T-bills and Bank Bills

Treasury bills are short-term government securities issued at a discount to face value and redeemed at par. Bank-accepted bills are similar instruments issued by corporations but guaranteed (accepted) by a major bank, which substitutes the bank's credit for the issuer's. Both are zero-coupon. Australian Treasury Notes (AOFM) and bank bills use simple interest ACT/365, while US T-bills (Treasury Direct) use the bank discount basis ACT/360.

Why it matters

A bank bill is an IOU bought cheap today and paid in full at maturity. The gap between purchase price and face value is the return. There are no coupons to collect or reinvest. A bank's acceptance is what makes a corporate bill bank-accepted. The bank stamps the bill, promising to pay if the issuer fails. That guarantee turns BHP's 90-day bill into something a money market fund treats as major-bank credit risk, not BHP credit risk.

Formulas

Australian bank bill price (simple interest, ACT/365)
P=FV1+y×d/365P = \frac{FV}{1 + y \times d/365}
AFMA convention for AUD bank bills and Treasury Notes. FVFV is face value, yy is annualised yield, dd is days to maturity.
US T-bill price (bank discount, ACT/360)
P=FV(1r×d360)P = FV \left(1 - r \times \frac{d}{360}\right)
TreasuryDirect quotation convention. rr is the discount rate, not the investment yield. Investment yield is always higher than the discount rate for the same instrument.

Worked examples

Scenario

A 90-day Australian bank bill, face value A$100,000, traded at a yield of y=5.00%y = 5.00\%.

Solution

Price P = 100{,}000/(1 + 0.05 \times 90/365) = 100{,}000/1.01233 = \text{A\}98{,}782.13$. The buyer pays A$98,782.13 today, receives A$100,000 in 90 days. Interest earned = \text{A\}1{,}217.87$ over 90 days.

Scenario

A 13-week US T-bill (91 days), face value US$10,000, sold at a discount rate of r=4.50%r = 4.50\%.

Solution

Price P = 10{,}000 \times (1 - 0.045 \times 91/360) = 10{,}000 \times 0.988625 = \text{US\}9{,}886.25$. The investment yield that the buyer actually earns is =(10,0009,886.25)/9,886.25×365/91=4.62%= (10{,}000 - 9{,}886.25)/9{,}886.25 \times 365/91 = 4.62\%, materially above the quoted $4.50\%$ discount rate.

Common mistakes

  • T-bills pay coupons. They are zero-coupon. The return is entirely the price discount, paid as a lump sum when face value is redeemed at maturity.
  • The quoted T-bill discount rate equals the yield earned. The discount rate understates the actual return because it expresses interest as a fraction of face value over a 360-day year, while the investor's outlay is the lower purchase price. The investment yield is always higher.
  • Bank bills carry corporate credit risk. The bank acceptance substitutes the accepting bank's credit. A bank-accepted bill issued by a corporate trades on the credit of the four major Australian banks, not the corporate, which is why bank bill yields cluster tightly with BBSW.

Revision bullets

  • Sold at a discount, redeemed at face value
  • Zero-coupon, no interim cash flows
  • T-bills are sovereign, bank bills are bank-accepted
  • AUD uses simple interest ACT/365
  • US T-bills quoted on discount ACT/360
  • Discount rate understates investment yield

Quick check

Australian bank bills are priced using

A US Treasury bill quoted at a discount rate of $4.00\%$ has an investment yield that is

Connected topics

In learning paths

Sources

  1. U.S. Department of the Treasury. Understanding Pricing and Interest Rates. TreasuryDirect, accessed 2026.
    Official explanation of the US T-bill discount rate convention and the auction price formula $P = FV(1 - r \times d/360)$.
  2. Australian Office of Financial Management. Treasury Notes. AOFM, accessed 2026.
    Sovereign short-term issuance description, confirming Treasury Notes are zero-coupon discount securities of less than 12 months.
  3. Hull (2022), §4.2
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Day-count conventions and the relationship between discount yields, money market yields, and bond-equivalent yields.
  4. Reserve Bank of Australia. The Domestic Market for Short-term Debt Securities. RBA Bulletin, September 2011.
    Description of the Australian bank-accepted bill market and the role of major banks in providing the acceptance.
  5. Fabozzi (2021), Ch. 12
    Fabozzi, Frank J. Bond Markets, Analysis, and Strategies. 10th ed. MIT Press, 2021. ISBN 978-0-262-04627-3.
    Standard textbook treatment of money market instruments, day-count conventions, and the discount versus investment yield distinction.
How to cite this page
Dr. Phil's Quant Lab. (2026). T-bills and Bank Bills. Derivatives Atlas. https://phucnguyenvan.com/concept/tbills