 30 year US yield to be higher than the swap rate in a
perfect market therefore the asset swap must be beneficial to the
asset swap seller after the default by the US government. This can
happen only if interest rates are very low after default. I do not
find this very plausible. I would expect sovereigns to default on
local currency debt after inflation has been tried and found to be
wanting. With double digit inflation, one would imagine Libor also to
be in double digits and the asset swap would be a huge liability to
the asset swap seller who would be receiving something like 4.5%
fixed. Considering this liability, the asset swap spread should be
less than the T-bill yield which in turn is less than Libor.

Thus it appears to me that a 30 year swap rate less than the 30
year UST yield is consistent with perfect markets only if we are
willing to make either of the two assumptions:

  1. The TED spread is expected to be negative implying that banks are
    safer than the US government; or
  2. A potential default by the US government would happen in an
    environment of very low rates where Libor would be very low.

I find both these assumptions implausible and would believe that
the phenomenon that we are seeing in 30 year swaps is due to the
limits to arbitrage arising from inadequate capital and leverage.

One final question that might trouble the reader is the assumption
that there is no counterparty risk in the swaps even when the
sovereign itself has defaulted. Actually, if we simply assume that all
the swaps terminate on default by the US government, the above
arguments still go through. The fixed rate payer in the interest rate
swap makes money before the default. If at this point, he is allowed
to pack up his bags and go home, that is fine in this model.

This has been a difficult piece of analysis for me and I would
welcome comments, suggestions and corrections.


12 responses to “Negative swap spread

  1. Arnaud September 16, 2009 at 8:17 pm

    Dear Javanth,

    negative swap spread already occured in Europe, and not only for Italy, Spain or Greece, but also Germany and France.
    For me, it just shows that investors are a bit worried of the huge debt which has been created. This uncertainty is of course higher for the long term future.
    On the opposite, swaps are more and more done through a clearing house, with daily or weekly margin calls, which obviously highly reduce the counterparty risk.

    I also agree with you that the lack of arbitrageur is not helping….too much regulation and attack against “speculators” is not helping the efficiency of the market, which at the end will cost more for the taxpayer (higher bond yield).


  2. Jade Bond September 16, 2009 at 10:05 pm

    Thanks for posting this. I’ve always wondered what the significance of these negative swap rates were. I’m certainly no expert, but I have a couple scenario ideas I’m not sure where included in your analysis.

    1) How would a failed auction at the US Treasury play into this. My understanding is that would not necessarily be a default, but could happen even in a low interest rate environment.

    2) In the 30-year horizon, it seems plausible for the U.S. to become an anomaly of economic distress while the rest of the world is more stable. I’m not talking about decoupling here, but simply the rates of interest and inflation in the U.S. being significantly higher than other developed nations. In other words, what if the high inflation scenario were isolated to the US? Can a US dollar LIBOR be hedged with a different currency LIBOR? It seems the US might not default while the dollar and US Treasurys collapse in value relative to non-US investors, who can take advantage of currency or international interest-rate spreads to compensate for their US dollar 30-year bond swaps.

  3. tradebum September 17, 2009 at 8:19 am

    Thank you for your analysis. I can’t help but wonder that there is no rhyme nor reason to much in the markets these days and may likely stay like this for some time. But I appreciate the clarity on the arbitrage and the lack of credit and leverage. Makes sense. Citigroups Pandit said that he was most concerned about the shadow banking system, that it was not really moving and that securitization is still a large issue. I am most concerned that Bernanke doesn’t seem to understand that Congress and americans have no stomach for anymore of this and when it all comes crashing, rioting will take the place of civility. But what do I know right?

  4. Geoff September 17, 2009 at 8:55 am

    The negative spread is the natural result of the spread of corporate or bank bonds over swap. A swap is the expected average of a stream of short term Libors; it says nothing of a banks ability to re-borrow each period. A bond, on the other hand, guarantees ongoing funding until maturity. That term funding is available only through the charging of a spread. A government bond, therefore, has a yield higher than swap, whenever the government’s term funding spread exceeds the term Ted-Libor swap spread.

    • mcooganj September 18, 2009 at 5:41 pm

      essentially you’re observing that bank bonds prive LIBOR ++, which is an example of the cost of tenor i talk about below.

      that is, if we take an average LIBOR bank’s bond, it’s always LIBOR ++. that’s cause there’s a premium for term money. same reason 3/6 floating basis is not zero.

  5. mcooganj September 17, 2009 at 4:50 pm

    isn’t it about the value of the cash?

    i think that this is the issue in the real market – as opposed to your perfect market. there is a value on the front and back principle exchange in the bond.

    essentially, you are treating a 30yr bond as a strip of 3m tbills, and saying that as 3m libor is above 3m tbill(fair assumption), 30yr swap (which is a weighted average of expected 3m libor over 30yrs) should be higher than 30yr bond (which isn’t a string of 3m tbills!).

    this makes sense, as far as it goes. but there is a value on the exchange. the swap is NPV off balance sheet on day 1, the 30yr bond is -$$ for 30yrs. this is why the coupon flow from a 30yr bond should be higher than the flow from rolling through 3m tbills.

    at very least, there must be some compensation for the relative difference in liquidity of 3m tbills (the world’s most liquid cash like instrument) and the bond (by appointment only, thanks)

    this ‘cost of tenor’ appears in all markets, and is why 6m libor is above 3m libor + a 3×6 FRA (given cash rate expectations). equivalently, it’s why 3/6 floating basis isn’t always 0bps.

    i think you might have basically assumed this away ini your analysis. i believe that this is the heart of the problem.

    as balance sheets open up (so that the value of the cash upfront drops) and as liquidity returns to the market, i think that the 30yr spread will go back to positive.

    i don’t think it’s a mystery.


  6. mcooganj September 17, 2009 at 4:51 pm

    swap is zero NPV

  7. Jay Herron January 23, 2010 at 3:35 am

    i currently have $753 million in fixed payor swaps that were part of a long-term debt structure that has been distressed since 1-month LIBOR went to all time lows. How probable is it that this metric is being manipulated by the LIBOR submitting banks because of the value it has on the SWAPs? It doesn’t cost them on the other side since they aren’t lending any money at the LIBOR.

  8. Red3 June 17, 2010 at 4:39 pm

    This is what happens when people who have never traded speak out on things they don’t understand.

    1) Negative swap spreads are nothing new.

    2) Of greatest importance is to understand that the spread (as with any “price”) IS NOT credit as such. It is SUPPLY & DEMAND. While it is customary to associate swap spreads with credit, it just not the whole story. In the real world supply & demand rules .. whether your imagination likes it or not.

    3) Crucially, there is nothing wrong with “arbitrage” because there is no arbitrage. If you actually tried to trade that spread you will find that the bid/offer will not allow an arb. This is the same issue as negative interest rates (e.g. in CHF and JPY not long ago). There was no arb there either. All it means is that supply/demand is pushing one side of the “non-arb” (i.e. they will not lend you money AND pay you interest, what actually happens is that they charge you a fee for “depositing” … and that’s the -ve bit, and its not on the borrowing).

    Finally, I am still astonished how self-appointed experts seem to know so little about the markets. It is a virtual fallacy that US banks have “a lot” of government bail-out. If you do even a little checking of the facts, you will find that:

    a) Most of the big banks were “strong armed” by Paulson to take money they did not want or need. This is well documented.

    b) Although about 700 billion was set aside for TARP, only about 530 Billion was used, but of that only about 245 Billion went to banks. All the rest (i.e. most of it) went to US government agencies (Fannie et al), and the two auto’s GM and Chrysler.

    Crucially, within 6-12 months the banks had repaid 185 Billion, plus 27 Billion in profit to the government (how could they do that if they were in so much “trouble”?).

    As of early 2010, net-net, there was only about 30 Billion of TARP with the banks. I cant imagine that anybody would thing 30 Billion to be “big” in a 14 Trillion GDP economy.

    c) MUCH WORSE, in respect of your comments, is that you seem to have ignored the 7 Trillion (with a T) that the US government put into the mortgage market (dominated by sub- and sub-sub-prime loans) .. which in fact was the primary cause of the melt-down.

    Moreover, the US Gov, via the Fed, had bailed out the government’s losses not just via 130 Billion to the GSE’s, but also by a shadow bail-out of 1.5 TRILLION (with a T) of US government created toxic mortgage products. That shadow bail-out was almost exclusively to buy-back 1.5 Trillion in GSE MBS’ … and guess what those are hedged with … swaps.

    Of course the Fed did all that by “printing money” (they no longer actually “print” it, they do it electronically by paying for the MBS’s electronically, and Congressional power allows them to just “say” they have the money)

    In a sense, this reduces the US Gov’s credit rating, since more than 50% of the GSE MBS’s were sub/sub/sub-prime, and they are likely to default .. alternatively, a left wing administration might consider this the US Gov’s attempt to atone for (part) of their sins by bailing out mortgagors/voters.

    Its no surprise that the swap market experiences distortions that are non-arbitragible when the might of the US Gov is behind a decidedly non-normal market activity.

    … go read this if you want a “simple” explanation:

    … or this, if you want the “full SP”:

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