How OIS Rates Relate to Federal Funds Rates
Article Quant Q&A · Author: Preetam
Summary
An overnight indexed swap (OIS) exchanges a fixed rate for the compounded return on a chosen overnight rate over the swap’s term. In the United States, the referenced Federal Funds rate is unsecured, so an OIS linked to it reflects expectations for compounded unsecured overnight funding. Other OIS contracts can reference secured rates, such as SOFR; whether the underlying lending rate is secured depends on the index, not on the swap itself.
The responses distinguish an OIS derivative from a loan: swap counterparties exchange rate exposure without lending the full notional, though margin may be required. The OIS fixed rate is set so the swap has zero value at inception and represents the market’s expected compounded overnight rate over the term. OIS rates are also used to discount collateralized derivatives because they can approximate the interest earned or paid on collateral. The discussion is conceptual and does not provide a pricing derivation; the relationship depends on the reference index and collateral terms.
Key ideas
- An OIS exchanges a fixed rate for the compounded value of a specified overnight index.
- A Federal Funds OIS references an unsecured overnight rate, while an OIS referencing SOFR uses a secured rate.
- An OIS is a derivative on overnight rates, not itself a secured or unsecured loan.
- The fixed OIS rate reflects the market’s pricing of compounded overnight rates over the swap term.
- OIS rates are commonly used to discount collateralized derivatives because they approximate collateral funding returns.
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# Difference between OIS Rate and Fed Funds Rate # Difference between OIS Rate and Fed Funds Rate I understand Fed Funds Rate is the rate at which banks lend/borrow to/from each other to maintain their daily reserve requirements at the Central Bank; also it is unsecured-meaning no collateral. Is this the same as the OIS rate? I read somewhere that this effectively the same as the Fed Fund Rate- however, OIS is supposed to be secured lending rate, unlike Fed Funds rate. So, how can they be the same, or even similar? Thanks. ## Answer by Dom (score 26) https://quant.stackexchange.com/a/29659 Since the financial crisis of 2008-9, banks have become less willing to lend to each other for periods of more than one day. They prefer to lend `overnight', and must do this at the overnight (O/N) rate which changes each day. However, if they wish to lend for periods of days, weeks or even months, the lender (and borrower) have to repeat the O/N deposit for every day of the period. Both borrower and lender are subject to the risk that the O/N rate will change. There are different overnight rates for each currency. In the UK, the Sterling Overnight Interbank Average Rate (SONIA) is used. This is an index calculated based on the average rate of unsecured overnight sterling transactions brokered by the Wholesale Market Brokers Association. Transactions must have a size greater than 25 Million GBP. In the US the equivalent index is the Fed Funds rate and in the Eurozone it is ESTER rate. ESTER, Federal funds and SONIA are unsecured rates. The purpose of OIS swaps is to allow banks to lock-in the cost of secured or unsecured overnight funding in advance. At the start of the lending period, the bank buys an OIS which will mature when the period of lending is to end. At the end of the lending period, the bank holds the rolled-up balance of all of the O/N reinvestments of the initial sum lent which it has just received back from the borrower. The OIS matures at this time. This amount held by the lending bank is identical to what the lender has to pay on one leg of the OIS. On the other leg the bank receives a fixed interest rate on the initial sum. This fixed rate is the OIS rate and it was set at the beginning of the OIS. The bank lender locked in this rate. OIS are not just for lenders. A borrower can also use an OIS to hedge their overnight rate risk. The OIS rate reflects the market's expectation of the cost of repeated overnight unsecured lending over periods of up to two weeks (sometimes more). Whether it is secured or not depends on which of the overnight rates it is linked to. Because it is based on overnight lending, it is assumed to have a lower credit risk than longer term interbank loans based on say 1M, 2M or 3M Libor and this is what drives the OIS-Libor spread. The OIS swap rate is the market's expectation of what the compounded daily (geometric average) index rate will be over the lifetime of the OIS. In USD the index rate is the fed funds rate which sets the cost of unsecured lending. In Euros the unsecured lending rate is set by EONIA and in Sterling it is called SONIA where ONIA stands for overnight index rate. However, more recent overnight indices like the USD-denominated SOFR are based on secured lending. Finally, your confusion may be due to the use of OIS for discounting of collateralised non-cleared derivatives. This has been a market practice since 2008. The OIS rate is used because it is close to the typical interest rate paid on the collateral that is held. It becomes the best estimate of the risk-neutral, risk-free rate in a world where the collateral has effectively eliminated counterparty risk. ## Answer by nbbo2 (score 9) https://quant.stackexchange.com/a/29647 Secured and unsecured refers to lending. However OIS is a swap based on FF, not a loan. It is a different animal. So OIS is a derivative, or a bet, based on the average of future (unsecured) FF rates over a period.. For example my name is Noob Rademayer, I am not a bank so I can't lend or borrow FF in the interbank market, but I can bet on the rate at which banks do. (For example I could bet that the cost of borrowing 1,000,000 in FF over the next 30 days will go up). To let me make these bets the counterparty may require me to put up a small amount of margin, however I still would not call that secured lending, it is just the normal margin for any derivative trade nowadays (enough to cover the loss if something goes wrong, maybe 1000 USD, not the full notional). On the other hand if I wanted to borrow 1 million USD from my broker I would have to put up more than 1 million in marketable securities; that is a secured loan. ## Answer by Lebaroux (score 4) https://quant.stackexchange.com/a/40036 The fixed leg of the OIS is an unsecured rate that is very close to Risk Free Rate (RFR) because of the combination of several reasons: - it is akin to a money market term deposit rate swapped against overnight deposit rates, compounded geometrically over the swap lifespan, so a net expected present value at inception of zero (Feynman-Kac) should reflect overnights lending rates levels (e.g. EFFR, OBFR, SOFR, EONIA, SOFIA), averaged over the swap lifespan - there is no exchange of principal, therefore the accrued exposure is minimal - settlement of an OIS is at termination, and - in a swap, the counter party risk is the replacement cost ## Answer by qwerty_uiop (score 0) https://quant.stackexchange.com/a/68512 In short, OIS: FF :: Forward Swap Rate: Forward Libor Rate In the OIS Swap, a fixed rate is exchanged for the FF rate. The fixed rate that makes the swap a par swap (i.e. the swap has net present value of 0 at the beginning of the swap) is called as the OIS rate. This is similar to the Vanilla IRS case, wherein a fixed rate is exchanged for the 3M Libor rates. The fixed rate that makes this a par swap is the forward swap rate. In some sense, the forward swap rate is a weighted average of the forward Libor rates. Hence it is representative but not exactly the same as the forward Libor rates belonging to the swap's tenor. You can then analyze the difference between the OIS rate and the FF rate in a similar manner, and also take into consideration the riskiness of the Libor rates and the FF rates on top of that.
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