Benchmark rates: from LIBOR to SOFR, €STR and SONIA

For decades, the interest on hundreds of trillions of dollars of loans, mortgages and derivatives was set each morning by a small group of large banks answering one question: what would it cost you to borrow? Then it emerged that some had been shading their answers. Replacing that number became one of the largest projects finance has ever undertaken.

A floating-rate loan needs a rate that both sides can look up, so that every payment can be worked out without arguing. That published rate is a benchmarkA published rate or price that contracts refer to, so that payments can be worked out without renegotiating.. For a generation the benchmark of choice was LIBORLondon Interbank Offered Rate: an average of banks' estimates of what it would cost them to borrow unsecured from other banks for a set term., the London Interbank Offered Rate.

How LIBOR worked. Each morning a panel of large banks told the administrator what it believed it would cost them to borrow unsecured from other banks, for terms from overnight to a year. The highest and lowest quarter of answers were dropped and the rest averaged. In its final years it was published for five currencies (US dollar, sterling, euro, Swiss franc and yen) and seven terms: 35 rates a day. Because it reflected lending to banks, it included a premium for bank credit risk, and it was known at the start of each interest period.

What went wrong. LIBOR was an estimate, not a measurement. After 2008 banks rarely borrowed from each other unsecured for three or six months, so many answers rested on judgement. Some traders asked colleagues to nudge submissions to help their positions, and during the crisis some banks kept their answers low so as not to look weak. Fines followed, and regulators concluded that a benchmark resting on so few real trades could not be saved.

The replacements: overnight risk-free rates

Regulators pushed each currency towards an overnight risk-free rateRisk-free rate: an overnight rate built from actual transactions, with little or no bank credit risk in it. (RFR): a rate built from a large volume of real overnight transactions. Overnight lending carries very little credit risk, and its markets are deep, so these rates are hard to bend.

A new problem: no term. LIBOR gave a three-month rate known at the start of the period. An RFR is an overnight rate. To use it for a three-month loan, the standard method is to compound it in arrearsWorking out a period's interest rate at the end of the period, from the overnight rates that actually occurred.: record each day's rate through the period and multiply up the daily growth. The rate is known only at the end. Loans often use a short “lookback”, using rates from a few business days earlier, so that the borrower knows the payment a few days before it is due. Some markets also publish forward-looking term ratesFixed today for a future period, such as three months, so the borrower knows the rate in advance. built from futures on the RFR, such as Term SOFR, for loans where borrowers want to know the rate up front.

Not every term benchmark disappeared. EURIBOR, the euro interbank rate, was reformed rather than replaced and is still widely used, while EONIA, the old euro overnight rate, was retired in January 2022 in favour of €STR.

Compounding in arrears uses one new symbol, $\prod$, which means “multiply together” in the way $\sum$ means “add up”. Let $r_i$ be the overnight rate on business day $i$, $n_i$ the calendar days it applies for, $d$ the number of business days and $D$ the calendar days in the period.

The interest on a loan of $N$ is then $N \times R \times D/360$, which is the same as $N$ times the product minus one. Use 365 throughout for SONIA.

Slide the number of fixings published back to zero and step forward one day at a time: the week's rate stays unknown until Friday's fixing arrives. Then raise Friday's rate and notice it counts three times, because it covers the weekend. Switch to SONIA to see the 365-day basis.

A company borrows US$10,000,000 from a Monday to the following Monday, at SOFR compounded in arrears, ACT/360, with no spread to keep the numbers clear. The overnight rates (illustrative) are Mon 4.31%, Tue 4.33%, Wed 4.30%, Thu 4.35%, Fri 4.32%.

After LIBOR, benchmarks became regulated products. The IOSCO Principles for Financial Benchmarks (2013) set out how a benchmark should be governed, built from real transactions where possible, and checked. The EU Benchmarks Regulation (2016), and the UK version that followed Brexit, require administrators to be authorised and let supervisors step in if a critical benchmark is at risk. Supervisors also pressed banks to make sure their old LIBOR contracts had workable fallbacks.

Looking ahead: interest rate swaps on these rates are the subject of L1.7.04.

• LIBOR was an average of banks' estimates, not trades. Thin markets and manipulation led regulators to wind it down, ending in September 2024.
• Each major currency now uses an overnight risk-free rate: SOFR (USD, secured), €STR (EUR), SONIA (GBP), TONA (JPY), SARON (CHF).
• These rates are built from large volumes of real overnight transactions, so they are hard to manipulate.
• For a term loan, the overnight rate is compounded in arrears: multiply the daily growth factors, subtract one, annualise. It is known only at the end.
• RFRs lack LIBOR's bank credit premium, so old contracts switched with a fixed spread adjustment.

Benchmark rate

A published rate or price that contracts refer to, so that payments can be worked out without renegotiating.

LIBOR

London Interbank Offered Rate: an average of banks' estimates of what it would cost them to borrow unsecured from other banks for a set term.

Risk-free rate (RFR)

Risk-free rate: an overnight rate built from actual transactions, with little or no bank credit risk in it.

SOFR

Secured Overnight Financing Rate: the US dollar rate on overnight repo backed by US Treasuries, published by the Federal Reserve Bank of New York.

€STR

Euro short-term rate: the rate euro-area banks pay to borrow unsecured overnight from wholesale lenders, published by the European Central Bank.

SONIA

Sterling Overnight Index Average: the rate on unsecured overnight sterling deposits, administered by the Bank of England.

Compounded in arrears

Working out a period's interest rate at the end of the period, from the overnight rates that actually occurred.

Term rate

Fixed today for a future period, such as three months, so the borrower knows the rate in advance.

Fallback

Contract wording that says which rate replaces a benchmark if it stops being published.

Spread adjustment

A fixed add-on to the new rate so that, on average, payments match what the old rate would have paid.