# Why would a 6M LIBOR rate be significantly above 3M LIBOR, ED futures and swap rates?

Just was just looking at the various interest rates and noticed this:

         Tenor         Rate

LIBOR:
3M          0.3585%
6M          0.6359%   <-- sticks out above others

ED Futures:

Z2 (Dec 12)     99.680   => approx  0.320%
H3 (Mar 13)     99.675   => approx  0.325%
M3 (Jun 13)     99.660   => approx  0.340%
...            ...

3M<->Fixed Swap Rates:
2Y          0.3665%
3Y          0.4390%
...            ...


Note that the 6M LIBOR rate (0.6359%) seems to stick out quite a bit above the Eurodollar Future rates and 2Y swap rates, all of which are around 0.35% give or take. This seems to create an "obvious" arbitrage opportunity, and yet this persists.

Why?

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The main problem is that you cannot achieve Libor in the markets. So the old-fashioned method of discounting at Libor doesn't work any more. As an example, if you compound up the 3m Libor with today's price on a 3x6 FRA, you won't get 6m Libor. Traditionally, that would mean arbitrage, but these days it's just a fact of life. You cannot achieve 3m Libor for the first 3m months, so the PV of that cashflow comes through a funding curve (e.g. OIS curve). At 3x6, because FRAs pay at the start discounted at the quoted rate, you can't achieve 3m Libor on that cash flow either. So the expectation that you could borrow the cashflow for the 3x6 FRA at today's 3m Libor, and lend the 6m at 6m Libor just doesn't work. You come up short, and that amount is the basis.

These days, it is safer to treat 3m and 6m Libor as two indices to which you have exposure, and which are correlated but not bound together. So doing 3m IRS gives you exposure to 3m Libor, which you can only correctly hedge or arbitrage using 3m instruments.

In USD this is simple enough, because most things are 3m. In EUR, GBP etc, longer term IRS are 6m, and short term IR is 3m, and you end up with a 3/6 basis exposure.

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If a bank lends 6m Libor and finances it by borrowing 3m Libor and borrowing forward 3x6 libor, this is not arbitrage, as the bank is assuming 6m credit risk whilst his financing is 3m credit risk. (There are also other factors like regulatory capital, tying up balance sheet for 6m, etc.) So the text book case where the 3x6 FRA (or front Eurodollar) is equal to the implied 3m forward rate derived from 3m and 6m libor fixings is an academic fiction. In reality the 3x6 FRA will always be lower than the impled forward calculated from the 3m and 6m fixings. This is "the basis". In the past it was negligible, but since 2008 it is significant.

(NB. Hardly any interbank lending takes place at 6m nowadays.)

As the swap rates that you cite are vs 3m floating rates, the fixed rate on those swaps reflects expectations of future 3m fixings, not 3x6, 6x9, ... implied forwards. That is why the 2y swap is about 37bps. If the 2y swap were vs 6m floating, it would probably trade around 60-70bps. In other words, the swap rates reflect the money market basis on the tenor of the floating leg.

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Well, 6m Libor isn't directly tradeable, none of the products above would use it for pricing. ED uses 3m, ir swaps floating leg also uses quarterly payments (hence 3m). How would you arbitrage 6m Libor?

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