What is BEY (Bond Equivalent Yield) of Short US Treasury Short Bill?

BEY (Bond Equivalent Yield), or Coupon Equivalent Yield, of Short US Treasury Bill (T-Bill) is the equivalent interest rate if you consider the price discount as the interest and the purchase price as the investment capital. Short T-Bills are T-Bills that mature in less than and equal to one half-year.

Note that BEY is referred as Investment Rate, or Investment/Interest Rate, in some US Treasury documents.

The following formula defines the BEY in a very easy-to-understand form:

$i={\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}\times {\displaystyle \frac{(F-P)}{P}}$
$P=\text{Purchase price}$
$F=\text{Face value}$
$i=\text{BEY (Bond Equivalent Yield)}$
$\mathrm{Days}=\text{Days to maturity}$
$\mathrm{Year}=\text{365 or 366}=\text{Actual number of days in the year}$

Different parts of the formula can be easily remembered as:

$\text{Interest (Price discount)}:F-P$
$\text{Simple interest percentage in decimal form}:{\displaystyle \frac{(F-P)}{P}}$
$\text{Annualization factor}:{\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}$

Of course, we can transform the about formula into different forms to calculate BEY, purchase price or face value:

$i={\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}\times \left({\displaystyle \frac{F}{P}-1}\right)$
$P={\displaystyle \frac{F}{(1+i\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})}}$
$F=P\times (1+i\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})$

Here is an example of 26-week T-Bill bought through TreasuryDirect.gov with a BEY (Bond Equivalent Yield) of 4.319%:

CUSIP: 912797NW3
Type: 26-Week Bill 
Par Amount: $10,000.00 (Face value) 
Purchase Price: $9,789.18

Investment/Interest Rate: 4.319% (BEY - Bond Equivalent Yield)
Price per $100: 97.891833

Discount: $210.82

Issue Date: 2024-12-26
Maturity Date: 2025-06-26

We can use this example to verify the BEY (Bond Equivalent Yield) formula:

$i={\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}\times \left({\displaystyle \frac{F}{P}-1}\right)={\displaystyle \frac{\mathrm{365}}{\mathrm{182}}}\times \left({\displaystyle \frac{\mathrm{10000}}{\mathrm{9789.18}}-1}\right)=0.04319037464306=\text{4.319\%}$
$P={\displaystyle \frac{F}{(1+i\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})}}={\displaystyle \frac{\mathrm{10000}}{(1+\mathrm{0.04319}\times {\displaystyle \frac{182}{365}})}}=9789.1817901479=\text{\$9,789.18}$
$F=P\times (1+i\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})=\mathrm{9789.18}\times (1+\mathrm{0.04319}\times {\displaystyle \frac{182}{\mathrm{365}}})$
$\mathrm{ }=9999.9981712997=\text{\$10,000.00}$

We have also provided a BEY (Bond Equivalent Yield) online calculator for you to use. Click this link "T-Bill 912797NW3 settled on 2024-12-26 with a price of 97.891833", you will see the BEY (Bond Equivalent Yield) of 4.3190% displayed.

Note that the BEY (Bond Equivalent Yield) formula uses the actual number of days in the year starting from the issue date. But a constant number of 360 days is used in the discount rate formula.

You can also find the BEY (Bond Equivalent Yield), also called Coupon Equivalent Yield, formula for short T-Bills in the "Price, Yield and Rate Calculations for a Treasury Bill" document provided by treasurydirect.gov.

Related topics:

BEY (Bond Equivalent Yield) to Price Converter for T-Bills

Price to BEY (Bond Equivalent Yield) Converter for T-Bills

⇒ BEY (Bond Equivalent Yield) of Long US Treasury Bill

⇐ High/Median/Low Rate of US Treasury Bill

⇑ Performance Measurements of US Treasury Bills

⇑⇑ US Treasury Securities