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2 min readTapeboard Staff

What is a Treasury Bill? Definition, Formula, and Example

A Treasury bill is a short-term U.S. government debt security sold at a discount to face value and maturing in one year or less, and its yield defines the risk-free rate used across all of finance.

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What is a Treasury Bill?

A Treasury bill (T-bill) is a short-term debt obligation issued by the U.S. Treasury with a maturity of 4, 8, 13, 17, 26, or 52 weeks. Unlike notes and bonds, T-bills pay no coupon. Investors buy them at a discount to face value and receive the full face value at maturity; the difference is the interest. Because they are backed by the full faith and credit of the U.S. government and mature in under a year, T-bills are the closest instrument in the world to a risk-free asset, and their yields anchor the risk-free rate in the Sharpe ratio, CAPM, and options pricing models.

How T-Bill Pricing and Yield Are Calculated

T-bills are quoted on a bank discount yield basis:

Discount yield = [(Face − Price) / Face] × (360 / Days to maturity)

The more meaningful figure for comparison with other investments is the bond-equivalent yield (BEY):

BEY = [(Face − Price) / Price] × (365 / Days to maturity)

The discount yield understates true return because it divides by face value (not the price paid) and uses a 360-day year. Always compare T-bills to CDs, money market funds, and dividend yields using BEY.

Worked Example

The Treasury auctions a 13-week (91-day) bill with a $10,000 face value at a price of $9,877.

  • Discount yield = [(10,000 − 9,877) / 10,000] × (360 / 91) = (123 / 10,000) × 3.956 = 4.87%
  • Bond-equivalent yield = (123 / 9,877) × (365 / 91) = 0.01245 × 4.011 = 4.99%

The investor earns $123 on $9,877 in 91 days with zero credit risk and no mark-to-market risk if held to maturity. Compare that to the dividend yield on SPY at roughly 1.3%: when T-bills yield near 5%, the hurdle rate for owning equities rises materially — the mechanical reason high bill yields pressure equity valuations.

When Traders Use T-Bills

  • Cash management: idle brokerage cash and margin collateral is parked in 4–13 week bills or bill ETFs like BIL and SGOV instead of earning nothing.
  • Risk-free benchmark: the 13-week bill rate is the standard risk-free input for the Sharpe ratio and equity risk premium calculations.
  • Recession and Fed-watching: the 10-year Treasury yield minus the 3-month bill yield is the Fed's preferred yield-curve inversion gauge.
  • Collateral: bills are the highest-quality collateral in repo and derivatives margining.

Limitations and Common Misconceptions

T-bills are not riskless in every sense. They carry reinvestment risk: when a 4-week bill matures, the next one may yield far less if the Fed is cutting. Sold before maturity, they carry small interest-rate risk — prices fall when yields rise. They are also taxed at the federal level (though exempt from state and local tax), which changes after-tax comparisons with municipal money markets. And a common error: quoting the discount yield as if it were the actual return — always convert to bond-equivalent yield before comparing.