# Why negative swap spreads are surprising

In some ways, the “Bond Crash/Course” was little more than my personal attempt to learn enough to understand this question. I am not quite there, yet, but I am a lot closer than when I started.

As I write, the 10-year swap spread remains inverted, albeit only slightly. Yesterday, the 7-year briefly joined it.

Let us suppose the 10-year swap spread were still negative 10bps and stayed that way through next week. The Treasury will auction a few billion dollars’ worth of 10-year notes next Thursday. Suppose you are a large global bank. Here is what you do.

1. Borrow $100 for 3 months in the London interbank market. By the definition of LIBOR, you will be able to borrow this money at the 3-month LIBOR rate. (Note that this is an unsecured loan.) 2. Participate in the Treasury auction. Purchase$100 worth of 10-year Treasuries. Suppose that auction clears at a yield of 3.8%. That means Treasury takes your $100 and gives you a 10-year note that pays you a coupon of$3.80 per year. (Note that whether those Treasuries yield 0.5% or 50% the following week, your coupon payments will always and forever be $3.80 per year. That is, your coupon payments do not depend on the market price of the bond after the auction finishes.) 3. Enter into a 10-year swap contract,$100 notional, where you pay fixed and receive LIBOR. If the swap spread is negative 10bps, then the fixed rate you will have to pay is $3.70 per year. So use your Treasury coupons to cover it with$0.10 to spare.
4. Every three months, pay off your unsecured loan with a new 3-month unsecured loan. By the definition of LIBOR, you can always do this at the then-current LIBOR rate. But that is exactly the rate you will receive from the variable side of your swap. So use the swap payments to cover the interest on each short-term loan exactly.
5. Pocket $0.10 per year, every year, leveraged to nothing and without committing any capital whatsoever. 6. Profit! Now, before I explain what I think is wrong with this strategy, let me explain what is not wrong with it. When presented with this arbitrage, finance professionals tend to respond, “You should use repos instead of borrowing unsecured at LIBOR, because you will get a better interest rate and earn an even better spread.” From there, they start talking about “5% haircuts” and “20-to-1 leverage” and “Sharpe ratios” and “swap spread volatility” and “posting collateral” and “leveraged speculative bets that the swap spread will normalize”. Such comments miss the point. Of course you get a better rate than LIBOR in the repo market, because repos are basically secured loans. But negative swap spreads are surprising precisely because LIBOR is an unsecured rate. There is no mystery when a secured loan yields less than Treasuries! If you fund this trade with repos, obviously you expose yourself to margin calls and haircuts and collateral requirements. (Finance professionals are used to this sort of trade. In fact, apparently a lot of them put it on.) But that is not the trade I am describing. I am describing a pure arbitrage; the financial equivalent of a perpetual motion machine. Once in place, this structure throws off$0.10 per year, every year, independent of any market-determined yields or spreads. And it appears to require zero capital: The LIBOR loan is unsecured, so that lender has no claim on your Treasury note. Therefore you can use the Treasury itself as collateral for the swap. Surely a Treasury paying $3.80 per year — actual cash, nothing synthetic — should be sufficient collateral for a$3.70/year fixed swap obligation?

And that is why negative swap spreads are surprising.

Next time: Why negative swap spreads are maybe not so surprising.

• mjturner

This might be a silly question, but why can’t you just borrow for 10yr at Libor and with the proceeds buy the Treausry bond?

• Not a silly question.

The answer is that LIBOR only exists for maturities of 1 year or less. By definition, it is the rate at which large banks can get a short-term unsecured loan in the London interbank market.

Swap rates themselves are supposedly equivalent to what LIBOR would be if it existed for longer maturities. I cover the derivation for this in the crash/course.

The arbitrage I suggest here is essentially just concatenating short-term LIBOR loans to synthesize a long-term LIBOR loan. For this to be lower interest than Treasuries is, as Jansen described, “spooky”. (Dang I miss that guy.)

• Cestwhat

“Participate in the Treasury auction. Purchase $100 worth of 10-year Treasuries. Suppose that auction clears at a yield of 3.8%. That means Treasury takes your$100 and gives you a 10-year note that pays you a coupon of $3.80 per year. (Note that whether those Treasuries yield 0.5% or 50% the following week, your coupon payments will always and forever be$3.80 per year. That is, your coupon payments do not depend on the market price of the bond after the auction finishes.)”

huh?

Your theoretical YTM is 3.80%, but the coupon is not going to be $3.80 per year. Ex. Lets, like you used above, assume that the swap spread is -10bp. Now lets take current pricing: 3.88% on the 10yr with a coupon of 3.625%. Fixed leg on the swap would therefore be 3.78%. So, every six months you’re going to be collecting$1.8125 in coupon payments. And every six months you would be making \$1.89 in fixed payments….(though, you’d want to match the timing of the swap pmts with the loan — i.e. every 3 months in your example). Anyway, case in point is that you have a funding cost on the fixed portion of the swap which you will have to meet. … (borrow from Fed for zilch using note as collateral anyone?)

• My understanding is that when Treasuries are auctioned, the coupon is set such that the bonds sell at par. That is, at the time of auction the coupon equals the yield. See the “Auction Structure” section of this NY Fed document.

And swap spreads are quoted relative to the par bond yield.

• Cestwhat

Ah, very good, I stand corrected (and thanks for the link — have just skimmed it, but will give it proper justice on the weekend) … and, in hindsight, the coupon setting mechanics makes perfect sense — YTM at auction would have equal PMT rate, otherwise they wouldn’t be being issued at par! (doh!). … Will have to look at the auction mechanics more closely in the case of an reopening (as “in the case of a note or TIPS reopening, the coupon rate on the new securities is identical to that on the outstanding securities and is not determined in the auction process”).

• negahban

@nemo

the 10 year pays a coupon every 6 months

• Andrew in Finland

I dont think as a bank you can ‘borrow at libor’. What you can do, is expect to be able to borrow in the range that the libor panel banks borrow at for a comparable bank to yourself.

A bank though can offer you a loan at libor for say a mortgage and have your interest rate float at the published libor but they will still need to be able to borrow at whatever rate is available in the interbank market where the panel of banks making up that currencies libor are saying they expect to be able to borrow at, where the BBA eliminate the top and bottom quartiles of panel responses, before averaging the remainder – something like that anyway.

And i assume i am not talking out of my preverbial here!

• Andrew in Finland

Since LIBOR is based on an opinion poll, the polled banks can for example say they can borrow at a lower rate than is actually the case to make it look like they have less bad loans than the next bank. So maybe it is not so spooky.