Treasury Bills ( T-Bills ) are Money Market instruments issued by the federal government to cover budget deficits which occur when expenses are greater than tax revenues. Treasury Bills are the most important type of debt issued by the federal government. Treasury bills are sold weekly through an auction process and they come in different terms-of-maturity and denominations. Treasury Bills are sold with original maturities of 28 days (4 weeks), 91 days (13 weeks), and 182 days (26 weeks) and they are typically issued in denominations of $10 million, $15 million, $50 million, $100 million and $500 million. The minimum denomination is $1000 for the purpose of giving individual investors the capability of investing in treasury bills directly from the U.S. Treasury. U.S Treasuries are backed by the U.S. government and have virtually no default risk. The U.S. government has never defaulted on a payment and therefore the interest rate paid on Treasury Bills is often referred to as "the risk-free rate". There is relatively low price risk due to their short maturities; and they can easily be converted into cash for low transaction costs due to their marketability.
How to Price Treasury Bills
U.S. Treasury Bills are sold to investors at a discount (less than par value). This is because treasury bills do not pay interest in the form of coupon payments so for an investor to earn interest on his Investment , he needs to purchase the Treasury bill for less than the amount he will receive when the U.S. treasury pays back the principle. The way to calculate the annualized discount yield that a T-bills is expected to pay is shown below.
How would you calculate the annualized discount yield of a $10,000 face value T-Bill that had 30 days until maturity and was selling in the market for $9900?
In this example the T-bill was purchased at a 1% discount [($10,000-$9,900)/$9,900]. The discount underestimates the true yield of this investment because it earned the 1.01% yield in only 30 days. The annualized yield is actually 12.16%. As we know there are more than 360 days in a year. The Bond equivalent yield assumes that there are 365 days in the year and that the price rather than the face value is reinvested in Tbills. This of course would only be accurate if the price of Tbills were to stay the same. The formula is shown below.
Notice that the yield is higher when using the bond equivalent yield.
The bond equivalent yield formula and the Annualized Discount Yield Formula can be rearranged to solve for the price of the Tbill as shown below.