Describe Treasury rates, repo rates and the Secured Overnight Financing Rate (SOFR), and clarify the meaning of the risk-free rate.
The idea
A Treasury rate is the yield on US government debt: bills for maturities up to one year, and notes and bonds beyond. It is nearly default-free, but it is not a clean risk-free proxy. Regulation, liquidity needs and the state tax exemption on its interest push Treasury yields below other low-risk rates. A repo is a sale of securities with an agreement to repurchase them at a higher price. Economically it is a collateralized loan. The repo rate is the annualized price difference over the cash lent, usually on actual/360. SOFR is the overnight rate on repo trades collateralized by Treasuries, published by the New York Fed. Because it is secured, it carries almost no bank credit premium, which is why it replaced unsecured LIBOR as the benchmark. The usual mistake is treating SOFR as an unsecured interbank rate.
Formulas
Repo rate on an actual/360 basis
repo rate = (P₁ − P₀) ÷ P₀ × (360 ÷ d)
- P₀
- the cash lent at the start, net of any haircut
- P₁
- the repurchase price
- d
- the days the repo runs
Interest is charged only on the cash lent, so a haircut lowers P₀ and the interest with it.
A practice question
Which description of the Secured Overnight Financing Rate (SOFR) is correct?
- A broad measure of the cost of borrowing cash overnight against Treasury securities as collateral - correct
- An average of unsecured overnight interbank loans reported by a panel of large banksWhy not: Describes an unsecured interbank rate such as the old LIBOR or the fed funds rate. SOFR is secured by Treasury collateral and built from transaction data.
- The yield on the three-month Treasury bill, auctioned weeklyWhy not: Confuses SOFR with a Treasury bill yield. SOFR is a repo rate for overnight cash loans, not a security yield.
- The rate at which the central bank lends reserves to commercial banks at its discount windowWhy not: Confuses SOFR with a central bank administered policy rate. SOFR is market-determined from repo transactions.
SOFR is built from overnight repurchase agreement transactions collateralized by US Treasury securities and is published by the Federal Reserve Bank of New York. It is secured and transaction-based, unlike panel-based unsecured rates.
A harder one
A dealer sells Treasury securities for USD 50,000,000 and agrees to repurchase them 45 days later for USD 50,280,000. Using the actual/360 money market convention, the annualized repo rate is closest to:
- 4.54%Why not: Annualizes with 365 days although the money market convention for repo is actual/360.
- 4.48% - correct
- 0.56%Why not: Reports the 45-day interest as a percentage of cash without annualizing it.
- 0.07%Why not: Multiplies by 45/360 instead of 360/45, shrinking the rate instead of annualizing it.
Interest = 280,000. Repo rate = (interest / cash lent) x (360 / days) = 0.00560 x 8 = 4.48%.
The hardest tier
A bank's treasury department compares an unsecured interbank benchmark with SOFR during a period of acute stress in the banking sector. The unsecured benchmark rises sharply relative to SOFR. Which explanation is most accurate?
- SOFR is set each day by the central bank's policy committee and so cannot respond to market stressWhy not: SOFR is derived from observed repo transactions, not set by a committee.
- SOFR is a term rate fixed at the start of each three-month period, so it cannot move within the periodWhy not: SOFR is an overnight rate that changes every day; it is not a term rate fixed in advance.
- Treasury collateral becomes riskier in a banking crisis, which pushes SOFR below the unsecured benchmarkWhy not: Mixes up cause and effect: the unsecured rate widens because it carries bank credit risk, not because collateral weakens.
- SOFR is secured by Treasury collateral, so lenders bear little exposure to bank credit risk, while the unsecured benchmark embeds a bank credit and liquidity premium - correct
Repo lenders hold Treasuries as collateral, so a bank's credit quality matters little for SOFR. An unsecured interbank rate compensates lenders for bank default and funding-liquidity risk, so it widens over SOFR in stress. This is why SOFR is regarded as a close-to-risk-free overnight rate.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Properties of Interest Rates
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