Treasury Bills and Discount Yield Quoting, Explained

A Treasury bill pays no coupon — you buy it below face value and receive the full face value at maturity, the entire return being the gap between the two. That's simple enough, but the number quoted in the market for a bill, the discount yield, is not the investor's actual annualized return. It's a specific, old convention that understates the real yield, and every bill trader needs to convert between the two without thinking twice.

A bill's quoted discount yield is calculated as a percentage of face value, not of the price actually paid — since the price paid is always less than face value, the discount yield is mechanically smaller than the bill's true, investment-basis return.

The discount-yield formula

Bills are quoted using:

d = \frac{F - P}{F} \times \frac{360}{n}

In words: take the dollar discount (face value minus price), divide by face value (not price), and annualize using a 360-day year convention. Two nonstandard choices are baked in here — dividing by face rather than price, and a 360-day rather than 365-day year — both are legacies of how bills were quoted a century ago and both make the discount yield understate the return an investor actually earns on the money they put up.

Discount yield divides the same dollar gain by the larger face value; investment yield divides it by the smaller price actually paid, so investment yield is always the bigger number.

Worked example

A 26-week (182-day) T-bill with $1,000,000 face value is quoted at a discount yield of 5.00%.

Dollar discount. Rearranging the formula: $F - P = d \times F \times n/360 = 0.05 \times 1{,}000{,}000 \times 182/360 = 25{,}278$ .
Price paid. $P = 1{,}000{,}000 - 25{,}278 = 974{,}722$ , i.e. $974,722.
True investment yield (bond-equivalent basis). Using price as the base and a 365-day year: $\frac{25{,}278}{974{,}722} \times \frac{365}{182} = 0.0520$ , or 5.20%.

The quoted 5.00% discount yield understates the roughly 5.20% an investor actually earns on the money invested — a 20 basis point gap purely from quoting convention, not from any difference in the actual cash flows.

What this means in practice

Every money-market desk converts discount yields to an investment (bond-equivalent) yield before comparing a bill to a coupon-bearing note or a bank deposit quoted on an actual/365 or actual/360 investment basis — comparing raw discount yields across instruments that use different conventions is comparing different units. Electronic trading systems do this conversion automatically, but understanding the mechanical reason discount yield is always the smaller number prevents a common newcomer mistake: assuming a bill yielding "5.00%" pays less than a deposit yielding "5.10%" without checking that they're quoted on the same basis.

Never compare a bill's quoted discount yield directly against a bond's yield to maturity or a deposit's stated rate without converting to a common basis — the discount-yield convention (dividing by face value, using a 360-day year) always makes a bill look cheaper in yield terms than its true return actually is.

Treasury Bills and Discount Yield Quoting

The discount-yield formula

Worked example

What this means in practice

Related concepts

Practice in interviews

Further reading