Discount Yield

Key takeaways

• Discount yield estimates the return on a bond sold at a discount to par and held to maturity.
• It uses money-market conventions (30-day month, 360-day year).
• Commonly applied to Treasury bills, commercial paper, municipal notes and zero-coupon bonds.
• It differs from yield-to-maturity and accretion because it expresses return relative to face value, not purchase price.

What discount yield is

The discount yield is a standardized way to compute the expected return on a discount security (one sold below its face value) if held until maturity. It is widely used for short-term, discount-issued instruments such as Treasury bills, commercial paper, municipal notes and zero-coupon bonds.

Formula

Discount yield (annualized) is calculated as:

Discount yield = (Discount / Face value) × (360 / Days to maturity)

where:
* Discount = Face value − Purchase price
* The 360/30 convention is used to annualize short-term money‑market yields.

Because the formula uses face value in the denominator, discount yield typically understates the effective return compared with yields computed on the purchase price (e.g., yield-to-maturity or holding-period yield).

Example

An investor buys a $10,000 Treasury bill for $9,700 (a $300 discount) that matures in 120 days.

Discount yield = (300 / 10,000) × (360 / 120) = 0.03 × 3 = 0.09 = 9%

So the standardized discount yield is 9% annualized by the 360-day convention.

Practical notes and limitations

• If the security is sold before maturity, the realized return will differ and must be calculated from the actual sale price.
• Discount yield uses face value rather than purchase price, so it does not reflect the true economic yield an investor earns on the money invested. For that, use holding-period yield or yield-to-maturity.
• The 30/360 convention simplifies comparisons across short-term instruments but is an approximation.

Discount yield versus accretion

Accretion is an accounting method that spreads a bond’s discount into income over the bond’s life. For example, if an investor buys a $1,000 bond for $920 (an $80 discount) with a 10-year maturity, that $80 is recorded as income over the 10 years. Methods include:
* Straight-line accretion — equal dollar amounts each period.
* Effective interest method — allocates discount based on an effective yield formula.

Discount yield is a market convention for reporting expected return on discount instruments; accretion governs how the discount is recognized as income over time.

Summary

Discount yield is a quick, standardized measure of return for discount-issued short-term securities using a 360-day year. It’s useful for comparisons but differs from more precise measures of investor return that use the purchase price or account for interim sale.