# Bank Discount Yield

Bank discount yield (or simply discount yield) is the annualized rate of return on a purely discount-based financial instrument such as T-bill, commercial paper or a repo calculated as the difference between the face value and issue price divided by face value multiplied by 360 divided by number of days between issue date and maturity date.

Money market instruments are investments with a maturity of less than one year. Majority of such instruments are issued at a price lower than their face value and they do not carry any periodic interest payments. The difference between their face value and their issue price is called discount and this represents the absolute amount of return earned by holders of such investments. In accordance with market convention, the return on bank discount basis is calculated with reference to the face value of the instrument.

$$ Return\ on\ Bank\ Discount\ Basis=\frac{Face\ Value\ -\ Issue\ Price}{Face\ Value} $$

## Formula

Bank discount yield is the rate of return calculated on bank discount basis annualized based on a 360-day year. It can be calculated using the following formula:

$$ BDY\\=\frac{F\ -\ P}{F}\times\frac{360}{t}\\=\frac{D}{F}\times\frac{360}{t} $$

Where **F** is the face value of the investment, **P** is the issue price of the investment and **t** is the number of days between the issue date and maturity date. **D** equals F minus P.

### Excel

Bank discount yield can be calculated using Microsoft Excel DISC function. DISC function syntax is DISC(settlement, maturity, pr, redemption, [basis]).

Settlement refers to the date of issue, maturity is the maturity date, pr stands for the issue price of the instrument and redemption refers to the face value i.e. the amount repaid to the holder at maturity date. [basis] is an optional argument that specifies the manner in which number of days must be calculated.

### Conversion to money market yield

Even though calculating return using the maturity value is not very useful, bank discount yield is common for money market instruments due to long-standing convention. It can be converted to the money market yield using the following equation:

$$ MMY=\frac{360\times BDY}{360\ -\ t\times BDY} $$

Money market yield is a more meaningful measure of return because it is calculated with reference to the issue price i.e. the investment made.

## Example

Calculate the bond discount yield for a recent auction of the following US T-bill:

CUSIP | Security Term | Auction Date | Issue Date | Maturity Date | Price per $100 |
---|---|---|---|---|---|

912796NW5 | 13-Week | 12/11/2017 | 12/14/2017 | 3/15/2018 | 99.666333 |

We know that the T-bill face value is $100 so we can calculate the bank discount yield as follows:

$$ BDY=\frac{$100\ -\ $99.666333}{$100}\times\frac{360}{91}=1.32\% $$