What is the discount yield (short answer)
– The discount yield is a simple percentage measure used to express the return on a short-term debt security that is issued below its face (par) value and held to maturity. It is commonly applied to Treasury bills, commercial paper and short-term municipal notes.
Key definition and assumptions
– Discount bond: a debt instrument sold for less than its face value and that repays full face value at maturity (examples: T-bills, zero‑coupon bonds).
– Discount yield convention: uses the bond’s face value in the denominator and a 360‑day year (30‑day months) to standardize comparisons across instruments.
– Important caveat: the discount yield assumes the investor holds the security to maturity and that there are no credit losses.
Formula (standard bank discount convention)
– Discount yield = (Discount / Face value) × (360 / Days to maturity)
– Discount = Face value − Purchase price
– “Days to maturity” is the actual calendar days remaining until the security pays face value.
Step‑by‑step checklist to compute discount yield
1. Confirm the security is a discount instrument (no coupon payments; issued below par).
2. Find the face (par) value and the purchase price.
3. Compute the dollar discount = face value − purchase price.
4. Count the days remaining until maturity.
5. Plug values into: (Discount / Face value) × (360 / Days to maturity).
6. Express the result as a percentage (multiply by 100).
7. Note the assumption: this yield applies for holding to maturity; selling early changes realized return.
Worked numeric example
– Situation: A Treasury bill has a face value of $10,000. You buy it for $9,700. It matures in 120 days.
1. Discount = $10,000 − $9,700 = $300.
2. Discount / Face value = $300 / $10,000 = 0.03.
3. Time factor = 360 / 120 = 3.
4. Discount yield = 0.03 × 3 = 0.09 → 9.0%.
– Interpretation: Using the bank‑discount convention, this instrument’s quoted discount yield is 9.0%. This is not the same as the yield measured on the basis of purchase price or an investor’s annualized holding‑period return.
How discount yield differs from other measures
– Versus holding‑period (or cash) yield: Discount yield uses face value in the denominator; holding‑period yield uses purchase price and therefore gives a different (usually higher) percentage return for the same example.
– Versus accretion (accounting of original‑issue discount): Accretion is an accounting process that recognizes the discount (difference between par and purchase price) as interest income over the life of the bond. For a $1,000 bond bought at $920 maturing in 10 years, the $80 discount can be booked into income gradually—either evenly each year (straight‑line) or by the effective interest method, which allocates more income earlier or later depending on implied yield.
When the quoted discount yield is most useful
– Comparing short‑term discount instruments (T‑bills, commercial paper, municipal notes) on a common basis.
– Quick standardization for dealers and market reporting using the 30/360 convention.
Limitations and practical notes
– The 360‑day year and face‑value denominator make this a convention, not an economic truth; it can understate the yield compared with calculations based on actual days and purchase price.
– If you sell before maturity, compute realized return from sale proceeds and accreted income as needed—don’t rely on the original discount yield alone.
– For tax reporting and accounting, different rules (for example, IRS rules on original issue discount) may apply.
Short checklist recap
– Verify instrument type → compute discount → count days to maturity → apply (Discount/Face)×(360/Days) → convert to percent → note holding‑to‑maturity assumption.
Sources for further reading
– Investopedia — Discount Yield: https://www.investopedia.com/terms/d/discount-yield.asp
– U.S. Department of the Treasury — Treasury bills (overview and schedules): https://www.treasurydirect.gov/indiv/research/indepth/treasurybill/treasurybill.htm
– FINRA — Understanding bonds and yields: https://www.finra.org/investors/learn-to-invest/types-investments/bonds
– Internal Revenue Service — Topic on Original Issue Discount (OID) taxation: https://www.irs.gov/taxtopics/tc
Worked numeric examples (step-by-step)
Example 1 — 91‑day T‑bill (bank discount yield)
– Given: face value = $1,000; purchase price = $980; days to maturity = 91.
– Step 1 — compute the dollar discount: Face − Price = 1,000 − 980 = $20.
– Step 2 — compute the discount rate on face: Discount/Face = 20 / 1,000 = 0.02.
– Step 3 — annualize on a 360‑day (bank) basis: Discount yield = 0.02 × (360 / 91) = 0.02 × 3.9560 = 0.07912 → 7.912% (discount yield).
Interpretation: The discount yield expresses the discount as a percent of face value, annualized on a 360‑day year. It is the standard quoted yield for many money‑market instruments but does not measure return on the money you put up.
Example 2 —