Treasury Bill

A bill's price is derived from a quoted rate rather than the reverse. Under the bank discount convention, the annualised rate equals the dollar discount divided by face value, multiplied by 360 divided by the days to maturity. Two features make this figure understated as a return: it divides the gain by par instead of by the amount actually invested, and it annualises on a 360-day year without compounding.

Two corrections exist. The money market yield, or holding period yield annualised on a 360-day basis, divides the dollar gain by the purchase price and scales by 360 over days held. The bond equivalent yield performs the same division by price but scales by 365 over days held, putting the bill on comparable footing with coupon-paying instruments. The effective annual yield compounds the holding period return over the number of periods in a year and is always the highest of the four figures for a positive-yielding bill.

The Treasury issues bills on a regular calendar, with four-week, eight-week, thirteen-week, seventeen-week, twenty-six-week and fifty-two-week maturities, supplemented by cash management bills used to bridge temporary funding gaps. Auctions are single-price: every accepted bid is filled at the highest discount rate required to clear the offered amount. Competitive bidders specify a rate and risk receiving nothing; non-competitive bidders, typically retail, accept the stop-out rate and are guaranteed an allocation up to a size limit.

In the secondary market, dealers quote bills in discount rate terms rather than price. Because a higher discount rate implies a lower price, the bid rate exceeds the ask rate on a screen, the inverse of the convention for coupon securities. Candidates who mechanically assume bid is below ask will invert the dealer's spread.

Bills anchor the short end of the U.S. yield curve and serve as the empirical stand-in for the risk-free rate in CAPM, in option pricing and in Sharpe ratio calculations, with the bill maturity matched to the horizon of the analysis. They are the preferred collateral in repurchase agreements and the dominant holding of government money market funds, which is why bill supply and demand feed directly into repo rates and short-term funding conditions.

Spreads between bill yields and interbank or overnight index swap rates are read as a gauge of perceived credit and liquidity stress in the banking system. Bills also carry no state or local income tax in the United States, a feature that raises their after-tax appeal to investors in high-tax jurisdictions relative to comparably rated commercial paper or certificates of deposit.

Expect to move between conventions in either direction. From a quoted discount rate, compute the dollar discount and the purchase price; from a price, recover the discount rate, the money market yield and the bond equivalent yield. Recognise that discount rates and add-on rates are not interchangeable: commercial paper and bills are quoted on a discount basis, while certificates of deposit, repos and bankers' acceptances in some markets are add-on instruments where interest is calculated on the principal advanced.

When a question asks which of several money market instruments offers the highest return, the intended work is to restate every quote on one common basis before ranking them. Also be prepared to explain why a bill has no reinvestment risk over its life, no coupon to reinvest, and negligible credit risk, but retains inflation and rollover risk for an investor with a longer horizon.