Treasury Bill

A Treasury bill is government borrowing at its shortest and simplest: a promise to pay a fixed amount on a date a few weeks to a year away, sold today at a discount. No coupons — buy at 98.8, receive 100, the 1.2 difference is your interest.

Bills sit at the very center of the financial system's idea of "safe": default risk negligible, price risk tiny (maturities are so short that rate moves barely dent them), and liquidity so deep you can convert billions to cash in minutes. When investors say they're "in cash", they usually mean this.

Governments run weekly auctions; money-market funds, corporations parking payroll, banks and foreign central banks absorb trillions of the stuff.

Quoting conventions (the archaic corner)

• Discount rate: US bills quote at a "discount yield" — the discount as % of face, on a 360-day year: \(d = \frac{100-P}{100}\cdot\frac{360}{n}\). It understates the true return.
• Bond-equivalent yield converts to a comparable investment yield on price paid and 365 days.

Auctions

Sold via single-price auctions: competitive bidders state yields; everyone pays the market-clearing ("stop-out") level. Bid-to-cover ratios and the tail (gap between average and stop-out) are watched as demand health checks.

Bills in the plumbing

• Collateral: the premier collateral in repo and derivatives margining.
• Supply swings matter: debt-ceiling episodes crush bill supply then flood it, pushing short rates around; money funds swing between bills and the Fed's RRP facility accordingly.
• The 3-month bill is a benchmark for "the" risk-free rate in countless models — and one leg of the famous yield-curve recession indicator (3m vs 10y).

Pricing

A bill is the purest zero-coupon instrument: \(P = 100 \cdot e^{-z(T)\,T}\) — bills define the front of the risk-free curve. Their yields decompose as expected policy rates over the horizon plus (tiny) term premium plus a convenience yield: bills persistently yield below comparable OIS because their moneyness (collateral value, regulatory status) is worth basis points. That spread — bills-OIS — is a live indicator of safe-asset scarcity.

The zero lower bound curiosity

Bills have traded at negative yields (Europe for years; US briefly) — buyers paying for safety and balance-sheet-friendly parking, an empirical measure of the convenience yield's size.

Bills vs. the alternatives

Money funds arbitrage bills against repo and the RRP; corporates against commercial paper and deposits. Supply shocks (post-debt-ceiling issuance floods) temporarily push \(\varepsilon\) positive — measurable, tradable, and a favorite natural experiment for money-market researchers.

Risk notes

Price risk is small but nonzero (a 1-year bill has duration ~1: a 100bp shock costs ~1%); the real institutional risks are settlement/operational and — as the 2023 debt-ceiling brinkmanship reminded everyone — the technical-default tail on specific maturity dates, visible as kinks in the bill curve around "X-dates".