Why LIBOR Tenors Diverge: Credit Risk and the 3/6 Basis
Summary
The document explains why six-month LIBOR can stand well above three-month LIBOR, Eurodollar futures, and swap rates without creating an executable arbitrage. The rates refer to different borrowing periods and, in some instruments, different floating-rate indices. A bank lending at six-month LIBOR while financing itself through three-month borrowing takes on a mismatch: its lending exposure carries six-month credit risk, while its funding and forward borrowing carry different risk and balance-sheet costs. The forward rate therefore need not equal the rate implied mechanically by the two LIBOR fixings.
The replies describe this difference as a tenor basis and note that LIBOR itself is not directly achievable as a funding rate. In a multi-curve setting, cash flows may be valued using a funding or discount curve such as OIS, while swaps and futures tied to three-month LIBOR expose traders to that index rather than six-month LIBOR. The quoted market levels are an illustration from the period described, not a current pricing guide. The discussion is a conceptual explanation and does not provide a complete valuation or arbitrage model.
Key ideas
- Different LIBOR tenors represent distinct funding exposures and need not move in lockstep.
- A six-month lending rate funded with three-month borrowing entails credit, funding, and balance-sheet mismatches.
- The resulting tenor basis can persist without offering an executable arbitrage.
- Three-month swaps and Eurodollar futures primarily reflect exposure to the three-month index.
- Valuation may use a separate funding or discount curve when LIBOR is not an achievable funding rate.
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Full text
# Why would a 6M LIBOR rate be significantly above 3M LIBOR, ED futures and swap rates?
# 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?
## Answer by Phil H (score 8, accepted)
https://quant.stackexchange.com/a/4256
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.
## Answer by paralogical (score 3)
https://quant.stackexchange.com/a/4315
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.
## Answer by Dmitry (score 0)
https://quant.stackexchange.com/a/4253
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?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.