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 澳洲幸运5官方开奖结果体彩网:at a discount, such as municipal and U.S. 澳洲幸运5官方开奖结果体彩网:Treasury bills. The quote is presented as a percentage of face value and is determined by discounting the bond by using a 360-澳洲幸运5官方开奖结果体彩网:day-count convention,🥂 which assumes there are twelve 30-day months in a year.

Understanding Bank Discount Basis

The bank discount basis is an 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:commercial paper and municipal notes, are issued at a discount from 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网: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% 🌠ไwould equate to an 8.11% yield based on a 365-day year.

$8\% \times \frac{ 365 }{ 360 } = 8.11\%$8%×360365​=8.11%

How To Calculate the Bank Discount Rate

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

 $\begin{aligned}&\text{Bank Discount Rate} = \frac{ \text{DPV} }{ \text{PV} } \times \frac { 360 }{ \text{Days to Maturity}} \\&\phantom{Bank Discount Rate} = \frac{ \text{PV} - \text{PP} }{ \text{PV} } \times \frac { 360 }{ \text{Days to Maturity}} \\&\textbf{where:} \\&\text{DPV} = \text{Discount from par value} \\&\text{PV} = \text{Par value} \\&\text{PP} = \text{Purchase price} \\\end{aligned}$​Bank Discount Rate=PVDPV​×Days to Maturity360​BankDiscountRate=PVPV−PP​×Days to Maturity360​where:DPV=Discount from par valuePV=Par valuePP=Purchase price​

Assume an investor purchases a $10,000 Treasury bill at a $300 discount from par value (a price of $9,700), aไnd 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} }$$10,000 par value$300 discount​×120 days to maturity360​

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 澳洲幸运5官方开奖结果体彩网: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 amoun🧸t 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 澳洲幸运5官方开奖结果体彩网:yield basis.