# Bank Discount Basis

## What Is Bank Discount Basis?

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.

### Key Takeaways

• The bank discount bias, or discount yield, calculates the expected return of a bond sold at a discount to its par value, or face value.
• It is most often used to determine the yield on treasury bills, commercial paper, and municipal notes.
• These bonds are purchased at a discount, held to maturity, and then sold at face value, netting the holders a profit.
• The bank discount bias, an annualized yield expressed as a percentage, is determined by using a 30-day month and a 360-day year.

## Understanding 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.

﻿ $8\% \times \frac{ 365 }{ 360 } = 8.11\%$﻿

If an investor sells a security before the maturity date, the rate of return earned will be based on the sale price of the security at the time. It might be higher or lower than the price the investor would have seen had the bond been held to maturity.

## How To Calculate the Bank Discount Rate

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

﻿ \begin{aligned}&\text{Bank Discount Rate} = \frac{ \text{DPV} }{ \text{PV} } \times \frac { 360 }{ \text{Days to Maturity}} \\&\phantom{Bank Discount Rate} = \frac{ \text{PV} - \text{PP} }{ \text{PV} } \times \frac { 360 }{ \text{Days to Maturity}} \\&\textbf{where:} \\&\text{DPV} = \text{Discount from par value} \\&\text{PV} = \text{Par value} \\&\text{PP} = \text{Purchase price} \\\end{aligned}﻿

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: ﻿ $\frac { \300 \text{ discount} }{ \10,000 \text{ par value} } \times \frac{ 360 }{ 120 \text{ days to maturity} }$﻿ or a 9% yield. ## Discount Yield vs. Bond 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, however, 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.

Article Sources
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1. U.S. Department of the Treasury, Bureau of the Fiscal Service. "Treasury Bills." Accessed Feb. 8, 2021.

2. U.S. Department of the Treasury, Bureau of the Fiscal Service. "Treasury Notes." Accessed Feb. 8, 2021.

3. U.S. Department of the Treasury, Bureau of the Fiscal Service. "Treasury Bonds." Accessed Feb. 8, 2021.