Bank discount basis, also known as discount yield, is a convention used by financial institutions when quoting prices for fixed-income securities sold at a discount, such as municipal and U.S. Treasury bills. The quote is presented as a percentage of face value and is determined by discounting the bond by using a 360-day-count convention, which assumes there are twelve 30-day months in a year.

## Breaking Down Bank Discount Basis

The bank discount basis is an annualized yield stated as a percentage. It is the return on investment generated by purchasing the instrument at a discount and then selling it par when the bond matures. Treasury bills, along with many forms of corporate commercial paper and municipal notes, are issued at a discount from par value (the face value). U.S. Treasury bills have a maximum maturity of 52 weeks, while Treasury notes and bonds have longer maturity dates.

While the 30/360 day-count convention is the standard banks use when quoting treasury bonds, the bank discount rate will be lower than the actual yield on your short-term money market investment, because there are 365 days in a year. Therefore, the rate should not be used as an exact measurement of the yield to be received. Over longer maturities, the day count convention will have a greater impact on the current "price" of a bond than if the time to maturity is much shorter.

To convert a 360-day yield to a 365-day yield, simply "gross up" the 360-day yield by the factor 365/360. A 360-day yield of 8% would equate to an 8.11% yield based on a 365-day year.

8% x (365 ÷ 360) = 8.11%

For more on comparing bond yields, see *"How to compare the yields of different bonds."*

## How To Calculate The Bank Discount Rate

The bank discount basis, or bank discount rate, is calculated using the following formula:

Bank discount rate = (Discount from par value ÷ par value) x (360 ÷ days to maturity)

= [ (par value – purchase price) / par value ] x (360 ÷ days to maturity)

Assume an investor purchases a $10,000 Treasury bill at a $300 discount from par value (a price of $9,700), and that the security matures in 120 days. In this case, the discount yield is:

($300 discount ÷ $10,000 par value) x (360 ÷ 120 days to maturity), or a 9% yield.

## The Differences Between Discount Yield and Accretion

Securities sold at a discount use the discount yield to calculate the investor's rate of return, and this method is different than bond accretion. Bonds that use bond accretion can be issued a par value, at a discount or at a premium, and accretion is used to move the discount amount into bond income over the remaining life of the bond.

Assume an investor purchases a $1,000 corporate bond for $920, and the bond matures in 10 years. Since the investor receives $1,000 at maturity, the $80 discount is bond income to the owner, along with the interest earned on the bond. Bond accretion means the $80 discount is posted to bond income over the 10-year life, and an investor can use a straight-line method or the effective interest rate method. Straight-line posts the same dollar amount into bond income each year, and the effective interest rate method uses a more complex formula to calculate the bond income amount. Bonds with a coupon can also be quoted at on a yield basis.