Why LIBOR Deposits and Swap Rates Do Not Imply Simple Arbitrage
Summary
The document examines why discount factors inferred from six- and twelve-month USD LIBOR do not reproduce a one-year swap rate in a simple semiannual swap equation. The discrepancy is explained as a tenor basis: a term LIBOR deposit and a swap referencing shorter-tenor LIBOR are different instruments, with different funding and credit exposures. Therefore, their rates cannot be substituted into one another as if they described identical cash flows.
The answers say that front-end swap curves are built from shorter-tenor instruments, historically including three-month Eurodollar futures, and that a one-year swap’s floating leg references three-month LIBOR. A twelve-month LIBOR quote instead reflects an unsecured term loan. The discussion notes that tenor and credit differences can persist, especially around funding stress; it also mentions a possible bank funding and hedging trade. The question’s approximate calculation and quoted market data are not enough to establish an arbitrage, and the answers do not quantify transaction costs, funding constraints, or precise curve construction.
Key ideas
- A twelve-month LIBOR deposit and a one-year swap referencing three-month LIBOR represent different transactions.
- The tenor basis reflects differences between term funding and a sequence of shorter-period floating payments.
- Front-end swap curves use instruments aligned with the swap’s floating reference tenor rather than simply using twelve-month LIBOR.
- A small mismatch in a simplified valuation equation does not alone establish an executable arbitrage opportunity.
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# Arbitrage on Libor and swap market # Arbitrage on Libor and swap market I must be wrong here, but still want to know where I am wrong. I found the data of Libor rate and swap rate from this link: http://www.interestrateswapstoday.com/libor-rates.html At the time, I read USD 6-month Libor rate: L6 = 2.8858% USD 12-month Libor rate: L12 = 3.1006% USD 1-year Swap rate: S1 = 2.828% Then, I calculate 6-month zero bond: P6 = 1/(1 + L6*0.5) = 0.9857762347093784 12-month zero bond: P12 = 1/(1+ L12) = 0.9699264601757894 If above 1-year swap rate is semi-annually settled (this is what I understood, but did not see official explanations), then one shall have 1 = S1*0.5*P6 + (S1*0.5+1)*P12 But, the right hand side is equal to 0.9975800962814657, strictly less than 1. Does it mean there is slight arbitrage opportunity, or otherwise I misunderstood the definition of the rates in the above? ## Answer by JoshK (score 3, accepted) https://quant.stackexchange.com/a/50509 You have discovered what is called the tenor basis. This is where theoretical finance and empirical finance part ways, at least a little bit. 12 month LIBOR means the rate at which I will give someone (AA credit - most likely another bank) a cash loan. I will send out the money and get it back 12 months later. If the borrower defaults then I'm in line with other unsecured creditors. The 1 year swap rate is the simply the fixed rate for a swap vs 3 month libor. Very little cash goes back and forth unless the market moves. They are two totally different transactions. The 12 month rate is almost always higher than the implied rate from the 3 month ED futures. There are various theories about why that should be. Some people believe that it reflects the risk of a longer loan and longer credit exposure. Fundamentally there is , sort of, an arbitrage. If you are money center bank you could lend to someone for 12 months and finance that by borrowing from ... depositors, other banks, etc ... for shorter terms. Roll it and make money. Hedge the rate exposure with 1y swaps. ## Answer by Edward Watson (score 1) https://quant.stackexchange.com/a/46960 More specifically the front end of the swap curve is constructed from 3m eurodollar futures and not the 6m, 12m libor. The credit crisis did help make that change. It's not because lIBOR was no longer believed to be a risk free rate as it's always been a bank funding rate essentially. It is because a vanilla libor 1yr swap is a derivative of 3m libor since that is the floating leg used to solve for the fixed leg. 12m libor and a 1yr swap are similar but they're different in that a 12m libor loan is a term loan and a 1yr swap is a revolving loan and in the crisis a 3m loan, or a series of 4 3 month loans, became a lot different than a 1yr loan. ## Answer by andrew.paul.acosta (score -2) https://quant.stackexchange.com/a/43022 Perhaps, but your result could be so close to 1.0000 that exact time each observation is gathered could be a factor. There could be a difference in a matter of seconds or minutes among when these numbers are collected. Also, your S1 is 3 digits after the decimal and the others have 4. This minor detail could also be cause of it being almost 1.0000 but not exactly.
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