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T-Bills: Rates and Pricing of Treasury Bills

Follow along here to see how T-Bills are quoted and find the bid and ask prices based on any principal amount.
  1. Define - Define Treasury Bills.
  2. Examples - Review how T-Bills are priced and quoted.
  3. Context - Use the term T-Bills in a sentence.
  4. Quiz - Test your knowledge.
by Paul Alan Davis, CFA, January 5, 2019
Updated: January 5, 2019
The way T-Bills are quoted today was established before computers, so it's quirky but fairly easy to learn. See more below.

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About T-Bills, Interest Rates and Pricing

Beginner

A T-Bill (Treasury Bill) is short-term debt security issued by the US Government, and specifically the Department of the Treasury. T-Bills are highly liquid investments meaning there are many buyers and sellers actively participating in the market which translates to low trading costs. T-Bill maturities are 1-year and under.

While no investment comes without risk, one reason scholars consider T-Bills a risk-free asset is because they are priced at a discount to face value, and mature at the face value, so the amount invested does not decline in value. Interest earned on T-Bills is returned as part of the face value which is higher than the purchased value.

Investors can buy T-Bills directly from the US Treasury, as well as other forms of US Government debt, like Treasury Notes and Bonds. Treasury Bills can be purchased with as little as $100. More information on weekly auctions can be found at the treasurydirect.gov website.

T-Bills are commonly issued with maturities in five weekly increments.

  • 4 weeks - approximately 28 days or 1 month
  • 8 weeks - approximately 56 days or 2 months
  • 13 weeks - approximately 91 days or 3 months
  • 26 weeks - approximately 162 days or 6 months
  • 52 weeks - approximately 364 days or 12 months

Days shown are approximations. The US Treasury accomodates for days that would normally fall on a weekend or holiday.

Sometimes a longer-dated maturity T-Bill will be re-opened when it nears maturity. For example, a 26 week T-Bill may be re-opened when it gets to 13 weeks remaining in its term. This practice saves administrative costs as that specific T-Bill will retain its CUSIP number, which is a unique identifier for each Treasury Bill.

Alternatively, some investors prefer to buy Treasury securities in their brokerage account on the secondary market. Pricing and quotes provided by brokerage firms or from publishers like the Wall Street Journal are explained below.

Synonym: Treasury Bills, risk-free asset

Examples of T-Bill Pricing

Trading practices for Treasury Bills were established well before the widespread adoption of computers. As a result, calculations were simplified so investors could understand yields and prices without a computer. Today we're left with this less than ideal practice.

T-Bill rates are quoted using Bid and Ask, like 2.388% and 2.378%, respectively. These are given as annual yields and an adjustment must be made for periods of less than a year. The buyer would buy at the price corresponding to the Ask and sell at the Bid. Because bond yields and prices move in opposite directions, the calculated Bid Price is lower than the Ask Price, as we will see below.

Because investors ultimately decide on the Face Value, it is most convenient to show yields so the investor can calculate prices themselves.

Quotations for T-Bills

The table below demonstrates quotations that might be found in publications or at brokerage trading accounts. Here we see five T-Bill quotes selected from about fifty available at any point in time.

A Treasury Bill Quote on Jan. 3, 2019
Maturity Bid Ask Chg Asked Yield
1/31/2019 2.288 2.278 -0.012 2.313
2/28/2019 2.303 2.293 0.015 2.333
4/04/2019 2.365 2.355 -0.005 2.402
6/06/2019 2.385 2.375 -0.023 2.433
1/02/2020 2.435 2.425 -0.090 2.520

Source: The Wall Street Journal Online Market Data Center, January 03, 2019

To translate:

  • Maturity - The maturity date of that specific T-Bill assigned its own CUSIP (not shown here).
  • Bid - The bid in % that translates to the price an investor could sell that specific T-Bill for (minus transaction costs).
  • Ask - The ask in % that translates to the price an investor could buy that specific T-Bill for (plus transaction costs).
  • Chg - The change from the previous day.
  • Asked Yield - The Ask translated using the Bond-Equivalent Yield method (see below).

As mentioned earlier, we still need to translate the Bid and Ask to a price depending on the investor's Face Value and for that see the Bank-Discount Method below.

Calculate T-Bill Prices Using the Bank-Discount Method

Let's use the following as background information for our two desired calculations: the Bid Price and Ask Price.

  • Face Value - $100,000
  • Maturity Date - 6/06/2019
  • Days to Maturity - 154 days (from 1/3/19)

For this we need the Bank-Discount Method, and so we're not just memorizing formulas, it's easier to interpret if we break the calculation into two steps. First calculate the Fractional Yield and second the Price (Bid and Ask).

  1. Fractional Yield = Quoted Yield * (Days to Maturity / 360)
  2. Price = Face Value * ( 1 - Fractional Yield)
Calculate the Bid Price for the Treasury Bill Maturing 6/06/19

Starting inside the parentheses, ( Days to Maturity / 360 ) can be interpreted as the number of days the T-Bill has until maturity as a fraction of a 360-day year (a flaw with the Bank-Discount Method intended to simplify the calculation before the use of computers). So we have 154 / 360, or 0.42778. This multiplied by Quoted Yield on the Bid side of 2.385%, or 0.02385, is 0.0102025.

Next, recall that an investor can invest in increments of their choosing with the Face Value, so $100, $1,000, $100,000 in our example, or odd amounts like $12,345 if the investor wants.

So, again from inside the parentheses we have ( 1 - Fractional Yield ), or ( 1 - 0.0102025), for 0.9897975. This is the discount that can be applied to any Face Value.

Now multiply that by the Face Value of $100,000, for a final Bid Price of $98,979.75. This is the price at which the investor can sell the T-Bill.

Calculate the Ask Price for the Treasury Bill Maturing 6/06/19

All of the steps are the same for the Ask Price except we use the Ask of 2.375 to arrive at a Fractional Yield of 0.010159722.

The discount is therefore 0.989840278 and when we multiply by the Face Value we get $98,984.03.

So translated to Bid Price and Ask Price we have $98,979.75 by $98,984.03. With that we can make two observations. First, it costs more to buy than sell, with the difference being the profit to the firm providing the trading venue.

Second, it shows the inverse relationship between yields and prices, which is common across debt securities. Note how the Bid yield was higher than the Ask and when translated to prices the opposite is the case.

Calculate the Asked Yield using the Bond-Equivalent Yield Method

Again, the Bank-Discount Method isn't a very accurate calculation because it simply takes a fractional year based on a 360-day year, and that's where the Bond-Equivalent Yield method comes into play. It is calculated based on the Ask side, using the following.

  • Ask Yield = ((Maturity Value / Invested Value) - 1) * ( 365 / Days to Maturity )

Assuming you bought the T-Bill at the Ask Price (above) then this is also the Invested Value. So dividing the first by the second, so $100,000.00 / $98,984.03, or 1.010263979, subtracting the 1 gives you a return of 1.0263979%.

Because this represents a return for less than one-half of a year, we need to adjust it to an annual figure, multiplying by 365 / 154 Days, for an Asked Yield of 2.4326963%, which matches what is provided in the table with a slight difference due to rounding.

Note how the Asked Yield would more reflect the investor's true rate of return and is slightly higher than the Ask quote of 2.375%.

As you can see, this math isn't simple, but is what traders and issuers came up with before the widespread adoption of computers, so we're left to learn the standard.

In a Sentence

Rex:  And that's how T-Bills  are quoted and priced. I'm exhausted.
Kim:  Okay, don't die on me now Rex. Pat wants me write this up so our clients understand it.

Video

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Video Script

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Quiz

Click box for answer.

The Bid Price for the 2/28/19 T-Bill on a $10,000 Face Value using the table above is $9,964.18. | True or False?

True

The Ask Price for the 2/28/19 T-Bill on a $10,000 Face Value using the table above is lower than the Bid Price. | True or False?

False

The Asked Yield for the 2/28/19 T-Bill on a $10,000 Face Value using the table above is 2.343%. | True or False?

False, it is 2.333%

Questions and Comments?

Still unclear on T-Bills and the concept of the Risk-free rate and portfolio management? Try out the course Quant 101, and specifically Ace Your Portfolio Theory Exam.

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