Discount yield is a face-value-based quote for short-term bills, distinct from the investor's price-based return, investment yield, and effective yield.
Discount yield, also called bank discount yield, is an annualized quotation that divides a bill’s discount from face value by its face value, not by the price paid. The U.S. Treasury bill convention uses a 360-day year.
It is a way to translate a bill’s price into a rate. It is not the same as the investor’s return on cash invested, an effective annual yield, or the discount rate used in every other financial calculation.
For a bill with one maturity payment and no interim coupons:
Here, (d) is the annualized discount yield as a decimal, (F) is face value, (P) is the bill’s price, and (D) is the number of days from settlement to maturity.
Rearranging gives the price implied by the quote:
Enter a 6% quote as 0.06, not 6. The days remaining are measured from settlement, which need not be the day the order was placed.
TreasuryDirect’s pricing explanation provides this quote-to-price relationship. The 360 is a quotation convention; it does not mean the investor actually holds the bill for 360 days.
Assume a hypothetical bill has $10,000 face value and 60 days remaining to maturity. Its price is $9,900, and there are no fees or taxes.
The reverse calculation confirms the price:
If the bill pays face value at maturity, the investor receives $10,000 after paying $9,900. The gain is $100, not 6% of $10,000 and not the entire maturity payment.
The return on the purchase outlay over those 60 days is:
This holding-period return is not annualized.
Using a 365-day year for the price-based annualizations in this example:
| Measure | Calculation basis | Result |
|---|---|---|
| Bank discount yield | $100 gain / $10,000 face value, multiplied by 360/60 | 6.0000% |
| Holding-period return | $100 gain / $9,900 invested | 1.0101% over 60 days |
| Simple annualized investment yield | Holding-period return multiplied by 365/60 | 6.1448% |
| Effective annual equivalent | Compound the 60-day wealth ratio over a 365-day year | 6.3047% |
The last two calculations are:
The effective figure expresses the short-period result on a compound annual basis. Actually earning it over a year would require suitable reinvestment opportunities; the bill does not promise that future rates will remain available.
The simple investment yield is higher than the discount yield here because it uses the smaller purchase-price denominator and a longer annualization basis. It does not represent an additional payment.
Substituting the bill-price formula into a simple price-based annualization gives:
Here, (Y) is the number of days in the chosen annualization year. For the example, (d=0.06), (D=60), and (Y=365):
This is a conversion between quotation bases, not a change to the bill’s price or payoff.
For U.S. Treasury bills, the official investment-rate calculation distinguishes bills of not more than one half-year to maturity from longer bills. The shorter-bill formula uses price and a 365- or 366-day basis as specified in the auction rules. Longer bills use a coupon-equivalent calculation rather than this simple annualization. See Treasury’s auction formulas, Appendix B, Section VI.
The Bond Equivalent Yield article covers that distinction. Do not label a generic simple annualization as an official investment rate without checking the applicable method.
A bill rate can refer to a Treasury bill, trade bill, or another short-term instrument. The name alone does not establish the quote convention.
Similarly, a coupon-paying bond can trade below face value, but its discount is not its entire return: it also has interim interest payments. Applying the one-payment bill formula would omit those coupons.
| Term | Meaning | Important distinction |
|---|---|---|
| Bank discount yield | Face-value-based bill quotation | Uses a discount from maturity value |
| Bond yield to maturity | Discount rate equating price and scheduled payments | Includes the timing of coupons and redemption |
| Current yield | Annual coupon divided by current price | Omits the gain or loss between price and redemption |
| Discounted-cash-flow discount rate | Rate used to value future cash flows | Not necessarily a bank discount quote |
A zero-coupon instrument can have a positive return even though its annual cash coupon is zero. Conversely, a price above the single promised maturity payment would imply a negative discount yield in this formula; that observation does not mean every premium-priced coupon bond has a negative return.
The $100 gain in the example depends on keeping the bill until it pays $10,000.
If it were instead sold after 30 days for $9,850, the investor would have a $50 loss before costs:
That sale return would replace the original hold-to-maturity outcome. The 6% purchase quote would not protect the investor from the loss.
Costs also matter. If a $5 purchase fee raised the outlay to $9,905, receiving $10,000 at maturity would produce a 60-day return of approximately 0.9591%, not 1.0101%. The quoted price and the investor’s all-in cash outlay are different inputs.
A higher quote does not resolve credit, liquidity, currency, or tax differences. Commercial and trade bills need issuer-specific analysis; they do not become equivalent to Treasury bills because they share a rate convention.
This article is general financial education, not personalized investment, treasury-management, or tax advice.